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1
Chang, Sooyoung, Jaedeok Seo, Seokbin Hong, Duck-Gyu Lee, and Wonjung Kim. "Dynamics of liquid imbibition through paper with intra-fibre pores." Journal of Fluid Mechanics 845 (April 20, 2018): 36–50. http://dx.doi.org/10.1017/jfm.2018.235.
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We present a combined experimental and theoretical investigation of the dynamics of liquid imbibition through paper. The Washburn equation is widely used to describe the dynamics of capillary flow through paper, but this classical model has limited accuracy, which often makes it difficult to use in developing analytic systems such as paper-based microfluidic devices. We here report that the internal cavity of the cellulose fibres composing paper is significantly responsible for the limited accuracy of the Washburn equation. Our experiments demonstrated that liquid can be absorbed in the internal cavity of the cellulose fibres as well as in the inter-fibre pores formed by the fibre network. We developed a mathematical model for liquid imbibition by considering the flow through the intra-fibre pores based on experimental measurements of the intra-structure of cellulose fibres. The model markedly improves the prediction of the liquid absorption length, compared with the results of the Washburn equation, thus revealing the physics behind the limits of the Washburn equation. This study suggests that the accurate description of capillary imbibition through paper require parameters characterizing the internal pores of the cellulose fibres comprising the paper. Our results not only provide a new insight into porous media flows with different sized pores, but also provide a theoretical background for flow control in paper-based microfluidic systems.
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Villagrán Zaccardi, Yury, Natalia Alderete, and Nele De Belie. "Lucas-Washburn vs Richards equation for the modelling of water absorption in cementitious materials." MATEC Web of Conferences 199 (2018): 02019. http://dx.doi.org/10.1051/matecconf/201819902019.
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The Lucas-Washburn equation is still being applied by a significant number of researchers for the modelling of water absorption in cementitious materials. A modern approach considers the extended Darcy’s law leading to the Richards equation instead. Three main assumptions are implied by the application of the Lucas-Washburn equation: the flow occurs in one direction only, the material is separated into one fully wet and one fully dry region, and pores are modelled as an assembly of parallel tubes of a particular radius. Its application to analyse experimental results allows defining these three assumptions as mere simplifications. Therefore, all the parameters comprised in the Lucas-Washburn model are apparent. Consequently, a very limited description of the transport properties of the material can be achieved. For many engineering purposes this would not be an issue, but for an intrinsic description of the material a more realistic model is required. This paper discusses the limitations of the Lucas-Washburn equation, and the advantages of the Richards equation regarding the modelling of water absorption in cementitious materials. The comparative analysis reveals the versatility of the Richards equation, with an approach that considers the material as a continuum and describes it through measurable parameters.
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Wang, Pan, Qingen Zhang, Muhan Wang, Bing Yin, Dongshuai Hou, and Yue Zhang. "Atomistic insights into cesium chloride solution transport through the ultra-confined calcium–silicate–hydrate channel." Physical Chemistry Chemical Physics 21, no. 22 (2019): 11892–902. http://dx.doi.org/10.1039/c8cp07676f.
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Cao, Bing-Yang, Min Yang, and Guo-Jie Hu. "Capillary filling dynamics of polymer melts in nanopores: experiments and rheological modelling." RSC Advances 6, no. 9 (2016): 7553–59. http://dx.doi.org/10.1039/c5ra24991k.
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The spontaneous capillarity-driven flow behaviors of PE melts through AAO nanopores suggest that the zero-shear-rate viscosity of the PE melts decreases, which can be predicted by a modified Lucas–Washburn law considering the polymer rheological model.
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Zhang, Xiao Dan, Jun Hao Qian, and Jun Wei Jia. "Ink Penetration Model Research Based on Ink Permeability." Applied Mechanics and Materials 731 (January 2015): 462–65. http://dx.doi.org/10.4028/www.scientific.net/amm.731.462.
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This article analyzes the mechanism of interaction between the ink and paper. The Washburn equation just based on static penetration, while in contact with the ink and paper, freedom infiltration process is a dynamic process. So it is further derived based on a model of the dynamic ink permeability of dynamic contact angle, and mathematical analyzes some of the important parameters of the dynamic model so that can strive a more accurate description of the state of penetration of ink into the paper, thereby theoretically predict the quality control of printed matter.
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Gorthi, Srinivas R., Sanjaya Kumar Meher, Gautam Biswas, and Pranab Kumar Mondal. "Capillary imbibition of non-Newtonian fluids in a microfluidic channel: analysis and experiments." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2242 (October 2020): 20200496. http://dx.doi.org/10.1098/rspa.2020.0496.
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We have presented an experimental analysis on the investigations of capillary filling dynamics of inelastic non-Newtonian fluids in the regime of surface tension dominated flows. We use the Ostwald–de Waele power-law model to describe the rheology of the non-Newtonian fluids. Our analysis primarily focuses on the experimental observations and revisits the theoretical understanding of the capillary dynamics from the perspective of filling kinematics at the interfacial scale. Notably, theoretical predictions of the filling length into the capillary largely endorse our experimental results. We study the effects of the shear-thinning nature of the fluid on the underlying filling phenomenon in the capillary-driven regime through a quantitative analysis. We further show that the dynamics of contact line motion in this regime plays an essential role in advancing the fluid front in the capillary. Our experimental results on the filling in a horizontal capillary re-establish the applicability of the Washburn analysis in predicting the filling characteristics of non-Newtonian fluids in a vertical capillary during early stage of filling (Digilov 2008 Langmuir 24 , 13 663–13 667 ( doi:10.1021/la801807j )). Finally, through a scaling analysis, we suggest that the late stage of filling by the shear-thinning fluids closely follows the variation x ~ t . Such a regime can be called the modified Washburn regime (Washburn 1921 Phys. Rev. 17 , 273–283 ( doi:10.1103/PhysRev.17.273 )).
