Relevant bibliographies by topics / Capillarity equation

Academic literature on the topic 'Capillarity equation'

Author: Grafiati
Published: 11 March 2023

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Contents

Consult the lists of relevant articles, books, theses, conference reports, and other scholarly sources on the topic 'Capillarity equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Journal articles on the topic "Capillarity equation"

1

Figliuzzi, B., and C. R. Buie. "Rise in optimized capillary channels." Journal of Fluid Mechanics 731 (August 14, 2013): 142–61. http://dx.doi.org/10.1017/jfm.2013.373.

Full text
Abstract:
AbstractMany technological applications rely on the phenomenon of wicking flow induced by capillarity. However, despite a continuing interest in the subject, the influence of the capillary geometry on the wicking dynamics remains underexploited. In numerous applications, the ability to promote wicking in a capillary is a key issue. In this article, a model describing the capillary rise of a liquid in a capillary of varying circular cross-section is presented. The wicking dynamics is described by an ordinary differential equation with a term dependent upon the shape of the capillary channel. Using optimal control theory, we were able to design optimized capillaries which promote faster wicking than uniform cylinders. Numerical simulations show that the height of the rising liquid was up to 50 % greater with the optimized shapes than with a uniform cylinder of optimal radius. Experiments on specially designed capillaries with silicone oil show a good agreement with the theory. The methods presented can be useful in the design and optimization of systems employing capillary-driven transport including micro-heat pipes or oil extracting devices.
APA, Harvard, Vancouver, ISO, and other styles
2

Bhatnagar, Rajat, and Robert Finn. "On the Capillarity Equation in Two Dimensions." Journal of Mathematical Fluid Mechanics 18, no. 4 (May 4, 2016): 731–38. http://dx.doi.org/10.1007/s00021-016-0257-6.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Liang, Fei-Tsen. "Global boundedness, interior gradient estimates, and boundary regularity for the mean curvature equation with boundary conditions." International Journal of Mathematics and Mathematical Sciences 2004, no. 18 (2004): 913–48. http://dx.doi.org/10.1155/s0161171204307039.

Full text
Abstract:
We obtain global estimates for the modulus, interior gradient estimates, and boundary Hölder continuity estimates for solutionsuto the capillarity problem and to the Dirichlet problem for the mean curvature equation merely in terms of the mean curvature, together with the boundary contact angle in the capillarity problem and the boundary values in the Dirichlet problem.
APA, Harvard, Vancouver, ISO, and other styles
4

Tritscher, Peter. "An integrable fourth-order nonlinear evolution equation applied to surface redistribution due to capillarity." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 38, no. 4 (April 1997): 518–41. http://dx.doi.org/10.1017/s0334270000000849.

Full text
Abstract:
AbstractMembers of an hierarchy of integrable nonlinear evolution equations, related to the well-known linearizable diffusion equation which has the diffusivity form as the reciprocal of the square of the concentration, are adapted to derive a new integrable nonlinear equation which models the surface evolution of an arbitrarily-oriented theoretical anisotropic material by the concomitant action of evaporation-condensation and surface diffusion. The constitutive relations are explicitly formulated and these show that the theoretical anisotropic material behaves like a liquid crystal. The integrable nonlinear equation may be used to advantage as test cases for numerical schemes. Its form has many attributes of the nonlinear governing equation for an isotropic material. Closed-form solutions are constructed for the evolution of a ramped surface by concomitant evaporation-condensation and surface diffusion.
APA, Harvard, Vancouver, ISO, and other styles
5

Roubíček, Tomáš. "Cahn-Hilliard equation with capillarity in actual deforming configurations." Discrete & Continuous Dynamical Systems - S 14, no. 1 (2021): 41–55. http://dx.doi.org/10.3934/dcdss.2020303.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

Rodr guez-Valverde, M. A., M. A. Cabrerizo-V lchez, and R. Hidalgo- lvarez. "The Young Laplace equation links capillarity with geometrical optics." European Journal of Physics 24, no. 2 (February 10, 2003): 159–68. http://dx.doi.org/10.1088/0143-0807/24/2/356.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Lu, Ning. "Generalized Soil Water Retention Equation for Adsorption and Capillarity." Journal of Geotechnical and Geoenvironmental Engineering 142, no. 10 (October 2016): 04016051. http://dx.doi.org/10.1061/(asce)gt.1943-5606.0001524.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Ning, Tao, Meng Xi, Bingtao Hu, Le Wang, Chuanqing Huang, and Junwei Su. "Effect of Viscosity Action and Capillarity on Pore-Scale Oil–Water Flowing Behaviors in a Low-Permeability Sandstone Waterflood." Energies 14, no. 24 (December 7, 2021): 8200. http://dx.doi.org/10.3390/en14248200.

Full text
Abstract:
Water flooding technology is an important measure to enhance oil recovery in oilfields. Understanding the pore-scale flow mechanism in the water flooding process is of great significance for the optimization of water flooding development schemes. Viscous action and capillarity are crucial factors in the determination of the oil recovery rate of water flooding. In this paper, a direct numerical simulation (DNS) method based on a Navier–Stokes equation and a volume of fluid (VOF) method is employed to investigate the dynamic behavior of the oil–water flow in the pore structure of a low-permeability sandstone reservoir in depth, and the influencing mechanism of viscous action and capillarity on the oil–water flow is explored. The results show that the inhomogeneity variation of viscous action resulted from the viscosity difference of oil and water, and the complex pore-scale oil–water two-phase flow dynamic behaviors exhibited by capillarity play a decisive role in determining the spatial sweep region and the final oil recovery rate. The larger the viscosity ratio is, the stronger the dynamic inhomogeneity will be as the displacement process proceeds, and the greater the difference in distribution of the volumetric flow rate in different channels, which will lead to the formation of a growing viscous fingering phenomenon, thus lowering the oil recovery rate. Under the same viscosity ratio, the absolute viscosity of the oil and water will also have an essential impact on the oil recovery rate by adjusting the relative importance between viscous action and capillarity. Capillarity is the direct cause of the rapid change of the flow velocity, the flow path diversion, and the formation of residual oil in the pore space. Furthermore, influenced by the wettability of the channel and the pore structure’s characteristics, the pore-scale behaviors of capillary force—including the capillary barrier induced by the abrupt change of pore channel positions, the inhibiting effect of capillary imbibition on the flow of parallel channels, and the blockage effect induced by the newly formed oil–water interface—play a vital role in determining the pore-scale oil–water flow dynamics, and influence the final oil recovery rate of the water flooding.
APA, Harvard, Vancouver, ISO, and other styles
9

Hua, Wei, Wei Wang, Weidong Zhou, Ruige Wu, and Zhenfeng Wang. "Experiment—Simulation Comparison in Liquid Filling Process Driven by Capillarity." Micromachines 13, no. 7 (July 12, 2022): 1098. http://dx.doi.org/10.3390/mi13071098.

