Journal articles: 'Capillary number'

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Guo, Hu, Ma Dou, Wang Hanqing, Fuyong Wang, Gu Yuanyuan, Zhaoyan Yu, Wang Yansheng, and Yiqiang Li. "Proper Use of Capillary Number in Chemical Flooding." Journal of Chemistry 2017 (2017): 1–11. http://dx.doi.org/10.1155/2017/4307368.

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Capillary number theory is very important for chemical flooding enhanced oil recovery. The difference between microscopic capillary number and the microscopic one is easy to confuse. After decades of development, great progress has been made in capillary number theory and it has important but sometimes incorrect application in EOR. The capillary number theory was based on capillary tube bundles and Darcy’s law hypothesis, and this should always be kept in mind when used in chemical flooding EOR. The flow in low permeability porous media often shows obvious non-Darcy effects, which is beyond Darcy’s law. Experiments data from ASP flooding and SP flooding showed that remaining oil saturation was not always decreasing as capillary number kept on increasing. Relative permeability was proved function of capillary number; its rate dependence was affected by capillary end effects. The mobility control should be given priority rather than lowering IFT. The displacement efficiency was not increased as displacement velocity increased as expected in heavy oil chemical flooding. Largest capillary number does not always make highest recovery in chemical flooding in heterogeneous reservoir. Misuse of CDC in EOR included the ignorance of mobility ratio, Darcy linear flow hypothesis, difference between microscopic capillary number and the microscopic one, and heterogeneity caused flow regime alteration. Displacement of continuous oil or remobilization of discontinuous oil was quite different.

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Willführ, Alper, Christina Brandenberger, Tanja Piatkowski, Roman Grothausmann, Jens Randel Nyengaard, Matthias Ochs, and Christian Mühlfeld. "Estimation of the number of alveolar capillaries by the Euler number (Euler-Poincaré characteristic)." American Journal of Physiology-Lung Cellular and Molecular Physiology 309, no. 11 (December 1, 2015): L1286—L1293. http://dx.doi.org/10.1152/ajplung.00410.2014.

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The lung parenchyma provides a maximal surface area of blood-containing capillaries that are in close contact with a large surface area of the air-containing alveoli. Volume and surface area of capillaries are the classic stereological parameters to characterize the alveolar capillary network (ACN) and have provided essential structure-function information of the lung. When loss (rarefaction) or gain (angiogenesis) of capillaries occurs, these parameters may not be sufficient to provide mechanistic insight. Therefore, it would be desirable to estimate the number of capillaries, as it contains more distinct and mechanistically oriented information. Here, we present a new stereological method to estimate the number of capillary loops in the ACN. One advantage of this method is that it is independent of the shape, size, or distribution of the capillaries. We used consecutive, 1 μm-thick sections from epoxy resin-embedded material as a physical disector. The Euler-Poincaré characteristic of capillary networks can be estimated by counting the easily recognizable topological constellations of “islands,” “bridges,” and “holes.” The total number of capillary loops in the ACN can then be calculated from the Euler-Poincaré characteristic. With the use of the established estimator of alveolar number, it is possible to obtain the mean number of capillary loops per alveolus. In conclusion, estimation of alveolar capillaries by design-based stereology is an efficient and unbiased method to characterize the ACN and may be particularly useful for studies on emphysema, pulmonary hypertension, or lung development.

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Zhang, Yan, Min Zhang, and Shujuan Qi. "Heat and Mass Transfer in a Thin Liquid Film over an Unsteady Stretching Surface in the Presence of Thermosolutal Capillarity and Variable Magnetic Field." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/8521580.