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Qu, Zhen Cai, Guang Xue Chen, Bao Lin Tang, and Shuang Shuang Wen. "Study on Model of Dot Gain in Ink-Jet Printing." Advanced Materials Research 236-238 (May 2011): 1405–9. http://dx.doi.org/10.4028/www.scientific.net/amr.236-238.1405.
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Ink-jet printing is a non-contact printing, drops are jetted on the substrates to form images through the nozzles at a certain speed. Dot is the smallest unit in printing; the qualities of printing are seriously affected by dot gain. Ink spreading and penetration are discussed in this paper, influences on dot gain in ink-jet printing are studied, the original Young's equation and Washburn formula are theoretically amended, more scientific and rational models and formulas are obtained in the actual process of ink-jet printing, which offers reference standard and theoretical basis to improve the quality of ink-jet printing.
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Peterson, Rorik A. "Assessing the role of differential frost heave in the origin of non-sorted circles." Quaternary Research 75, no. 2 (March 2011): 325–33. http://dx.doi.org/10.1016/j.yqres.2010.08.003.
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AbstractA. L. Washburn famously proposed and reviewed 19 hypotheses for the origin of patterned ground in periglacial environments over 50 years ago (Washburn, 1956). Of these 19 mechanisms, only a few have been analyzed starting from a fundamental description of the physics to assess their potential contribution to the initiation of patterned ground. Here, differential frost heave (DFH) is investigated as the origin of non-sorted circles in periglacial landscapes. Model results indicating that DFH can spontaneously lead to patterned ground are compared to measurements of patterned ground in the Canadian Arctic Archipelago. The characteristic size of the predicted emerging pattern depends strongly on the maximum depth of freezing but is only weakly dependent on the soil composition. The predicted emerging patterns may also be dramatically different in size with a small change in active layer when a relatively thin (~ 10 cm) insulating snow covers the ground during freezing. The model predicted trends agree with field observations of pattern size and active layer depth at two distinct sites. Although two data points cannot conclusively indicate a trend, this correlation gives support for the possibility of determining some subsurface properties using remote sensing images of surface patterned ground.
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Samayoa, Didier, Liliana Álvarez Romero, Lilian Aurora Ochoa Ontiveros, Lucero Priscila Damian Adame, Ehcatl Victoria-Tobon, and Gabriel Romero Paredes. "Fractal imbibition in Koch's curve-like capillar tubes." Revista Mexicana de Física 64, no. 3 (April 30, 2018): 291. http://dx.doi.org/10.31349/revmexfis.64.291.
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Fractal geometry eects in capillary imbibition process are studied.Capillary rise analysis in Koch's curve-like tubes were be carried out withiterations i = 0; 1; 2; 3; 4; 5. The behaviour was characterized in function oftime, fractal geometry and height of capillary rise. An geometrical relationshipfor fractal dimension of ow tortuosity (dr) in porous media is obtained.The analytical model of Lucas-Washburn-Cai to describe the capillary rise byspontaneus imbibition in tubes with deterministic fractal geometry is adjusted.The equilibrium height time as function of fractal dimension of ow tortuosity incapillary tubes with tortuous path is also derived.
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Cai, Shaobin, Li Zhang, Lixin Kang, Yongfei Yang, Wenlong Jing, Lei Zhang, Chao Xu, Hai Sun, and Mozhdeh Sajjadi. "Spontaneous Imbibition in a Fractal Network Model with Different Wettabilities." Water 13, no. 17 (August 29, 2021): 2370. http://dx.doi.org/10.3390/w13172370.
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In this work, we derived a mathematical model for spontaneous imbibition in a Y-shaped branching network model. The classic Lucas–Washburn equation was used for modeling the imbibition process occurring in the Y-shape model. Then, a mathematical model for the Newtonian fluid’s imbibition was derived to reveal the relationship between dimensionless imbibition time and length ratio, radius ratio, and wetting strength. The dimensionless imbibition time in the model was adopted to compare with that of the capillary bundle model. Different length and radius ratios were considered in the adjacent two-stage channels, and different wettabilities were considered in the different branches. The optimal radius ratio, length ratio, and wetting strength were calculated under the condition of the shortest imbibition time. In addition, the shortest dimensionless imbibition time of the three-stage Y-shaped branching network model was calculated when the wettability changes randomly. The results indicate that the imbibition time changed mostly when the wettability of the second branch changed, and the second branch was the most sensitive to wettability in the model.
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Pirard, R., S. Blacher, F. Brouers, and J. P. Pirard. "Interpretation of mercury porosimetry applied to aerogels." Journal of Materials Research 10, no. 8 (August 1995): 2114–19. http://dx.doi.org/10.1557/jmr.1995.2114.
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The observation of aerogels submitted to a pressure of mercury indicates that this porous material is compacted and not intruded by the mercury. Consequently, the classical Washburn equation cannot be applied. A relation is established between the pressure P of compaction and the size L of the largest pores. The size of pores is estimated by using the nitrogen adsorption-desorption isotherms analysis and SEM measurements. A relation is found in which P is proportional to L−4 The new relation is applied to mercury porosimetry. Finally, a mechanical model is proposed that reproduces successfully the behavior of aerogels under high pressure of mercury.
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Kasetsirikul, Surasak, Muhammad J. A. Shiddiky, and Nam-Trung Nguyen. "Wicking in Paper Strips under Consideration of Liquid Absorption Capacity." Chemosensors 8, no. 3 (August 6, 2020): 65. http://dx.doi.org/10.3390/chemosensors8030065.