Full text
Abstract:
This paper studies modifications made to the Bosanquet equation in order to fit the experimental observations of the liquid filling process in circular tubes that occurs by capillary force. It is reported that there is a significant difference between experimental observations and the results predicted by the Bosanquet equation; hence, it is reasonable to investigate these differences intensively. Here, we modified the Bosanquet equation such that it could consider more factors that contribute to the filling process. First, we introduced the air flowing out of the tube as the liquid inflow. Next, we considered the increase in hydraulic resistance due to the surface roughness of the inner tube. Finally, we further considered the advancing contact angle, which varies during the filling process. When these three factors were included, the modified Bosanquet equation was well correlated with the experimental results, and the R square—which indicates the fitting quality between the simulation and the experiment—significantly increased to above 0.99.
APA, Harvard, Vancouver, ISO, and other styles
10

Li, Shi-Ming, and Danesh K. Tafti. "A Mean-Field Pressure Formulation for Liquid-Vapor Flows." Journal of Fluids Engineering 129, no. 7 (December 28, 2006): 894–901. http://dx.doi.org/10.1115/1.2742730.

Full text
Abstract:
A nonlocal pressure equation is derived from mean-field free energy theory for calculating liquid-vapor systems. The proposed equation is validated analytically by showing that it reduces to van der Waals’ square-gradient approximation under the assumption of slow density variations. The proposed nonlocal pressure is implemented in the mean-field free energy lattice Boltzmann method (LBM). The LBM is applied to simulate equilibrium liquid-vapor interface properties and interface dynamics of capillary waves and oscillating droplets in vapor. Computed results are validated with Maxwell constructions of liquid-vapor coexistence densities, theoretical relationship of variation of surface tension with temperature, theoretical planar interface density profiles, Laplace’s law of capillarity, dispersion relationship between frequency and wave number of capillary waves, and the relationship between radius and the oscillating frequency of droplets in vapor. It is shown that the nonlocal pressure formulation gives excellent agreement with theory.
APA, Harvard, Vancouver, ISO, and other styles
More sources

Dissertations / Theses on the topic "Capillarity equation"

1

Rivetti, Sabrina. "Bounded variation solutions of capillarity-type equations." Doctoral thesis, Università degli studi di Trieste, 2014. http://hdl.handle.net/10077/10161.

Full text
Abstract:
2012/2013
We investigate by different techniques, the solvability of a class of capillarity-type problems, in a bounded N-dimensional domain. Since our approach is variational, the natural context where this problem has to be settled is the space of bounded variation functions. Solutions of our equation are defined as subcritical points of the associated action functional.
We first introduce a lower and upper solution method in the space of bounded variation functions. We prove the existence of solutions in the case where the lower solution is smaller than the upper solution. A solution, bracketed by the given lower and upper solutions, is obtained as a local minimizer of the associated functional without any assumption on the boundedness of the right-hand side of the equation. In this context we also prove order stability results for the minimum and the maximum solution lying between the given lower and upper solutions. Next we develop an asymmetric version of the Poincaré inequality in the space of bounded variation functions. Several properties of the curve C are then derived and basically relying on these results, we discuss the solvability of the capillarity-type problem, assuming a suitable control on the interaction of the supremum and the infimum of the function at the right-hand side with the curve C. Non-existence and multiplicity results are investigated as well. The one-dimensional case, which sometimes presents a different behaviour, is also discussed. In particular, we provide an existence result which recovers the case of non-ordered lower and upper solutions.
XXV Ciclo
1985
APA, Harvard, Vancouver, ISO, and other styles
2

Alvarellos, Jose. "Fundamental Studies of Capillary Forces in Porous Media." Diss., Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5314.

Full text
Abstract:
The contact angle defined by Young's equation depends on the ratio between solid and liquid surface energies. Young's contact angle is constant for a given system, and cannot explain the stability of fluid droplets in capillary tubes. Within this framework, large variations in contact angle and explained aassuming surface roughness, heterogeneity or contamination. This research explores the static and dynamic behavior of fluid droplets within capillary tubes and the variations in contact angle among interacting menisci. Various cases are considered including wetting and non-wetting gluids, droplets in inclined capillary tubes or subjected to a pressure difference, within one-dimensional and three-dimensional capillary systems, and under static or dynamic conditions (either harmonic fluid pressure or tube oscillation). The research approach is based on complementary analytical modeling (total energy formulation) and experimental techniques (microscopic observations). The evolution of meniscus curvatures and droplet displacements are studied in all cases. Analytical and experimental results show that droplets can be stable within capillary tubes even under the influence of an external force, the resulting contact angles are not constant, and bariations from Young's contact angle aare extensively justified as menisci interaction. Menisci introduce stiffness, therefore two immiscible Newtonian fluids behave as a Maxwellian fluid, and droplets can exhibit resonance or relaxation spectral features.
APA, Harvard, Vancouver, ISO, and other styles
3

Kamat, Madhusudan Sunil. "Soil moisture change due to variable water table." Thesis, Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54922.

Full text
Abstract:
The thesis numerically models and investigates the effect of a variable water table on the soil moisture content. The modelling is done using COMSOL and Richards' equation. The temporal variation plots can be used to find the capillarity of the soil and its impact on other phenomenon such as vapor intrusion and infiltration.
APA, Harvard, Vancouver, ISO, and other styles
4

DE, LUCA ALESSANDRA. "On some nonlocal issues: unique continuation from the boundary and capillarity problems for anisotropic kernels." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2022. http://hdl.handle.net/10281/378950.