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The heat and mass transfer characteristics of a liquid film which contain thermosolutal capillarity and a variable magnetic field over an unsteady stretching sheet have been investigated. The governing equations for momentum, energy, and concentration are established and transformed to a set of coupled ordinary equations with the aid of similarity transformation. The analytical solutions are obtained using the double-parameter transformation perturbation expansion method. The effects of various relevant parameters such as unsteady parameter, Prandtl number, Schmidt number, thermocapillary number, and solutal capillary number on the velocity, temperature, and concentration fields are discussed and presented graphically. Results show that increasing values of thermocapillary number and solutal capillary number both lead to a decrease in the temperature and concentration fields. Furthermore, the influences of thermocapillary number on various fields are more remarkable in comparison to the solutal capillary number.

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Canbazoğlu, Suat, and Fazıl Canbulut. "A note on the flow coefficients of capillary tube and small orifice restrictors exposed to very low Reynolds number flow." Industrial Lubrication and Tribology 57, no. 3 (June 1, 2005): 116–20. http://dx.doi.org/10.1108/00368790510595084.

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PurposeThe main objective of this study was to obtain the flow restricting capacity by determining their flow coefficients and to investigate the unsteady flow with low Reynolds number in the flow‐restricting devices such as orifices and capillary tubes having small diameters.Design/methodology/approachThere is an enormous literature on the flow of Newtonian fluids through capillaries and orifices particularly in many application fields of the mechanical and chemical engineering. But most of the experimental results in literature are given for steady flows at moderate and high Reynolds numbers (Re>500). In this study, the unsteady flow at low Reynolds number (10<Re<650) through flow‐restricting devices such as orifices and capillary tubes having very small diameters between 0.35 and 0.70 mm were experimentally investigated.FindingsThe capillary tubes have much more capillarity property with respect to equal diameter orifices. Increasing the ratio of capillary tube length to tube diameter and decreasing the ratio of orifice diameter to pipe diameter before orifice increase the throttling or restricting property of the orifices and the capillary tubes. The orifices can be preferred to the capillary tubes having the same diameter at the same system pressure for the hydraulic systems or circuits requiring small velocity variations. The capillary tubes provide higher pressure losses and they can be also used as hydraulic accumulators in hydraulic control devices to attenuate flow‐induced vibrations because of their large pressure coefficients. An important feature of the results obtained for capillary tubes and small orifices is that as the d/D for orifices increases and the L/d reduces for capillary tubes, higher values C are obtained and the transition from viscous to inertia‐controlled flow appears to take place at lower Reynolds numbers. This may be explained by the fact that for small orifices with high d/D ratios and for capillary tubes with small L/d ratios, the losses due to viscous shear are small. Another important feature of the results is that the least variations in C for small orifices and the higher variations in C for capillary tubes occur when the d/D and L/d ratios are smallest. This has favourable implications in hydraulic control devices since a constant value for the C may be assumed even at relatively low values of Re.Originality/valueTo the authors' knowledge, there is not enough information in the literature about the flow coefficients of unsteady flows through capillary tubes and small orifices at low Reynolds numbers. This paper fulfils this gap.

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Truby, J. M., S. P. Mueller, E. W. Llewellin, and H. M. Mader. "The rheology of three-phase suspensions at low bubble capillary number." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2173 (January 2015): 20140557. http://dx.doi.org/10.1098/rspa.2014.0557.

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We develop a model for the rheology of a three-phase suspension of bubbles and particles in a Newtonian liquid undergoing steady flow. We adopt an ‘effective-medium’ approach in which the bubbly liquid is treated as a continuous medium which suspends the particles. The resulting three-phase model combines separate two-phase models for bubble suspension rheology and particle suspension rheology, which are taken from the literature. The model is validated against new experimental data for three-phase suspensions of bubbles and spherical particles, collected in the low bubble capillary number regime. Good agreement is found across the experimental range of particle volume fraction ( 0 ≤ ϕ p ≲ 0.5 ) and bubble volume fraction ( 0 ≤ ϕ b ≲ 0.3 ). Consistent with model predictions, experimental results demonstrate that adding bubbles to a dilute particle suspension at low capillarity increases its viscosity, while adding bubbles to a concentrated particle suspension decreases its viscosity. The model accounts for particle anisometry and is easily extended to account for variable capillarity, but has not been experimentally validated for these cases.