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Paper-based microfluidic devices have the potential of being a low-cost platform for diagnostic devices. Electrical circuit analogy (ECA) model has been used to model the wicking process in paper-based microfluidic devices. However, material characteristics such as absorption capacity cannot be included in the previous ECA models. This paper proposes a new model to describe the wicking process with liquid absorption in a paper strip. We observed that the fluid continues to flow in a paper strip, even after the fluid reservoir has been removed. This phenomenon is caused by the ability of the paper to store liquid in its matrix. The model presented in this paper is derived from the analogy to the current response of an electric circuit with a capacitance. All coefficients in the model are fitted with data of capillary rise experiments and compared with direct measurement of the absorption capacity. The theoretical data of the model agrees well with experimental data and the conventional Washburn model. Considering liquid absorption capacity as a capacitance helps to explain the relationship between material characteristics and the wicking mechanism.
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MacDonald, Brendan D. "Flow of liquids through paper." Journal of Fluid Mechanics 852 (August 2, 2018): 1–4. http://dx.doi.org/10.1017/jfm.2018.536.
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The flow of liquids through paper is challenging to model due to the complexity and disordered layout of the fibre matrix. The expanding use and capability of microfluidic paper-based analytical devices ($\unicode[STIX]{x1D707}$PADs) and their requirement for precision has increased the need to accurately predict the flow of liquids through paper. Many studies have developed models and revealed some of the physical mechanisms responsible for the flow behaviour, but we still lack a complete understanding, particularly in relation to how the fluid fills the various voids with a wide range of shapes and sizes in the fibre matrix of paper. In the featured article, Chang et al. (J. Fluid Mech., vol. 845, 2018, 36–50) used a combined experimental and theoretical approach to uncover the importance of the liquid filling the intra-fibre pores, showed that this results in deviation from the flow behaviour predicted by the Lucas–Washburn equation and developed a model which accounts for this effect.
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Bogoyavlenskiy, Vladislav A., Andrew C. Giamis, and Eric J. Cotts. "Mean-field dynamics of free surface flows through obstacle arrays in a narrow passage: amendments of the Washburn model." Fluid Dynamics Research 35, no. 1 (July 2004): 23–35. http://dx.doi.org/10.1016/j.fluiddyn.2004.04.001.
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Obryk, M. K., P. T. Doran, E. D. Waddington, and C. P. Mckay. "The influence of föhn winds on Glacial Lake Washburn and palaeotemperatures in the McMurdo Dry Valleys, Antarctica, during the Last Glacial Maximum." Antarctic Science 29, no. 5 (March 17, 2017): 457–67. http://dx.doi.org/10.1017/s0954102017000062.
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AbstractLarge glacial lakes, including Glacial Lake Washburn, were present in the McMurdo Dry Valleys, Antarctica, during the Last Glacial Maximum (LGM) despite a colder and drier climate. To address the mechanism capable of generating enough meltwater to sustain these large lakes, a conceptual model was developed based on the warming potential of infrequent contemporary föhn winds. The model suggests that föhn winds were capable of generating enough meltwater to sustain large glacial lakes during the LGM by increasing degree days above freezing (DDAF) and prolonging the melt season. A present-day relationship between infrequent summer föhn winds and DDAF was established. It is assumed that the Taylor Dome ice core record represents large-scale palaeoclimatic variations for the McMurdo Dry Valleys region. This analysis suggests that because of the warming influence of the more frequent föhn winds, summer DDAF in the McMurdo Dry Valleys during the LGM were equivalent to present-day values, but this enhanced summer signal is not preserved in the annually averaged ice core temperature record.
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Song, Kui, Ruijie Huang, and Xiaoling Hu. "Imbibition of Newtonian Fluids in Paper-like Materials with the Infinitesimal Control Volume Method." Micromachines 12, no. 11 (November 12, 2021): 1391. http://dx.doi.org/10.3390/mi12111391.
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Paper-based microfluidic devices are widely used in point-of-care testing applications. Imbibition study of paper porous media is important for fluid controlling, and then significant to the applications of paper-based microfluidic devices. Here we propose an analytical approach based on the infinitesimal control volume method to study the imbibition of Newtonian fluids in commonly used paper-like materials. Three common paper shapes (rectangular paper strips, fan-shaped and circular paper sheets) are investigated with three modeling methods (corresponding to equivalent tiny pores with circle, square and regular triangle cross section respectively). A model is derived for liquid imbibition in rectangular paper strips, and the control equations for liquid imbibition in fan-shaped and circular paper sheets are also derived. The model is verified by imbibition experiments done using the mixed cellulose ester filter paper and pure water. The relation of imbibition distance and time is similar to that of the Lucas−Washburn (L−W) model. In addition, a new porosity measurement method based on the imbibition in circular paper sheets is proposed and verified. Finally, the flow rates are investigated. This study can provide guidance for the design of different shapes of paper, and for better applications of paper-based microfluidic devices.
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Huang, X. B., X. X.W., J. J. Song, C. G. Bai, R. D. Zhang, and M. J. Zhou. "Contact angle of water on iron ore fines: Measurement and analysis." Journal of Mining and Metallurgy, Section B: Metallurgy 51, no. 1 (2015): 33–40. http://dx.doi.org/10.2298/jmmb140903010h.
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The relative contact angle (?RCA) for seven iron ore fines was measured by using Washburn Osmotic Pressure method under laboratory conditions. By choosing cyclohexane as the reference that can perfectly wet iron ore particles, the relative contact angles were measured and varied from 57? to 73?. With the volume % of goethite (?G) as the variable, a new model for relative contact angle was developed. The expected relative contact angle for pure goethite is about 56?, while that for goethite free samples is about 77?. Physical properties, such as surface morphology (SMI) and pore volume (Vpore) can influence the relative contact angle. The ?G can be expressed as a function of SMI and VPore. Thus, we inferred that the relative contact angle is a function of ?G for the iron ores used. The measured relative contact angles were found to be in good agreement (Radj 2 >0.97) with the calculated ones based on the research from Iveson, et al. (2004). Comparing with the model developed by Iveson et al.(2004), the new model for contact angle proposed in this paper is similar, but more detailed with two meaningful physical parameters. The modification of physicochemical properties on iron ores would be another topic in the further study on granulation.