Full text
Abstract:
Lo scopo della presente tesi è quello di discutere i risultati ottenuti durante i miei studi di dottorato, principalmente rivolti a problemi non locali. Per prima cosa ci occupiamo di principi di continuazione unica forte ed espansioni asintotiche locali in determinati punti del bordo per soluzioni di due diverse classi di equazioni ellittiche. In particolare, partiamo con lo studio di una classe di equazioni ellittiche frazionarie in un dominio limitato sotto una condizione al contorno di Dirichlet omogenea esterna. Per fare ciò, sfruttiamo la procedura di estensione di Caffarelli-Silvestre, grazie alla quale il problema non locale può essere riformulato in modo equivalente come problema locale in una dimensione in più, generando un problema con condizioni miste. Dopodichè, utilizziamo un'idea classica di Garofalo e Lin per ottenere una condizione di raddoppio tramite una formula di monotonia per la funzione di Almgren. Per superare le difficoltà legate alla perdita di regolarità in corrispondenza della transizione tra le regioni di Dirichlet e di Neumann, introduciamo una nuova tecnica basata su un argomento di approssimazione, che ci permette di derivare una cosiddetta identità di tipo Pohozaev necessaria per stimare la derivata della funzione di Almgren . Otteniamo così un risultato di continuazione unica forte nel contesto locale, che viene a sua volta combinato con l’analisi di blow-up per dedurre espansioni asintotiche locali e, di conseguenza, una continuazione unica forte anche nel contesto non locale. Inoltre forniamo anche un risultato di continuazione unica forte dal bordo di una fessura per le soluzioni di una classe specifica di equazioni ellittiche del secondo ordine in un dominio limitato aperto con una frattura, su cui è assegnata una condizione al contorno di Dirichlet omogenea. Questo problema locale è correlato a un caso particolare dello studio descritto sopra, in virtù di una forte connessione tra questo tipo di problemi e i problemi al contorno con condizioni miste. Nella presente dissertazione, trattiamo anche una teoria della capillarità non locale. In particolare, consideriamo nuclei di interazione più generali che sono possibilmente anisotropici e non necessariamente invarianti rispetto allo stesso riscalamento. In particolare, la perdita di invarianza è modellata utilizzando due diversi esponenti frazionari per tenere conto della possibilità che il contenitore e l'ambiente presentino caratteristiche diverse rispetto alle interazioni delle particelle. Determiniamo inoltre una legge di Young non locale per l'angolo di contatto tra la gocciolina e la superficie del contenitore e discutiamo la solvibilità e l’unicità della soluzione dell'equazione corrispondente in termini di nuclei di interazione e del relativo coefficiente di adesione.
The aim of the present thesis is to discuss the results obtained during my PhD studies, mainly devoted to nonlocal issues. We first deal with strong unique continuation principles and local asymptotic expansions at certain boundary points for solutions of two different classes of elliptic equations. We start the investigation by a class of fractional elliptic equations in a bounded domain under some outer homogeneous Dirichlet boundary condition. To do this, we exploit the Caffarelli-Silvestre extension procedure, which allows us to get an equivalent formulation of the nonlocal problem as a local problem in one dimension more, consisting in a mixed Dirichlet-Neumann boundary value problem. Then, we use a classical idea by Garofalo and Lin to obtain a doubling-type condition via a monotonicity formula for a suitable Almgren-type frequency function. To overcome the difficulties related to the lack of regularity at the Dirichlet-Neumann junction, we introduce a new technique based on an approximation argument, which leads us to derive a so-called Pohozaev-type identity needed to estimate the derivative of the Almgren function. Thus we gain a strong unique continuation result in the local context, which is in turn combined with blow-up arguments to deduce local asymptotics and, consequently, a strong unique continuation result in the nonlocal setting as well. We also provide a strong unique continuation result from the edge of a crack for the solutions to a specific class of second order elliptic equations in an open bounded domain with a fracture, on which a homogeneous Dirichlet boundary condition is prescribed, in the presence of potentials satisfying either a negligibility condition with respect to the inverse-square weight or some suitable integrability properties. This local problem is related to a particular case of the setting described above, by virtue of a strong connection between this type of problems and the mixed Dirichlet-Neumann boundary value problems. We also treat a capillarity theory of nonlocal type. In our setting, we consider more general interaction kernels that are possibly anisotropic and not necessarily invariant under scaling. In particular, the lack of scale invariance is modeled via two different fractional exponents in order to take into account the possibility that the container and the environment present different features with respect to particle interactions. We determine a nonlocal Young's law for the contact angle between the droplet and the surface of the container and discuss the unique solvability of the corresponding equation in terms of the interaction kernels and of the relative adhesion coefficient.
APA, Harvard, Vancouver, ISO, and other styles
5

Deng, Shengfu. "A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28254.

Full text
Abstract:
Three-dimensional gravity-capillary steady waves on water of finite-depth, which are uniformly translating in a horizontal propagation direction and periodic in a transverse direction, are considered. The exact Euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is the time-like variable. The existence of the solutions of the system is determined by two non-dimensional constants: the Bond number b and λ (the inverse of the square of the Froude number). The property of Sobolev spaces and the spectral analysis show that the spectrum of the linear part consists of isolated eigenvalues of finite algebraic multiplicity and the number of purely imaginary eigenvalues are finite. The distribution of eigenvalues is described by b and λ. Assume that C1 is the curve in (b,λ)-plane on which the first two eigenvalues for three-dimensional waves collide at the imaginary axis, and that the intersection point of the curve C1 with the line λ=1 is (b0,1) where b0>0. Two cases (b0,1) and (b,λ) â C1 where 0< b< b0 are investigated. A center-manifold reduction technique and a normal form analysis are applied to show that for each case the dynamical system can be reduced to a system of ordinary differential equations with finite dimensions. The dominant system for the case (b0,1) is coupled Schrödinger-KdV equations while it is a Schrödinger equation for another case (b,λ) â C1. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation method and adjusting some appropriate constants.
Ph. D.
APA, Harvard, Vancouver, ISO, and other styles
6

MacLaurin, James Normand. "The buckling of capillaries in tumours." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:ba252220-3c06-4d49-8696-655f6fefcd31.

Full text
Abstract:
Capillaries in tumours are often severely buckled (in a plane perpendicular to the axis) and / or chaotic in their direction. We develop a model of these phenomena using nonlinear solid mechanics. Our model focusses on the immediate surrounding of a capillary. The vessel and surrounding tissue are modelled as concentric annulii. The growth is dependent on the concentration of a nutrient (oxygen) diffusing from the vessel into the tumour interstitium. The stress is modelled using a multiplicative decomposition of the deformation gradient F=F_e F_g. The stress is determined by substituting the elastic deformation gradient F_e (which gives the deformation gradient from the hypothetical configuration to the current configuration) into a hyperelastic constitutive model as per classical solid mechanics. We use a Blatz-Ko model, parameterised using uniaxial compression experiments. The entire system is in quasi-static equilibrium, with the divergence of the stress tensor equal to zero. We determine the onset of buckling using a linear stability analysis. We then investigate the postbuckling behaviour by introducing higher order perturbations in the deformation and growth before using the Fredholm Alternative to obtain the magnitude of the buckle. Our results demonstrate that the growth-induced stresses are sufficient for the capillary to buckle in the absence of external loading and / or constraints. Planar buckling usually occurs after 2-5 times the cellular proliferation timescale. Buckles with axial variation almost always go unstable after planar buckles. Buckles of fine wavelength are initially preferred by the system, but over time buckles of large wavelength become energetically more favourable. The tumoural hoop stress T_{ThetaTheta} is the most invariant (Eulerian) variable at the time of buckling: it is typically of the order of the tumoural Young's Modulus when this occurs.
APA, Harvard, Vancouver, ISO, and other styles
7

Burtea, Cosmin. "Méthodes d'analyse de Fourier en hydrodynamique : des mascarets aux fluides avec capillarité." Thesis, Paris Est, 2017. http://www.theses.fr/2017PESC1047/document.