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Hawkes, Elizabeth D., and James E. Neffendorf. "Kestenbaum׳s capillary number test - A forgotten sign?" Multiple Sclerosis and Related Disorders 3, no. 6 (November 2014): 735–37. http://dx.doi.org/10.1016/j.msard.2014.09.087.

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Kutter, Bruce L. "Effects of capillary number, Bond number, and gas solubility on water saturation of sand specimens." Canadian Geotechnical Journal 50, no. 2 (February 2013): 133–44. http://dx.doi.org/10.1139/cgj-2011-0250.

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To better understand how to prepare completely water-saturated specimens or centrifuge models from dry sand, the mechanisms of the infiltration and filling of pores in sand are studied. Complete saturation has been shown by others to be especially important in studies involving the triggering of liquefaction. This paper discusses how the degree of saturation obtained during infiltration increases with the “Bond number”, Bo (ratio of body forces and capillary forces), and the “capillary number”, Ca (ratio of viscous forces and capillary forces), as well as the solubility of gas bubbles in the pore fluid. Bo is varied by changing the particle size, fluid density, and centrifugal acceleration. Ca is varied by changing the fluid viscosity and infiltration rate. The dissolution of gas is encouraged by replacing pore air by CO2 (56 times more soluble in water than N2), by de-airing the liquid prior to infiltration or by increasing the pore fluid pressure after infiltration. Infiltration experiments performed at 1g and in a centrifuge are presented. A new technique for measuring the degree of saturation is also presented. Quantitative pressure–saturation relations are presented for different gasses, illustrating the importance of replacement of air by CO2. Spinning a specimen in a centrifuge during infiltration is also useful for speeding up the saturation process and for achieving higher degrees of saturation.

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8

Jansons, Kalvis M. "Moving contact lines at non-zero capillary number." Journal of Fluid Mechanics 167, no. -1 (June 1986): 393. http://dx.doi.org/10.1017/s0022112086002860.

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Al-Fossail, Khalid, and Lyman L. Handy. "Correlation between capillary number and residual water saturation." Journal of Colloid and Interface Science 134, no. 1 (January 1990): 256–63. http://dx.doi.org/10.1016/0021-9797(90)90273-q.

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Zhu, L., E. Lauga, and L. Brandt. "Low-Reynolds-number swimming in a capillary tube." Journal of Fluid Mechanics 726 (May 31, 2013): 285–311. http://dx.doi.org/10.1017/jfm.2013.225.

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AbstractWe use the boundary element method to study the low-Reynolds-number locomotion of a spherical model microorganism in a circular tube. The swimmer propels itself by tangential or normal surface motion in a tube whose radius is of the order of the swimmer size. Hydrodynamic interactions with the tube walls significantly affect the average swimming speed and power consumption of the model microorganism. In the case of swimming parallel to the tube axis, the locomotion speed is always reduced (respectively, increased) for swimmers with tangential (respectively, normal) deformation. In all cases, the rate of work necessary for swimming is increased by confinement. Swimmers with no force dipoles in the far field generally follow helical trajectories, solely induced by hydrodynamic interactions with the tube walls, and in qualitative agreement with recent experimental observations for Paramecium. Swimmers of the puller type always display stable locomotion at a location which depends on the strength of their force dipoles: swimmers with weak dipoles (small $\alpha $) swim in the centre of the tube while those with strong dipoles (large $\alpha $) swim near the walls. In contrast, pusher swimmers and those employing normal deformation are unstable and end up crashing into the walls of the tube. Similar dynamics is observed for swimming into a curved tube. These results could be relevant for the future design of artificial microswimmers in confined geometries.

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Seebergh, Jill E., and John C. Berg. "Dynamic wetting in the low capillary number regime." Chemical Engineering Science 47, no. 17-18 (December 1992): 4455–64. http://dx.doi.org/10.1016/0009-2509(92)85123-s.