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Ghillani, Noemi, Michael Heinz, and Tatiana Gambaryan-Roisman. "Capillary rise and evaporation of a liquid in a corner between a plane and a cylinder: A model of imbibition into a nanofiber mat coating." European Physical Journal Special Topics 229, no. 10 (September 2020): 1799–818. http://dx.doi.org/10.1140/epjst/e2020-000011-y.
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Abstract Wetting of surfaces with porous coating is relevant for a wide variety of technical applications, such as printing technologies and heat transfer enhancement. Imbibition and evaporation of liquids on surfaces covered with porous layers are responsible for significant improvement of cooling efficiency during drop impact cooling and flow boiling on such surfaces. Up to now, no reliable model exists which is able to predict the kinetics of imbibition coupled with evaporation on surfaces with porous coatings. In this work, we consider one of possible mechanisms of imbibition on a substrate covered by a nanofiber mat. This is the capillary pressure-driven flow in a corner formed between a flat substrate and a fiber attached to it. The shape and the area of the cross-section occupied by the liquid as well as the capillary pressure change along the flow direction. A theoretical/numerical model of simultaneous imbibition and evaporation is developed, in which viscosity, surface tension and evaporation are taken into account. At the beginning of the process the imbibition length is proportional to the square root of time, in agreement with the Lucas-Washburn law. As the influence of evaporation becomes significant, the imbibition rate decreases. The model predictions are compared with experimental data for imbibition of water-ethanol mixtures into nanofiber mat coatings.
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Kumar, Ashutosh, Hojat Heidari-Bafroui, Nassim Rahmani, Constantine Anagnostopoulos, and Mohammad Faghri. "Modeling of Paper-Based Bi-Material Cantilever Actuator for Microfluidic Biosensors." Biosensors 13, no. 6 (May 26, 2023): 580. http://dx.doi.org/10.3390/bios13060580.
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This research explores the dynamics of a fluidically loaded Bi-Material cantilever (B-MaC), a critical component of μPADs (microfluidic paper-based analytical devices) used in point-of-care diagnostics. Constructed from Scotch Tape and Whatman Grade 41 filter paper strips, the B-MaC’s behavior under fluid imbibition is examined. A capillary fluid flow model is formulated for the B-MaC, adhering to the Lucas–Washburn (LW) equation, and supported by empirical data. This paper further investigates the stress–strain relationship to estimate the modulus of the B-MaC at various saturation levels and to predict the behavior of the fluidically loaded cantilever. The study shows that the Young’s modulus of Whatman Grade 41 filter paper drastically decreases to approximately 20 MPa (about 7% of its dry-state value) upon full saturation. This significant decrease in flexural rigidity, in conjunction with the hygroexpansive strain and coefficient of hygroexpansion (empirically deduced to be 0.008), is essential in determining the B-MaC’s deflection. The proposed moderate deflection formulation effectively predicts the B-MaC’s behavior under fluidic loading, emphasizing the measurement of maximum (tip) deflection using interfacial boundary conditions for the B-MaC’s wet and dry regions. This knowledge of tip deflection will prove instrumental in optimizing the design parameters of B-MaCs.
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Mahdhi, Noureddine, Norah Salem Alsaiari, Abdelfattah Amari, and Mohamed Ali Chakhoum. "Effect of TiO2 Nanoparticles on Capillary-Driven Flow in Water Nanofilters Based on Chitosan Cellulose and Polyvinylidene Fluoride Nanocomposites: A Theoretical Study." Polymers 14, no. 14 (July 17, 2022): 2908. http://dx.doi.org/10.3390/polym14142908.
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In this study, a novel concept of nanofiltration process of drinking water based on capillary-driven nanofiltration is demonstrated using a bio-based nanocomposites’ nanofilter as free power: a green and sustainable solution. Based on Lifshitz and Young–Laplace theories, we show that the chitosan (CS), cellulose acetate (CLA), and Polyvinylidene fluoride (PVDF) polymer matrixes demonstrate hydrophobic behavior, which leads to the draining of water from nanopores when negative capillary pressure is applied and consequently prevents the capillary-driven nanofiltration process. By incorporating 10%, 20%, and 30% volume fraction of titanium dioxide (TiO2) nanoparticles (NPs) to the polymers’ matrixes, we demonstrate a wetting conversion from hydrophobic to hydrophilic behavior of these polymer nanocomposites. Subsequently, the threshold volume fraction of the TiO2 NPs for the conversion from draining (hydrophobic) to filling (hydrophilic) by capillary pressure were found to be equal to 5.1%, 10.9%, and 13.9%, respectively, for CS/TiO2, CLA/TiO2, and PVDF/TiO2 nanocomposites. Then, we demonstrated the negligible effect of the gravity force on capillary rise as well as the capillary-driven flow for nanoscale pore size. For nanofilters with the same effective nanopore radius, porosity, pore shape factor, and tortuosity, results from the modified Lucas–Washburn model show that the capillary rise as well as the capillary-driven water volume increase with increased volume fraction of the TiO2 NPs for all nanocomposite nanofilter. Interestingly, the capillary-driven water volume was in range (5.26–6.39) L/h·m2 with 30% volume fraction of TiO2 NPs, which support our idea for capillary-driven nanofiltration as zero energy consumption nano-filtration process. Correspondingly, the biodegradable CS/TiO2 and CLA/TiO2 nanocomposites nanofilter demonstrate capillary-driven water volume higher, ~1.5 and ~1.2 times, respectively, more than the synthetic PVDF/TiO2 nanocomposite.