Full text
Abstract:
Dans la première partie de cette thèse on étudie les systèmes abcd qui ont été dérivés par J.L. Bona, M. Chen et J.-C. Saut en 2002. Ces systèmes sont des modèles approximant le problème d'ondes hydrodynamiques dans le régime de Boussinesq, à savoir, des vagues de faible amplitude et de grande longueur d'onde. Dans les deux premiers chapitres on considère le problème d'existence en temps long à savoir la construction de solutions pour les systèmes abcd qui ont leur temps d'existence minoré par $1/varepsilon$ où $varepsilon$ est le rapport entre une amplitude typique du vague et la profondeur du canal. Dans un premier temps on considère des données initiales appartenant aux espaces de Sobolev qui sont inclus dans l'espace des fonctions continues qui s'annulent à l'infini. D'un point de vue physique cette situatuion correspond à des vagues sont localisées en espace. Le point clé est la construction d'une fonctionnelle non linéaire d'énergie qui contrôle certaines normes de Sobolev sur un intervalle de temps long. Pour y arriver, on travaille avec des équations localisées en fréquence. Cette approche nous permet d'obtenir des résultats d'existence en temps long en demandant moins de régularité sur les données initiales. Un deuxième avantage de notre méthode est que l'on peut traiter d'une manière unifiée presque tous les cas correspondant aux différentes valeurs des paramètres abcd. Dans le deuxième chapitre on montre des résultats d'existence en temps long pour le cas des données ayant un comportement non trivial à l'infini.Ce type des données est relevant pour l'étude de la propagation des mascarets. L'idée qui est à la base de ces résultats est de considérer un découpage convenable de la donnée initiale en hautes et basses fréquences. Dans le troisième chapitre on emploie des schémas de volumes finis afin de construire des solutions numériques. On utilise ensuite nos schémas pour étudier l'interaction d'ondes progressives.La deuxième partie de ce manuscrit est consacrée à l'étude des problèmes de régularité optimale pour le système de Navier-Stokes qui régi l'évolution d'un fluide incompressible, inhomogène et pour le système Navier-Stokes-Korteweg utilisé pour prendre en compte les effets de capillarité. Plus précisément, on montre que ces systèmes sont bien-posés dans leurs espaces critiques, à savoir, les espaces quiont la même invariance par changement d'échelle que les systèmes eux-mêmes. Pour pouvoir démontrer ce type de résultats on a besoin d'établir de nouvelles estimations pour un problème de type Stokes avec des coefficients variables
The first part of the present thesis deals with the so -called abcd systems which were derived by J.L. Bona, M. Chen and J.-C. Saut back in 2002. These systems are approximation models for the waterwaves problem in the Boussinesq regime, that is, waves of small amplitude and long wavelength. In the first two chapters we address the long time existence problem which consists in constructing solutions for the Cauchy problem associated to the abcd systems and prove that the maximal time of existence is bounded from below by some physically relevant quantity. First, we consider the case of initial data belonging to some Sobolev spaces imbedded in the space of continuous functions which vanish at infinity. Physically, this corresponds to spatially localized waves. The key ingredient is to construct a nonlinear energy functional which controls appropriate Sobolev norms on the desired time scales. This is accomplished by working with spectrally localized equations. The two important features of our method is that we require lower regularity levels in order to develop a long time existence theory and we may treat in an uni ed manner most of the cases corresponding to the di erent values of the parameters. In the second chapter, we prove the long time existence results for the case of data thatdoes not necessarily vanish at in nity. This is especially useful if one has in mind bore propagation. One of the key ideas of the proof is to consider a well-adapted high-low frequency decomposition of the initial data. In the third chapter, we propose infinite volume schemes in order to construct numerical solutions. We use these schemes in order to study traveling waves interaction.The second part of this manuscript, is devoted to the study of optimal regularity issues for the incompressible inhomogeneous Navier-Stokes system and the Navier-Stokes-Korteweg system used in order to take in account capillarity effects. More precisely, we prove that these systems are well-posed in their truly critical spaces i.e. the spaces that have the same scale invariance as the system itself. Inorder to achieve this we derive new estimates for a Stoke-like problem with time independent variable coefficients
APA, Harvard, Vancouver, ISO, and other styles
8

Colinet, Pierre. "Amplitude equations and nonlinear dynamics of surface-tension and buoyancy-driven convective instabilities." Doctoral thesis, Universite Libre de Bruxelles, 1997. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212204.

Full text
Abstract:

This work is a theoretical contribution to the study of thermo-hydrodynamic instabilities in fluids submitted to surface-tension (Marangoni) and buoyancy (Rayleigh) effects in layered (Benard) configurations. The driving constraint consists in a thermal (or a concentrational) gradient orthogonal to the plane of the layer(s).

Linear, weakly nonlinear as well as strongly nonlinear analyses are carried out, with emphasis on high Prandtl (or Schmidt) number fluids, although some results are also given for low-Prandtl number liquid metals. Attention is mostly devoted to the mechanisms responsible for the onset of complex spatio-temporal behaviours in these systems, as well as to the theoretical explanation of some existing experimental results.

As far as linear stability analyses (of the diffusive reference state) are concerned, a number of different effects are studied, such as Benard convection in two layers coupled at an interface (for which a general classification of instability modes is proposed), surface deformation effects and phase-change effects (non-equilibrium evaporation). Moreover, a number of different monotonous and oscillatory instability modes (leading respectively to patterns and waves in the nonlinear regime) are identified. In the case of oscillatory modes in a liquid layer with deformable interface heated from above, our analysis generalises and clarifies earlier works on the subject. A new Rayleigh-Marangoni oscillatory mode is also described for a liquid layer with an undeformable interface heated from above (coupling between internal and surface waves).

Weakly nonlinear analyses are then presented, first for monotonous modes in a 3D system. Emphasis is placed on the derivation of amplitude (Ginzburg-Landau) equations, with universal structure determined by the general symmetry properties of the physical system considered. These equations are thus valid outside the context of hydrodynamic instabilities, although they generally depend on a certain number of numerical coefficients which are calculated for the specific convective systems studied. The nonlinear competitions of patterns such as convective rolls, hexagons and squares is studied, showing the preference for hexagons with upflow at the centre in the surface-tension-driven case (and moderate Prandtl number), and of rolls in the buoyancy-induced case.

A transition to square patterns recently observed in experiments is also explained by amplitude equation analysis. The role of several fluid properties and of heat transfer conditions at the free interface is examined, for one-layer and two-layer systems. We also analyse modulation effects (spatial variation of the envelope of the patterns) in hexagonal patterns, leading to the description of secondary instabilities of supercritical hexagons (Busse balloon) in terms of phase diffusion equations, and of pentagon-heptagon defects in the hexagonal structures. In the frame of a general non-variational system of amplitude equations, we show that the pentagon-heptagon defects are generally not motionless, and may even lead to complex spatio-temporal dynamics (via a process of multiplication of defects in hexagonal structures).

The onset of waves is also studied in weakly nonlinear 2D situations. The competition between travelling and standing waves is first analysed in a two-layer Rayleigh-Benard system (competition between thermal and mechanical coupling of the layers), in the vicinity of special values of the parameters for which a multiple (Takens-Bogdanov) bifurcation occurs. The behaviours in the vicinity of this point are numerically explored. Then, the interaction between waves and steady patterns with different wavenumbers is analysed. Spatially quasiperiodic (mixed) states are found to be stable in some range when the interaction between waves and patterns is non-resonant, while several transitions to chaotic dynamics (among which an infinite sequence of homoclinic bifurcations) occur when it is resonant. Some of these results have quite general validity, because they are shown to be entirely determined by quadratic interactions in amplitude equations.