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Salim, Thamir K. "The Effect of the Capillary Tube Coil Number on the Refrigeration System Performance." Tikrit Journal of Engineering Sciences 19, no. 2 (June 30, 2012): 18–29. http://dx.doi.org/10.25130/tjes.19.2.03.

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The capillary tube performance for (R134a) is experimentally investigated. The experimental setup is a real vapor compression refrigeration system. All properties of the refrigeration system are measured for various mass flow rate from (13 – 23 kg/hr) and capillary tube coil number (0-4) with fixed length (150 cm) and capillary diameter (2.5mm).The results showed that the theoretical compression power increases by (65.8 %) as the condenser temperature increases by (2.71%), also the theoretical compression power decreases by (10.3 %) as the capillary tube coil number increases.The study shows also that the cooling capacity increases by (65.3%) as the evaporator temperature increases by (8.4 %), and the cooling capacity increases by (1.6%)as the capillary tube coil number increases in the range (0-4).The coefficient of performance decreases by (43.4 %), as the mass flow rate increases by (76.9%), also the coefficient of performance increases by (13.51 %) as the capillary tube coil number increases in the range (0-4).Through this study, it was found that the best coil number in refrigeration cycle at the lowest mass flow rate (31 Kg/hr) and at high mass flow rate (23 Kg/hr) is (coil number = 4), this will give the highest performance, cooling capacity and lowest theoretical compression power.An experimental relationship has been adopted between the coefficients of performance (COP) against (- 5.6032+e 0.0413*nco. /0.0051*m ).

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Brown, Julian, Todd A. Briscoe, Richard Harding, Megan L. Cock, John F. Bertram, and Jane M. Black. "GLOMERULAR NUMBER AND CAPILLARY DIMENSIONS IN THE NORMAL LAMB KIDNEY." Image Analysis & Stereology 21, no. 3 (May 3, 2011): 157. http://dx.doi.org/10.5566/ias.v21.p157-164.

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Reduced nephron endowment, either inherited or acquired, has been linked to adult renal pathology as well as hypertension. The sheep provides an excellent model for studying nephrogenesis and renal development because, as in humans, nephrogenesis is complete before birth. In the present study, the physical disector/fractionator method was used to estimate the total number of glomeruli, and thereby nephrons, in normal lambs. Glomerular capillary parameters including mean capillary length per glomerulus, mean capillary surface area per glomerulus and total renal filtration surface area (TRFSA) were also estimated. Total glomerular, and hence nephron number was 333,832 ± 69,560 (mean± standard deviation). TRFSA was 10.95 ± 3.64 x 104 mm2• These results establish a methodology for future investigations, using the sheep as a model, into the effects of depleted nephrogenesis on renal pathology in later life.

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Wang, Lanlan, Hongzhong Liu, Weitao Jiang, Rui Li, Fang Li, Zhongbo Yang, Lei Yin, Yongsheng Shi, and Bangdao Chen. "Capillary number encouraged the construction of smart biomimetic eyes." Journal of Materials Chemistry C 3, no. 23 (2015): 5896–902. http://dx.doi.org/10.1039/c5tc00270b.

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Liu, Haihu, and Yonghao Zhang. "Lattice Boltzmann Simulation of Droplet Generation in a Microfluidic Cross-Junction." Communications in Computational Physics 9, no. 5 (May 2011): 1235–56. http://dx.doi.org/10.4208/cicp.231009.101110s.

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AbstractUsing the lattice Boltzmann multiphase model, numerical simulations have been performed to understand the dynamics of droplet formation in a microfluidic cross-junction. The influence of capillary number, flow rate ratio, viscosity ratio, and viscosity of the continuous phase on droplet formation has been systematically studied over a wide range of capillary numbers. Two different regimes, namely the squeezinglike regime and the dripping regime, are clearly identified with the transition occurring at a critical capillary number Cacr. Generally, large flow rate ratio is expected to produce big droplets, while increasing capillary number will reduce droplet size. In the squeezing-like regime (Ca ≤ Cacr), droplet breakup process is dominated by the squeezing pressure and the viscous force; while in the dripping regime (Ca ≤ Cacr), the viscous force is dominant and the droplet size becomes independent of the flow rate ratio as the capillary number increases. In addition, the droplet size weakly depends on the viscosity ratio in both regimes and decreases when the viscosity of the continuous phase increases. Finally, a scaling law is established to predict the droplet size.