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FEELEY, T. C., M. A. COSCA, and C. R. LINDSAY. "Petrogenesis and Implications of Calc-Alkaline Cryptic Hybrid Magmas from Washburn Volcano, Absaroka Volcanic Province, USA." Journal of Petrology 43, no. 4 (April 1, 2002): 663–703. http://dx.doi.org/10.1093/petrology/43.4.663.
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Abstract The petrogenesis of calc-alkaline magmatism in the Eocene Absaroka Volcanic Province (AVP) is investigated at Washburn volcano, a major eruptive center in the low-K western belt of the AVP. New 40Ar/39Ar age determinations indicate that magmatism at the volcano commenced as early as 55 Ma and continued until at least 52 Ma. Although mineral and whole-rock compositional data reflect near equilibrium crystallization of modal phenocrysts, petrogenetic modeling demonstrates that intermediate composition magmas are hybrids formed by mixing variably fractionated and contaminated mantle-derived melts and heterogeneous silicic crustal melts. Nd and Sr isotopic compositions along with trace element data indicate that silicic melts in the Washburn system are derived from deep-crustal rocks broadly similar in composition to granulite-facies xenoliths in the Wyoming Province. Our preferred explanation for these features is that mantle-derived basaltic magma intruded repeatedly in the deep continental crust leading to fractional crystallization, silicic melt production, and homogenization of magmas, followed by ascent to shallow reservoirs and crystallization of new plagioclase-rich mineral assemblages in equilibrium with the intermediate hybrid liquids. The implications of this process are that (1) some calc-alkaline magmas may only be recognized as hybrids on purely chemical grounds, particularly in systems where mixing precedes and is widely separated from crystallization in space and time, and (2) given the role ascribed to crustal processes at Washburn volcano, the variation between rocks that follow calc-alkaline trends in the western AVP and those that follow shoshonitic trends in the east cannot simply reflect higher pressures of fractionation to the east in Moho-level magma chambers in the absence of crustal interaction.
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Koplik, J., and T. J. Lasseter. "Two-Phase Flow in Random Network Models of Porous Media." Society of Petroleum Engineers Journal 25, no. 01 (February 1, 1985): 89–100. http://dx.doi.org/10.2118/11014-pa.
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Abstract To explore how the microscopic geometry of a pore space affects the macroscopic characteristics of fluid flow in porous media, we have used approximate solutions of the porous media, we have used approximate solutions of the Navier-Stokes equations to calculate the flow of two fluids in random networks. The model pore space consists of an array of pores of variable radius connected to a random number of nearest neighbors by throats of variable length and radius. The various size and connectedness distributions may be arbitrarily assigned, as are the wetting characteristics of the two fluids in the pore space. The fluids are assumed to be incompressible, immiscible. Newtonian, and of equal viscosity. In the calculation, we use Stokes flow results for the motion of the individual fluids and incorporate microscopic capillary force by using the Washburn approximation. At any time, the problem is mathematically identical to a random electrical network of resistors, batteries, and diodes. From the numerical solution of the latter, we compute the fluid velocities and saturation rates of change and use a discrete timestepping procedure to follow the subsequent motion. The scale of the computation has restricted us so far to networks of hundreds of pores in two dimensions (2D). Within these limitations, we discuss the dependence of residual oil saturations and interface shapes on network geometry and flow conditions. Introduction A significant limitation to our understanding of the dynamics of multiphase fluids in porous media is the inability to connect the physics at the microscopic scale to the macroscopic phenomena observed in the laboratory and in the field. Within individual pores, the motion of fluids and menisci can be discussed, at least approximately, in terms of the microgeometry and the physical characteristics of the liquids. gases, and solids present. On the macroscopic scale, the multiphase Darcy equations involving several empirical parameters-relative permeabilities and average capillary pressures permeabilities and average capillary pressures conventionally are used. The connection between these two levels of description, if there is one, has never been elucidated despite years of effort (as reviewed by Scheidegger ). In consequence, it is difficult to predict the behavior of oil reservoirs in advance, and considerable waste of money, effort, and resources can ensue. Economic issues aside, this situation provides another example of a pervasive problem in physics: macroscopic averaging of a random problem in physics: macroscopic averaging of a random microscopically disordered medium to predict large-scale behavior from a knowledge of small-scale dynamics. In optimal circumstances, existing methods in the physics literature (i.e., Ziman ) can be used to carry out physics literature (i.e., Ziman ) can be used to carry out the averaging. For fluid problems, for example, percolation theory has been applied to the spatial distribution of percolation theory has been applied to the spatial distribution of fluids in a pore space, both in static situations and in quasistatic displacement. Another set of ideas, effective medium theories, has been applied to electrical conductivity and its fluid analog, absolute permeability. The general fluid displacement problem, when both permeability. The general fluid displacement problem, when both capillary and viscous forces are present, is related to a class of physics problems that are as yet unresolved, such as crystal growth, surface evolution, and dynamic percolation. In this situation, we are forced to resort to percolation. In this situation, we are forced to resort to brute-force numerical modeling, both as a means of obtaining statistical information and as a guide to approximations that may permit future analytical work. In this paper, we describe our initial efforts to calculate the motion of two fluids in porous media from the microscopic scale up, starting from the Stokes equations and boundary conditions in this pore space. As usual, we model the porous medium as a network of similarly shaped, but randomly sized, elements. The key to the calculation is the mathematical analogy between the fluid problem and an appropriate electrical network of random problem and an appropriate electrical network of random resistors, batteries, and diodes. The calculation is a very difficult one, numerically speaking, and to date we have been restricted to fairly small 2D networks of hundreds of pores. We expect, however, that with more sophisticated programming methods our approach can be applied to three-dimensional (3D) networks of thousands of pores. pores. After this work was in progress, we came across a paper of Singhal and Somerton where a similar calculational framework was used but with a different emphasis. Those authors considered a single realization of a small network of triangular channels of random sizes with flow regimes randomly assigned in each channel and compute the relative permeabilities and capillary pressure curves of the network. Our emphasis in this paper is on time-dependent phenomena and statistical averaging of flow quantities. We also note the somewhat related work by Payatakes et al., who considered a square lattice of Payatakes et al., who considered a square lattice of converging/diverging tubes meeting at point nodes and simulate the dislodgement of blobs of trapped oil. Subsequently, Dias and Payatakes used the same geometry and calculational rules similar to those employed here to study fluid displacement. SPEJ P. 89
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Dias, Madalena M., and Alkiviades C. Payatakes. "Network models for two-phase flow in porous media Part 2. Motion of oil ganglia." Journal of Fluid Mechanics 164 (March 1986): 337–58. http://dx.doi.org/10.1017/s0022112086002586.