Finally, models of strongly nonlinear surface-tension-driven convection are derived and analysed, which are thought to be representative of the transitions to thermal turbulence occurring at very high driving gradient. The role of the fastest growing modes (intrinsic length scale) is discussed, as well as scalings of steady regimes and their secondary instabilities (due to instability of the thermal boundary layer), leading to chaotic spatio-temporal dynamics whose preliminary analysis (energy spectrum) reveals features characteristic of hydrodynamic turbulence. Some of the (2D and 3D) results presented are in qualitative agreement with experiments (interfacial turbulence).


Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

APA, Harvard, Vancouver, ISO, and other styles
9

Cancès, Clément. "Écoulements diphasiques en milieux poreux hétérogènes : modélisation et analyse des effets liés aux discontinuités de la pression capillaire." Phd thesis, Université de Provence - Aix-Marseille I, 2008. http://tel.archives-ouvertes.fr/tel-00335506.

Full text
Abstract:
On s'intéresse à l'écoulement d'un mélange d'eau et d'huile dans une matrice poreuse supposée hétérogène, et plus particulièrement apposition de différentes sous-matrices poreuses supposées homogènes. Si la modélisation et l'analyse des écoulements diphasiques dans des milieux poreux homogènes a fait l'objet de nombreuses études préalables, ce travail s'intéresse aux phénomènes liés aux forces provenant de la pression capillaire au niveau des interfaces entre des milieux différents.
Dans un premier temps, on suppose que l'on peut connecter les pressions au niveau des interfaces. Cela nécessite des hypothèses sur les profils de pression capillaire, afin que les raccords soient possibles. On démontre l'existence d'une solution faible du problème parabolique dégénéré obtenu par convergence d'une famille de solutions approchées obtenues à l'aide d'un schéma Volumes Finis. L'unicité est garantie, sous hypothèse sur les dégénérescence, par une méthode de dédoublement de variable aboutissant à un principe de contraction $L^1$.
La modélisation ne garantit pas forcément que le raccord des pressions capillaires aux interfaces soit possible. Dans le chapitre 3, on donne une condition de raccord graphique des pressions capillaires aux interfaces qui permet de traiter des cas beaucoup plus généraux. On montre que de le problème avec raccords graphiques admet une solution. Un résultat d'unicité et de contraction $L^1$ est donné dans le cas unidimensionnel.
Dans le chapitre 4, on montre la convergence d'une approximation Volumes Finis vers l'unique solution du problème unidimensionnel. Ce résultat utilise une borne uniforme sur les flux discrets, analogie discrète de la preuve dans le cas continue faite au chapitre précédent.
On étudie dans les chapitres 5 et 6 la limite des solutions lorsque la dépendance de la pression capillaire par rapport à l'inconnue saturation devient très faible, et que la pression capillaire ne dépend plus que du sous milieux poreux homogène. Il apparaît alors des phénomènes différents selon l'orientation des forces de gravité et de capillarité. Soit la solution su problème est la solution entropique d'une équation hyperbolique à flux discontinus, soit une solution faible, entropique à l'intérieur des sous-domaines homogènes, et laissant apparaître un choc non classique à l'interface.
APA, Harvard, Vancouver, ISO, and other styles
10

Annavarapu, Rama Kishore. "Elastocapillary Behavior and Wettability Control in Nanoporous Microstructures." University of Toledo / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=toledo1544705326035201.

Full text
APA, Harvard, Vancouver, ISO, and other styles
More sources

Books on the topic "Capillarity equation"

1

Berti, Massimiliano, and Jean-Marc Delort. Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-99486-4.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

C, Hsieh K., and Langley Research Center, eds. Stability of capillary surfaces in rectangular containers: The right square cylinder. [Washington, DC]: National Aeronautics and Space Administration, Langley Research Center, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
3

Southeast Geometry Seminar (15th 2009 University of Alabama at Birmingham). Geometric analysis, mathematical relativity, and nonlinear partial differential equations: Southeast Geometry Seminars Emory University, Georgia Institute of Technology, University of Alabama, Birmingham, and the University of Tennessee, 2009-2011. Edited by Ghomi Mohammad 1969-. Providence, Rhode Island: American Mathematical Society, 2013.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
4

Gagneux, Gerard, and Olivier Millet. Discrete Mechanics of Capillary Bridges. Elsevier, 2018.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
5

Delort, Jean-Marc, and Massimiliano Berti. Almost Global Solutions of Capillary-Gravity Water Waves Equations on the Circle. Springer, 2018.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
6

van Hinsbergh, Victor W. M. Physiology of blood vessels. Oxford University Press, 2017. http://dx.doi.org/10.1093/med/9780198755777.003.0002.

Full text
Abstract:
This chapter covers two major fields of the blood circulation: ‘distribution’ and ‘exchange’. After a short survey of the types of vessels, which form the circulation system together with the heart, the chapter describes how hydrostatic pressure derived from the heartbeat and vascular resistance determine the volume of blood that is locally delivered per time unit. The vascular resistance depends on the length of the vessel, blood viscosity, and, in particular, on the diameter of the vessel, as formulated in the Poiseuille-Hagen equation. Blood flow can be determined in vivo by different imaging modalities. A summary is provided of how smooth muscle cell contraction is regulated at the cellular level, and how neuronal, humoral, and paracrine factors affect smooth muscle contraction and thereby blood pressure and blood volume distribution among tissues. Subsequently the exchange of solutes and macromolecules over the capillary endothelium and the contribution of its surface layer, the glycocalyx, are discussed. After a description of the Starling equation for capillary exchange, new insights are summarized(in the so-called glycocalyx cleft model) that led to a new view on exchange along the capillary and on the contribution of oncotic pressure. Finally mechanisms are indicated in brief that play a role in keeping the blood volume constant, as a constant volume is a prerequisite for adequate functioning of the circulatory system.
APA, Harvard, Vancouver, ISO, and other styles
7

Stability of capillary surfaces in rectangular containers: The right square cylinder. [Washington, DC]: National Aeronautics and Space Administration, Langley Research Center, 1998.

Find full text
APA, Harvard, Vancouver, ISO, and other styles
8

Dussaule, Jean-Claude, Martin Flamant, and Christos Chatziantoniou. Function of the normal glomerulus. Edited by Neil Turner. Oxford University Press, 2018. http://dx.doi.org/10.1093/med/9780199592548.003.0044_update_001.