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JOEKAR-NIASAR, V., S. M. HASSANIZADEH, and H. K. DAHLE. "Non-equilibrium effects in capillarity and interfacial area in two-phase flow: dynamic pore-network modelling." Journal of Fluid Mechanics 655 (July 5, 2010): 38–71. http://dx.doi.org/10.1017/s0022112010000704.

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Current macroscopic theories of two-phase flow in porous media are based on the extended Darcy's law and an algebraic relationship between capillary pressure and saturation. Both of these equations have been challenged in recent years, primarily based on theoretical works using a thermodynamic approach, which have led to new governing equations for two-phase flow in porous media. In these equations, new terms appear related to the fluid–fluid interfacial area and non-equilibrium capillarity effects. Although there has been a growing number of experimental works aimed at investigating the new equations, a full study of their significance has been difficult as some quantities are hard to measure and experiments are costly and time-consuming. In this regard, pore-scale computational tools can play a valuable role. In this paper, we develop a new dynamic pore-network simulator for two-phase flow in porous media, called DYPOSIT. Using this tool, we investigate macroscopic relationships among average capillary pressure, average phase pressures, saturation and specific interfacial area. We provide evidence that at macroscale, average capillary pressure–saturation–interfacial area points fall on a single surface regardless of flow conditions and fluid properties. We demonstrate that the traditional capillary pressure–saturation relationship is not valid under dynamic conditions, as predicted by the theory. Instead, one has to employ the non-equilibrium capillary theory, according to which the fluids pressure difference is a function of the time rate of saturation change. We study the behaviour of non-equilibrium capillarity coefficient, specific interfacial area, and its production rate versus saturation and viscosity ratio.A major feature of our pore-network model is a new computational algorithm, which considers capillary diffusion. Pressure field is calculated for each fluid separately, and saturation is computed in a semi-implicit way. This provides more numerical stability, compared with previous models, especially for unfavourable viscosity ratios and small capillary number values.

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Chen, Tao Ping, Biao Qiu, and Qi Hao Hu. "Modification and Application of Capillary Number to Oil Displacement in Low Permeability Reservoirs." Advanced Materials Research 868 (December 2013): 522–28. http://dx.doi.org/10.4028/www.scientific.net/amr.868.522.

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As concerning the limitations of the classic capillary number theory in the applications to the oil displacement with the ultra low interfacial intension system in low permeability reservoirs, considering the flow velocity of water/oil displacement through pores in low permeability reservoirs and the mechanism of displacement of the remaining oil in the parallel pores, and considering the influences of ultra low interfacial intension on oil/water relative permeability and the influences of non-homogeneity on the recovery, the expression of modification of the capillary number was given. The relation curves of recovery and capillary number were plotted through the displacement experiments with the ultra low interfacial intension system in low permeability cores. Some points on the application of capillary number to the oil displacement with the ultra low interfacial tension system were given, and the reasonable ways of enhancing the recovery of water flooding low permeability reservoirs with ultra low interfacial intension system were shown.

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Mohammadi-Khanaposhtani, Mohammad, Yousef Kazemzadeh, and Reza Daneshfar. "Positive coupling effect in gas condensate flow: Role of capillary number, Scheludko number and Weber number." Journal of Petroleum Science and Engineering 203 (August 2021): 108490. http://dx.doi.org/10.1016/j.petrol.2021.108490.