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The behaviour of non-wetting ganglia undergoing immiscible displacement in a porous medium is studied with the help of a theoretical simulator. The porous medium is represented by a network of randomly sized unit cells of the constricted-tube type. The fluid of a non-wetting ganglion is in contact with the wetting fluid at menisci which are assumed to be spherical cups. The flow in every constricted unit cell occupied by a single fluid is modelled as flow in a sinusoidal tube. The flow in every unit cell that contains a meniscus and portions of both fluids is treated with a combination of a Washburn-type analysis and a lubrication-theory approximation. The flow problem is thus reduced to a system of linear equations the solution of which gives the instantaneous pressures on the nodes, the flowrates through the unit cells, and the velocities of the menisci. The motion of a ganglion is determined by assuming quasi-static flow, taking a small time increment, updating the positions of the menisci, and iterating. The behaviour of solitary ganglia is studied under conditions of quasi-static displacement (Ca slightly larger than critical), as well as dynamic displacement (Ca substantially larger than critical). Shape evolution, rate of flow, mode of break-up, and stranding are examined. The stranding and break-up coefficients are determined as functions of the capillary number and the ganglion size for a 100 × 200 sandpack. The dependence of the average ganglion velocity on ganglion size, capillary number, viscosity ratio and dynamic contact angle is examined for the simple case of motion between straight rows of spheres. It is found, among other things, that when μo < μw the velocity of ganglia can be substantially larger than that of the displacing fluid.
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Shishatsky, J. I., A. M. Barbashin, and S. A. Nickel. "Development of mathematical model of extraction from lupine with cheese serum by applying low-frequency mechanical vibrations." Proceedings of the Voronezh State University of Engineering Technologies 81, no. 1 (July 18, 2019): 36–41. http://dx.doi.org/10.20914/2310-1202-2019-1-36-41.
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It is noted that the model is designed to create the largest possible pressure change in the cheese whey in the extractor, since the rate of transfer of the target components is proportional to the pressure difference at the ends of the capillaries. The mathematical description of impregnation as the main or important auxiliary operation is given in detail. The equations for the impregnated part of the capillary, the ratio of impregnation rates at different times are given. From the above dependencies, the equation Washburne regarding the time of impregnation. The formulas for calculating the volume of extractant passed through the capillary, serum and forced out of the capillary air taking into account the viscous resistance of the latter. After integration of the equation of the speed of capillary impregnation of the obtained expression allows to estimate the final value of the impregnation in the initial stage. For different cases of capillary impregnation expressions are written at atmospheric pressure, vacuuming and overpressure. The introduction of dimensionless values allowed to simplify the solution and to obtain an expression for calculating the time of pore impregnation. The analysis of the equation of dimensionless impregnation time taking into account the application of low-frequency mechanical vibrations is made. It is noted that the processes of impregnation and extraction occur simultaneously, so the impregnation time is often neglected, which impoverishes the understanding of the physics of the process, reduces the accuracy of the calculation. Taking into account the diffusion unsteadiness of the process of substance transfer due to hydrodynamic unsteadiness, the equation containing the effective diffusion coefficient is written. The equation of unsteady diffusion for a spherical lupine particle in a batch extractor is supplemented with initial and boundary conditions. Taking into account the balance equation, the kinetic equation of the process is obtained. We studied the distribution of pores in the particle lupine along the radii and squares, the calculated value of the porosity of the particle. The values of De and Bi are determined by the method of graphical solution of the balance equation, the equation of kinetics and the parameters included in these equations. Conclusions on the work.
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Schnell, D. J., and G. Blobel. "Identification of intermediates in the pathway of protein import into chloroplasts and their localization to envelope contact sites." Journal of Cell Biology 120, no. 1 (January 1, 1993): 103–15. http://dx.doi.org/10.1083/jcb.120.1.103.
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We have used a hybrid precursor protein to study the pathway of protein import into chloroplasts. This hybrid (pS/protA) consists of the precursor to the small subunit of Rubisco (pS) fused to the IgG binding domains of staphylococcal protein A. The pS/protA is efficiently imported into isolated chloroplasts and is processed to its mature form (S/protA). In addition to the mature stromal form, two intermediates in the pathway of pS/protA import were identified at early time points in the import reaction. The first intermediate represents unprocessed pS/protA bound to the outer surface of the chloroplast envelope and is analogous to a previously characterized form of pS that is specifically bound to the chloroplast surface and can be subsequently translocated in the stroma (Cline, K., M. Werner-Washburne, T. H. Lubben, and K. Keegstra. 1985. J. Biol. Chem. 260:3691-3696.) The second intermediate represents a partially translocated form of the precursor that remains associated with the envelope membrane. This form is processed to mature S/protA, but remains susceptible to exogenously added protease in intact chloroplasts. We conclude that the envelope associated S/protA is spanning both the outer and inner chloroplast membranes en route to the stroma. Biochemical and immunochemical localization of the two translocation intermediates indicates that both forms are exposed at the surface of the outer membrane at sites where the outer and inner membrane are closely apposed. These contact zones appear to be organized in a reticular network on the outer envelope. We propose a model for protein import into chloroplasts that has as its central features two distinct protein conducting channels in the outer and inner envelope membranes, each gated open by a distinct subdomain of the pS signal sequence.