Full text
Abstract:
Glomerular filtration, the first step leading to the formation of primitive urine, is a passive phenomenon. The composition of this primitive urine is the consequence of the ultrafiltration of plasma depending on renal blood flow, on hydrostatic pressure of glomerular capillary, and on glomerular coefficient of ultrafiltration. Glomerular filtration rate (GFR) can be precisely measured by the calculation of the clearance of freely filtrated exogenous substances that are neither metabolized nor reabsorbed nor secreted by tubules: its mean value is 125 mL/min/1.73 m² in men and 110 mL/min/1.73 m² in women, which represents 20% of renal blood flow. In clinical practice, estimates of GFR are obtained by the measurement of creatininaemia followed by the application of various equations (MDRD or CKD-EPI) and more recently by the measurement of plasmatic C-cystatin. Under physiological conditions, GFR is a stable parameter that is regulated by the intrinsic vascular and tubular autoregulation, by the balance between paracrine and endocrine agents acting as vasoconstrictors and vasodilators, and by the effects of renal sympathetic nerves. The mechanisms controlling GFR regulation are complex. This is due to the variety of vasoactive agents and their targets, and multiple interactions between them. Nevertheless, the relative stability of GFR during important variations of systemic haemodynamics and volaemia is due to three major operating mechanisms: autoregulation of the afferent arteriolar resistance, local synthesis and action of angiotensin II, and the sensitivity of renal resistance vessels to respond to NO release.
APA, Harvard, Vancouver, ISO, and other styles

Book chapters on the topic "Capillarity equation"

1

Bidaut-Veron, Marie-Françoise. "New Results Concerning the Singular Solutions of the Capillarity Equation." In Variational Methods for Free Surface Interfaces, 191–96. New York, NY: Springer New York, 1987. http://dx.doi.org/10.1007/978-1-4612-4656-5_22.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Finn, Robert. "Capillary Forces on Partially Immersed Plates." In Differential and Difference Equations with Applications, 13–25. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-7333-6_2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
3

Awasthi, Mukesh Kumar, Rishi Asthana, and Ziya Uddin. "Evaporative Capillary Instability of Swirling Fluid Layer with Mass Transfer." In Differential Equations in Engineering, 37–54. Boca Raton: CRC Press, 2021. http://dx.doi.org/10.1201/9781003105145-2.

Full text
APA, Harvard, Vancouver, ISO, and other styles
4

Fialka, M., and S. Vašut. "Special Case of Oscillatory Differential Equation for Capillary." In Progress and Trends in Rheology V, 469–70. Heidelberg: Steinkopff, 1998. http://dx.doi.org/10.1007/978-3-642-51062-5_227.

Full text
APA, Harvard, Vancouver, ISO, and other styles
5

Craig, Walter, and Catherine Sulem. "Normal Form Transformations for Capillary-Gravity Water Waves." In Hamiltonian Partial Differential Equations and Applications, 73–110. New York, NY: Springer New York, 2015. http://dx.doi.org/10.1007/978-1-4939-2950-4_3.

Full text
APA, Harvard, Vancouver, ISO, and other styles
6

van Brummelen, E. H., M. Shokrpour-Roudbari, and G. J. van Zwieten. "Elasto-Capillarity Simulations Based on the Navier–Stokes–Cahn–Hilliard Equations." In Advances in Computational Fluid-Structure Interaction and Flow Simulation, 451–62. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-40827-9_35.

Full text
APA, Harvard, Vancouver, ISO, and other styles
7

Cuvelier, C., A. Segal, and A. A. van Steenhoven. "Capillary Free Boundaries governed by the Navier-Stokes Equations." In Finite Element Methods and Navier-Stokes Equations, 418–31. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-010-9333-0_15.

Full text
APA, Harvard, Vancouver, ISO, and other styles
8

Magiera, Jim, and Christian Rohde. "Analysis and Numerics of Sharp and Diffuse Interface Models for Droplet Dynamics." In Fluid Mechanics and Its Applications, 67–86. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-09008-0_4.

Full text
Abstract:
AbstractThe modelling of liquid–vapour flow with phase transition poses many challenges, both on the theoretical level, as well as on the level of discretisation methods. Therefore, accurate mathematical models and efficient numerical methods are required. In that, we focus on two modelling approaches: the sharp-interface (SI) approach and the diffuse-interface (DI) approach. For the SI-approach, representing the phase boundary as a co-dimension-1 manifold, we develop and validate analytical Riemann solvers for basic isothermal two-phase flow scenarios. This ansatz becomes cumbersome for increasingly complex thermodynamical settings. A more versatile multiscale interface solver, that is based on molecular dynamics simulations, is able to accurately describe the evolution of phase boundaries in the temperature-dependent case. It is shown to be even applicable to two-phase flow of multiple components. Despite the successful developments for the SI approach, these models fail if the interface undergoes topological changes. To understand merging and splitting phenomena for droplet ensembles, we consider DI models of second gradient type. For these Navier–Stokes–Korteweg systems, that can be seen as a third order extension of the Navier–Stokes equations, we propose variants that are more accessible to standard numerical schemes. More precisely, we reformulate the capillarity operator to restore the hyperbolicity of the Euler operator in the full system.
APA, Harvard, Vancouver, ISO, and other styles
9

Levine, Howard A. "Numerical Searches for Ground State Solutions of a Modified Capillary Equation and for Solutions of the Charge Balance Equation." In Mathematical Sciences Research Institute Publications, 55–83. New York, NY: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-9608-6_5.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

Cuvelier, C., and R. M. S. M. Schulkes. "Numerical analysis of capillary free boundaries governed by the Navier-Stokes equations." In Numerical Methods for Free Boundary Problems, 123–27. Basel: Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-5715-4_9.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Conference papers on the topic "Capillarity equation"

1

Wemhoff, Aaron P. "Dependence of the Equation of State in Surface Tension Prediction by the Theory of Capillarity." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10221.

Full text
Abstract:
The theory of capillarity was originally developed by J. D. van der Waals to provide a means of predicting interfacial (surface) tension data using saturation pressure and liquid-vapor density data. This theory was recently extended to the Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson fluid models. The latter two equations of state are more advanced than the Redlich-Kwong model in that they use an acentric factor to predict saturated vapor pressure values more in agreement with experimental data. However, the agreement in the predicted interfacial tension values is worse for the latter two models compared to the Redlich-Kwong model. This study features a sensitivity analysis to show that the predicted interfacial tension values are more sensitive to vapor density than liquid density and vapor pressure, and that increasing the vapor density reduces the corresponding predicted interfacial tension value. Furthermore, all three fluid models tend to overpredict interfacial tension when experimental data are applied in their predictive equations. This study finds that the reason why the simpler Redlich-Kwong model predicts better interfacial tension values than the two advanced models is because the former overpredicts vapor density moreso than the two advanced cubic fluid models, and this in turn reduces the prediction of interfacial tension to make its value more comparable to experimental data.
APA, Harvard, Vancouver, ISO, and other styles
2

Tong, Albert Y., and Zhaoyuan Wang. "A Numerical Method for Capillarity-Driven Free Surface Flows." In ASME 2005 Fluids Engineering Division Summer Meeting. ASMEDC, 2005. http://dx.doi.org/10.1115/fedsm2005-77274.

Full text
Abstract:
The continuum surface force (CSF) method has been extensively employed in the volume-of-fluid (VOF), level set (LS) and front tracking methods to model surface tension force. It is a robust method requiring relatively easy implementation. However, it is known to generate spurious currents near the interface that may lead to disastrous interface instabilities and failures of grid convergence. A different surface tension implementation algorithm, referred to as the pressure boundary method (PBM), is introduced in this study. The surface tension force is incorporated into the Navier-Stokes equation via a capillary pressure gradient while the free surface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method. It has been shown that the spurious currents are greatly reduced by the present method with the sharp pressure boundary condition preserved. The numerical results of several cases have been compared with data reported in the literature and are found to be in a close agreement.
APA, Harvard, Vancouver, ISO, and other styles
3

Radhakrishnan, Anand N. P., Marc Pradas, Serafim Kalliadasis, and Asterios Gavriilidis. "Nonlinear Dynamics of Gas-Liquid Separation in a Capillary Microseparator." In ASME 2018 16th International Conference on Nanochannels, Microchannels, and Minichannels. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/icnmm2018-7613.