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Li, P. C., G. L. Lehmann, J. Cascio, T. Driscoll, Y. J. Huang, and E. J. Cotts. "Underflow Process for Direct-Chip-Attachment Packaging." MRS Proceedings 515 (1998). http://dx.doi.org/10.1557/proc-515-117.
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ABSTRACTIn flip-chip packaging an underfill mixture is placed into the chip-to-substrate standoff created by the array of solder bumps, using a capillary flow process. The flow behavior is a complex function of the mixture properties, the wetting properties, and the flow geometry. This paper reports on the use of a plane channel capillary flow to characterize underfill materials. The measured flow behavior provides evidence that both the contact angle (θ) and the suspension viscosity (μapp) vary with time under the Influence of changing flow conditions. This nonlinear fluid behavior is modeled for the flow of both model suspensions and commercial underfill materials using an extended Washburn model.
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Philip, Jeffy John, Joydeb Mukherjee, Sandip Sarkar, and Sandip K. Saha. "Capillary Filling Dynamics of Electromagnetohydrodynamic Flow of Non-Newtonian Fluids." Journal of Fluids Engineering 142, no. 4 (January 24, 2020). http://dx.doi.org/10.1115/1.4045210.
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Abstract In this work, we aim to develop a mathematical model for capillary filling dynamics of electromagnetohydrodynamic flow of non-Newtonian fluids. An axially applied electric field and a transverse magnetic field are considered to elucidate the electromagnetohydrodynamic transport through the microcapillary. Assuming a non-Newtonian power-law obeying fluids, we analyze the transient evolution of the electromagnetohydrodynamic capillary positions by considering the magnitude of the total force balance via finite volume-based numerical formalism. We have highlighted the various rheological regimes in the horizontal capillary through a scaling analysis. For the Newtonian fluids, corresponding inviscid linear Washburn regime is also analyzed and compared with the power-law obeying fluids. Furthermore, we have also derived closed-form analytical expressions for the electromagnetohydrodynamic velocity, pressure gradient, and transient evolution of the capillary positions by using couple stress parameter model to characterize the fluid rheological behaviors. We perform a comparison test of the coupled stress parameter model with the results from the literature for a similar set of fluid rheological parameters. The comparison results are found to be in good agreement.
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Perré, Patrick, Dang Mao Nguyen, and Giana Almeida. "A macroscopic Washburn approach of liquid imbibition in wood derived from X-ray tomography observations." Scientific Reports 12, no. 1 (February 2, 2022). http://dx.doi.org/10.1038/s41598-022-05508-0.
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AbstractImbibition of water and silicone oil in poplar and spruce is investigated at the anatomical level by X-ray tomography observations and at the macroscopic level by imbibition kinetics. Imbibition mechanisms depend on both liquid and species. In poplar, oil penetrates vessels with a small contact angle, consistent with the value measured on solid wood (ca. $$20^{\circ }$$ 20 ∘ ). Surprisingly, no direct penetration of water was observed in vessels. The large contact angle for water blocks the capillary rise at the scars between vessel cells. In spruce, oil and water penetrate primarily in latewood, where bordered pits remain open. Subsequently, water slowly invades the rest of the growth ring, while transversal migration is quasi-absent for oil. These 3D observations were quantified to feed a simple imbibition model that satisfactorily simulates macroscopic imbibition kinetics. A 1D approach is sufficient for oil imbibition while a 2D approach is required for water, revealing dual scale effects.
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Danielik, Vladimír, Milan Králik, Marta Ambrová, Jana Jurišová, Michal Jablonský, Katarína Vizárová, and Izabela Vajová. "Two level deacidification mathematical model for the description of transport of solid alkaline particles and diffusion of ions in a treated acid paper." Cellulose, May 11, 2023. http://dx.doi.org/10.1007/s10570-023-05225-5.
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AbstractIndustrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO4)2) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper.
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Wang, Mingcan, Weijun Shen, Tianran Ma, Zhi Zeng, and Fengchang Yang. "Mechanisms of the imbibition behavior in shales: A critical review." AIP Advances 13, no. 8 (August 1, 2023). http://dx.doi.org/10.1063/5.0161989.
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Despite the success of hydraulic fracturing in yielding large production increases from shale gas reservoirs, uncertainties associated with basic transport processes require understanding in order to improve the efficiency and minimize environmental impacts. The hydraulic fracturing process brings in large volumes of water into shale reservoir formations, most of which remains unrecoverable and interferes with shale gas production. The imbibition behavior in shales is commonly observed during the hydraulic fracturing process, and the mechanism greatly influences the hydrocarbon recovery in shale gas reservoirs. In this review, the imbibition models in shales are briefly summarized using the Lucas–Washburn model, piston repulsion model, capillary bundle model, and scalar model. Then the experimental study and numerical simulation of shale imbibition are discussed. Moreover, the influencing factors of the imbibition behavior in shales are analyzed, such as shale and fluid properties. Finally, the main conclusions and the future research direction prospects of the imbibition behavior in shale gas reservoirs are summarized. An accurate description of the imbibition behavior in shale is crucial for optimizing the hydraulic fracturing design and enhancing shale gas production in the development of shale gas reservoirs. It is proposed that the research on the individual influencing factors of shale percolation and the geological mechanism under coupling should be strengthened and that the research on the experimental aspects of shale powder percolation should be emphasized.
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Mortimer, Patrick K., and Andrew W. Woods. "Immiscible capillary flows in non-uniform channels." Journal of Fluid Mechanics 925 (August 26, 2021). http://dx.doi.org/10.1017/jfm.2021.693.
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We consider the release of preferentially wetting fluid in a laterally extensive V-shaped channel initially filled with a second fluid, presenting solutions for the initial exchange flow and the late time spreading of the wetting fluid along the narrow part of the channel. We also show that, if there is a buoyancy force acting in the cross-channel direction, the early time exchange flow depends on the Bond number, and the intermediate time slumping flow may initially be dominated by buoyancy, but at long times becomes controlled by capillarity. Where there is an along-channel component of gravity we show that the flow spreads out downslope, with capillarity controlling the structure of the nose. We then consider the case where the channel is connected to a reservoir of wetting fluid at constant pressure. We show that, depending on this pressure, either a zero flux exchange flow develops, or a net inflow through the whole width of the channel develops, as in the classical Washburn, Lucas, Bell and Cameron capillary imbibition flow. We show these flows are analogous to the classical model for one-dimensional capillary driven flows in porous media, with the current width in the channel corresponding to the saturation in the pore space.
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Helbrecht, Christiane, Markus Langhans, Tobias Meckel, Markus Biesalski, and Samuel Schabel. "Analyses of the effects of fiber diameter, fiber fibrillation, and fines content on the pore structure and capillary flow using laboratory sheets of regenerated fibers." Nordic Pulp & Paper Research Journal, July 19, 2023. http://dx.doi.org/10.1515/npprj-2022-0077.
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Abstract The aim of this work is to investigate the influence of fiber fibrillation and fines on the pore structure of well-defined regenerated fiber sheets as well as the water flow through the sheet. For this purpose, sheets were produced with refined, fibrillated fibers only, with unfibrillated fibers and fines, as well as with fibrillated fibers and fines. Next, the samples were analyzed by brightfield and fluorescence microscopy, mercury porosimetry, and an ascending test. Both the fibrils and the added fines reach into the pores between the fibers or are deposited there. As a result, pore size decreases and capillary flow slows down. The two effects overlap when the fiber surface is fibrillated and fines are present. Sheets with thicker fibers form a pore structure with larger pores in between the fibers. However, such a change in pore size has no significant influence on the flow of water through the sheet in the performed ascending tests. It is shown that a statistical model with the parameters fibrillation and fines content can be used to describe the ascending rate nearly as well as the Lucas–Washburn equation. Consequently, the equation could be improved by the addition of further fiber and sheet properties.
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Shiri, Yousef, and Seyed Mohammad Javad Seyed Sabour. "Analytical, Experimental, and Numerical Study of Capillary Rise Dynamics from Inertial to Viscous Flow." Physics of Fluids, September 7, 2022. http://dx.doi.org/10.1063/5.0111688.
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Fundamental understanding of capillary rise dynamics and precise evaluation of imbibition processes should be considered in many natural and industrial phenomena. The assumptions considered to solve the capillary rise motion usually neglect specific forces which limit the reliability of the derived solutions. In the present study, the dominant forces and regimes involved in the initial moments of the capillary rise imbibition process in a tube were investigated analytically, experimentally, and numerically. Analytical solutions available in the literature were discussed, and then, their validity was verified by comparing them to the experimental observations and numerical results. Comparing the capillary rise behavior at the initial stages revealed significant differences between the theoretical models and the numerical lattice Boltzmann method. This behavior is attributed to simplifying assumptions and ignoring the entrance effect, dynamic contact angle, and the inertial term in the theoretical model. By removing these assumptions in numerical formulations, closer results to the experimental records were observed. In the present study, for the first time, capillary rise dynamics were divided into five steps: (1) transition regime with h~t2; (2) purely inertial (stage one) with h~t; (3) viscous-inertial or crossover (stage two) with h~log10(t); (4) purely viscous (stage three) with h~t1/2; and (5) gravitational-viscous with a constant h. It was known that stage one was purely dominated by the inertial forces, then the influence of viscosity increased (viscous-inertial flow), and finally, the effect of inertia faded and the flow became purely viscous and approached the Lucas-Washburn law.
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Li, Haidong, Fuming Chen, Haitao Cheng, Jianchao Deng, Ge Wang, and Fengbo Sun. "Large-span Bamboo Fiber-based Composites, Part I: A Prediction Model based on the Lucas-Washburn Equation Describing the Resin Content of Bamboo Fiber Impregnated with Different PVAC/PF Concentrations." BioResources 9, no. 4 (September 8, 2014). http://dx.doi.org/10.15376/biores.9.4.6408-6419.
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R. L. Dodge, M. L. Keeling, D. H. C. "Washburne Anticline Delta Structure: Model Based on Integration of Thematic Mapper, Seismic, and Well-Log Data: ABSTRACT." AAPG Bulletin 73 (1989). http://dx.doi.org/10.1306/703c9dbb-1707-11d7-8645000102c1865d.
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Van Toan, Dinh. "Development of Enterprises in Universities and Policy Implications for University Governance Reform in Vietnam." VNU Journal of Science: Economics and Business 35, no. 1 (March 22, 2019). http://dx.doi.org/10.25073/2588-1108/vnueab.4201.
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The article focuses on analyzing the content and relationship between the development of enterprises, enterprise-university models and governance in higher education institutions, thereby providing policy recommendations on innovation in university governance in Vietnam. In the article, documents from internationally published researches as well as arguments on the mentioned subjects are analyzed and synthesized. Results of surveys and analysis on the status of universities in Vietnam that are presented in the article also demonstrate a detailed picture of difficulties and issues in enterprise development and transition into enterprise-university model. On this basis, the article provides recommendations for universities and on the issues that require government’s intervention through supportive policies and mechanisms to accelerate the process of university governance reform in the current period of 4.0 revolution in university education.
Keywords
Higher education institutions, Developing enterprise in universities, University-enterprise model, University governance
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