Full text
Abstract:
Micro-engineered devices (MED) are seeing a significant growth in performing separation processes1. Such devices have been implemented in a range of applications from chemical catalytic reactors to product purification systems like microdistillation. One of the biggest advantages of these devices is the dominance of capillarity and interfacial tension forces. A field where MEDs have been used is in gas-liquid separations. These are encountered, for example, after a chemical reactor, where a gaseous component being produced needs immediate removal from the reactor, because it can affect subsequent reactions. The gaseous phase can be effectively removed using an MED with an array of microcapillaries. Phase-separation can then be brought about in a controlled manner along these capillary structures. For a device made from a hydrophilic material (e.g. Si or glass), the wetted phase (e.g. water) flows through the capillaries, while the non-wetted dispersed phase (e.g. gas) is prevented from entering the capillaries, due to capillary pressure. Separation of liquid-liquid flows can also be achieved via this approach. However, the underlying mechanism of phase separation is far from being fully understood. The pressure at which the gas phase enters the capillaries (gas-to-liquid breakthrough) can be estimated from the Young-Laplace equation, governed by the surface tension (γ) of the wetted phase, capillary width (d) and height (h), and the interface equilibrium contact angle (θeq). Similarly, the liquid-to-gas breakthrough pressure (i.e. the point at which complete liquid separation ceases and liquid exits through the gas outlet) can be estimated from the pressure drop across the capillaries via the Hagen-Poiseuille (HP) equation. Several groups reported deviations from these estimates and therefore, included various parameters to account for the deviations. These parameters usually account for (i) flow of wetted phase through ‘n’ capillaries in parallel, (ii) modification of geometric correction factor of Mortensen et al., 2005 2 and (iii) liquid slug length (LS) and number of capillaries (n) during separation. LS has either been measured upstream of the capillary zone or estimated from a scaling law proposed by Garstecki et al., 2006 3. However, this approach does not address the balance between the superficial inlet velocity and net outflow of liquid through each capillary (qc). Another shortcoming of these models has been the estimation of the apparent contact angle (θapp), which plays a critical role in predicting liquid-to-gas breakthrough. θapp is either assumed to be equal to θeq or measured with various techniques, e.g. through capillary rise or a static droplet on a flat substrate, which is significantly different from actual dynamic contact angles during separation. In other cases, the Cox-Voinov model has been used to calculate θapp from θeq and capillary number. Hence, the empirical models available in the literature do not predict realistic breakthrough pressures with sufficient accuracy. Therefore, a more detailed in situ investigation of the critical liquid slug properties during separation is necessary. Here we report advancements in the fundamental understanding of two-phase separation in a gas-liquid separation (GLS) device through a theoretical model developed based on critical events occurring at the gas-liquid interfaces during separation.
APA, Harvard, Vancouver, ISO, and other styles
4

Wang, Zhaoyuan, and Albert Y. Tong. "A Sharp Surface Tension Modeling Method for Capillarity-Dominant Two-Phase Incompressible Flows." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-42455.

Full text
Abstract:
A surface tension implementation algorithm for two-phase incompressible interfacial flows is presented in this study. The surface tension effect is treated as a jump condition at the interface and incorporated into the Navier-Stokes equation via a capillary pressure gradient. The interface is tracked by a coupled level set and volume-of-fluid (CLSVOF) method based on the finite-volume formulation on a fixed Eulerian grid. It has been shown in a stationary benchmark test the spurious currents are greatly reduced and the sharp pressure jump across the interface is well preserved. Numerical instabilities caused by the sharp treatment on a fixed grid are avoided. Several dynamic tests are performed to further validate the accuracy and versatility of the present method, the results of which are in good agreement with data reported in the literature.
APA, Harvard, Vancouver, ISO, and other styles
5

Haq, M. Ashraful, and Shao Wang. "Lubricant Evaporation and Flow due to Laser Heating With a Skewed Temperature Distribution Induced by Disk Motion." In ASME 2017 Conference on Information Storage and Processing Systems collocated with the ASME 2017 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/isps2017-5477.

Full text
Abstract:
Due to the fast disk rotation, the temperature distribution on the disk under laser illumination in heat-assisted magnetic recording (HAMR) tends to deviate significantly from an axisymmetric distribution. A lognormal approximation scheme for the temperature distribution containing a tail based on a fast-moving heat source solution was proposed for use in an equation for the lubricant film involving evaporation, surface tension, disjoining pressure and thin-film enhanced effective viscosity. The results reveal the process of formation of a lubricant trough: an indent of the lubricant profile first forms and grows to a steady-state depth, followed by a continuous extension at the rate of the disk velocity. Both evaporation and thermal capillarity due to the surface tension gradient contribute greatly to the creation of a trough in the lubricant profile while the latter also causes boundary ridges. Unlike the Gaussian temperature-based solution, the local minimum of the lubricant thickness occurs at the trailing edge of the thermal spot.
APA, Harvard, Vancouver, ISO, and other styles
6

Yd, Sumith, and Shalabh C. Maroo. "A New Algorithm for Contact Angle Estimation in Molecular Dynamics Simulations." In ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/icnmm2015-48569.

Full text
Abstract:
It is important to study contact angle of a liquid on a solid surface to understand its wetting properties, capillarity and surface interaction energy. While performing transient molecular dynamics (MD) simulations it requires calculating the time evolution of contact angle. This is a tedious effort to do manually or with image processing algorithms. In this work we propose a new algorithm to estimate contact angle from MD simulations directly and in a computationally efficient way. This algorithm segregates the droplet molecules from the vapor molecules using Mahalanobis distance (MND) technique. Then the density is smeared onto a 2D grid using 4th order B-spline interpolation function. The vapor liquid interface data is estimated from the grid using density filtering. With the interface data a circle is fitted using Landau method. The equation of this circle is solved for obtaining the contact angle. This procedure is repeated by rotating the droplet about the vertical axis. We have applied this algorithm to a number of studies (different potentials and thermostat methods) which involves the MD simulation of water.
APA, Harvard, Vancouver, ISO, and other styles
7

Li, Zhuoran, Jiahui You, and Guan Qin. "Pore-Scale Modellings on the Impacts of Hydrate Distribution Morphology on Gas and Water Transport in Hydrate-Bearing Sediments." In SPE Canadian Energy Technology Conference. SPE, 2022. http://dx.doi.org/10.2118/208983-ms.

Full text
Abstract:
Abstract Gas and water transport behavior, which is controlled by the pore characteristics and capillarity in hydrate-bearing sediments (HBS), is one of the key factors affecting the gas production. Hydrate distribution morphology (HDM) can significantly influence the pore structures of HBS, affecting the relative permeabilities of gas and water. To elucidate the impacts of HDM in microscopic scale, a phase-field lattice Boltzmann (LB) model is developed to describe the gas and water transport in HBS.To simulate the transport of immiscible fluids, which exist obvious density and viscosity contrasts, a phase-field LB model with the conservative form of interface-tracking equation is developed to suppress the spurious currents at phase interfaces. To describe the fluid-solid interactions, the bounce-back condition is applied for both solid phases (hydrate and grains) to achieve the non-slip condition and the wettability condition is applied for grains and hydrate to describe the wettability behavior. To improve the numerical stability, the multi-relaxation-time (MRT) collision operator is applied and the discretization schemes with 8th order accuracy for the gradient operator are selected. In this work, we first validated our model by applying several benchmark cases aiming at fluids with obvious density contrasts such as the layered Couette/Poiseuille flows, Rayleigh–Taylor instability. Then the synthetic geometries of the pore-filling and grain-coating HBS with several hydrate saturation (Shyd) were constructed by guaranteeing the same extent of connectivity. Then the steady-state relative permeability measurement and drainage capillary pressure measurement processes were simulated by the LB model for two HDM cases under several Shyd. The results showed that in the hydrophilic HBS, the relative permeability of gas in the pore-filling case is obviously larger than that in the grain-coating case at the same Shyd, and larger capillary pressure can be obtained in the pore-filling case. In addition, as the Shyd increased, it would notably enhance these differences of fluids relative permeability and capillary pressure between two HDM cases. Because the HDM can not only influence the pore space structures but also the wettability of the porous medium by creating solid surfaces of varying wettability, the distribution and transport of fluid phases in different HDM cases can be obviously affected. The phase-filed LB model applied in this study is capable to handle and suppress the spurious currents at phase interfaces, ensuring a satisfactory numerical stability and accuracy. Thus, the real density and viscosity contrasts between the water and gas under the in-situ thermodynamic conditions can be considered in the simulation. The impacts of HDM on the gas and water transport were quantitively analyzed by simulating multiphase flow processes in HBS.
APA, Harvard, Vancouver, ISO, and other styles
8

Eddy, D. B. "Reservoir Capillary Equilibrium: A Derived Equation." In Annual Technical Meeting. Petroleum Society of Canada, 1995. http://dx.doi.org/10.2118/95-74.

Full text
APA, Harvard, Vancouver, ISO, and other styles
9

Popov, A. V., I. V. Suloev, and Alexander V. Vinogradov. "Application of the parabolic wave equation to the simulation of refractive x-ray multilenses." In International Conference on X-ray and Neutron Capillary Optics, edited by Muradin A. Kumakhov. SPIE, 2002. http://dx.doi.org/10.1117/12.489768.

Full text
APA, Harvard, Vancouver, ISO, and other styles
10

GROVES, M. D. "THREE-DIMENSIONAL SOLITARY GRAVITY-CAPILLARY WATER WAVES." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0003.

Full text
APA, Harvard, Vancouver, ISO, and other styles

Reports on the topic "Capillarity equation"

1

Jang, Jaewon. Verification of capillary pressure functions and relative permeability equations for gas production. Office of Scientific and Technical Information (OSTI), July 2016. http://dx.doi.org/10.2172/1337017.

Full text
APA, Harvard, Vancouver, ISO, and other styles
2

Snyder, Victor A., Dani Or, Amos Hadas, and S. Assouline. Characterization of Post-Tillage Soil Fragmentation and Rejoining Affecting Soil Pore Space Evolution and Transport Properties. United States Department of Agriculture, April 2002. http://dx.doi.org/10.32747/2002.7580670.bard.

Full text
Abstract:
Tillage modifies soil structure, altering conditions for plant growth and transport processes through the soil. However, the resulting loose structure is unstable and susceptible to collapse due to aggregate fragmentation during wetting and drying cycles, and coalescense of moist aggregates by internal capillary forces and external compactive stresses. Presently, limited understanding of these complex processes often leads to consideration of the soil plow layer as a static porous medium. With the purpose of filling some of this knowledge gap, the objectives of this Project were to: 1) Identify and quantify the major factors causing breakdown of primary soil fragments produced by tillage into smaller secondary fragments; 2) Identify and quantify the. physical processes involved in the coalescence of primary and secondary fragments and surfaces of weakness; 3) Measure temporal changes in pore-size distributions and hydraulic properties of reconstructed aggregate beds as a function of specified initial conditions and wetting/drying events; and 4) Construct a process-based model of post-tillage changes in soil structural and hydraulic properties of the plow layer and validate it against field experiments. A dynamic theory of capillary-driven plastic deformation of adjoining aggregates was developed, where instantaneous rate of change in geometry of aggregates and inter-aggregate pores was related to current geometry of the solid-gas-liquid system and measured soil rheological functions. The theory and supporting data showed that consolidation of aggregate beds is largely an event-driven process, restricted to a fairly narrow range of soil water contents where capillary suction is great enough to generate coalescence but where soil mechanical strength is still low enough to allow plastic deforn1ation of aggregates. The theory was also used to explain effects of transient external loading on compaction of aggregate beds. A stochastic forInalism was developed for modeling soil pore space evolution, based on the Fokker Planck equation (FPE). Analytical solutions for the FPE were developed, with parameters which can be measured empirically or related to the mechanistic aggregate deformation model. Pre-existing results from field experiments were used to illustrate how the FPE formalism can be applied to field data. Fragmentation of soil clods after tillage was observed to be an event-driven (as opposed to continuous) process that occurred only during wetting, and only as clods approached the saturation point. The major mechanism of fragmentation of large aggregates seemed to be differential soil swelling behind the wetting front. Aggregate "explosion" due to air entrapment seemed limited to small aggregates wetted simultaneously over their entire surface. Breakdown of large aggregates from 11 clay soils during successive wetting and drying cycles produced fragment size distributions which differed primarily by a scale factor l (essentially equivalent to the Van Bavel mean weight diameter), so that evolution of fragment size distributions could be modeled in terms of changes in l. For a given number of wetting and drying cycles, l decreased systematically with increasing plasticity index. When air-dry soil clods were slightly weakened by a single wetting event, and then allowed to "age" for six weeks at constant high water content, drop-shatter resistance in aged relative to non-aged clods was found to increase in proportion to plasticity index. This seemed consistent with the rheological model, which predicts faster plastic coalescence around small voids and sharp cracks (with resulting soil strengthening) in soils with low resistance to plastic yield and flow. A new theory of crack growth in "idealized" elastoplastic materials was formulated, with potential application to soil fracture phenomena. The theory was preliminarily (and successfully) tested using carbon steel, a ductile material which closely approximates ideal elastoplastic behavior, and for which the necessary fracture data existed in the literature.
APA, Harvard, Vancouver, ISO, and other styles
You might also be interested in the extended bibliographies on the topic 'Capillarity equation' for particular source types:
Journal articles Dissertations / Theses
We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!

To the bibliography