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Desjardins, C., and B. R. Duling. "Heparinase treatment suggests a role for the endothelial cell glycocalyx in regulation of capillary hematocrit." American Journal of Physiology-Heart and Circulatory Physiology 258, no. 3 (March 1, 1990): H647—H654. http://dx.doi.org/10.1152/ajpheart.1990.258.3.h647.

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Physiological stimuli induce rapid and unexplained increases in the number of red blood cells within capillaries of skeletal muscle. We hypothesized that such alterations in intracapillary red cell numbers might be due to an undefined interaction between one or more components of blood and the luminal surface of the capillary. This proposition was tested by in situ microperfusion of capillaries with enzymes directed against macromolecules likely to be expressed on the surface of endothelial cells. The instantaneous fractional volume of red blood cells within a capillary (tube hematocrit) was used as an index of a capillary's response to enzyme microperfusion. Five to 8 min of perfusion with enzyme vehicle (0.25% albumin-Ringer solution) produced no significant alteration in capillary tube hematocrit. Perfusion with solutions containing heparinase raised the tube hematocrit at least twofold (P less than 0.05) without a significant change in red cell velocity. Heat-denatured heparinase and other enzymes such as neuraminidase, hyaluronidase, papain, pronase E, and clostripain had no detectable effect on the tube hematocrit (P greater than 0.05). After enzyme treatment, application of adenosine (10(-4) M) or oxygen caused brisk vasomotor responses in arterioles feeding perfused capillary units, but the usual changes in the tube hematocrit were not observed. Thus heparinase treatment results in a sustained elevation in the capillary tube hematocrit and a dissociation of the typical relationship between vasomotor changes and red cell distribution in capillaries. These findings suggest that physiological stimuli which alter the number of red blood cells within capillaries may operate by modifying interactions between plasma and one or more components on the luminal surface of capillaries.

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Bhat, Pradeep P., Osman A. Basaran, and Matteo Pasquali. "Dynamics of viscoelastic liquid filaments: Low capillary number flows." Journal of Non-Newtonian Fluid Mechanics 150, no. 2-3 (April 2008): 211–25. http://dx.doi.org/10.1016/j.jnnfm.2007.10.021.

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Sheng, James J. "Preferred calculation formula and buoyancy effect on capillary number." Asia-Pacific Journal of Chemical Engineering 10, no. 3 (March 20, 2015): 400–410. http://dx.doi.org/10.1002/apj.1883.

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Argentina, M., A. Cohen, Y. Bouret, N. Fraysse, and C. Raufaste. "One-dimensional capillary jumps." Journal of Fluid Mechanics 765 (January 15, 2015): 1–16. http://dx.doi.org/10.1017/jfm.2014.717.

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AbstractIn flows where the ratio of inertia to gravity varies strongly, large variations in the fluid thickness appear and hydraulic jumps arise, as depicted by Rayleigh. We report a new family of hydraulic jumps, where the capillary effects dominate the gravitational acceleration. The Bond number – which measures the importance of gravitational body forces compared to surface tension – must be small in order to observe such objects using capillarity as a driving force. For water, the typical length should be smaller than 3 mm. Nevertheless, for such small scales, solid boundaries induce viscous stresses, which dominate inertia, and capillary jumps should not be described by the inertial shock wave theory that one would deduce from Bélanger or Rayleigh for hydraulic jumps. In order to get rid of viscous shears, we consider Plateau borders, which are the microchannels defined by the merging of three films inside liquid foams, and we show that capillary jumps propagate along these deformable conduits. We derive a simple model that predicts the velocity, geometry and shape of such fronts. A strong analogy with Rayleigh’s description is pointed out. In addition, we carried out experiments on a single Plateau border generated with soap films to observe and characterize these capillary jumps. Our theoretical predictions agree remarkably well with the experimental measurements.

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Alipour Tabrizy, Vahid. "Investigation of CO2 Enhanced Oil Recovery Using Dimensionless Groups in Wettability Modified Chalk and Sandstone Rocks." Journal of Petroleum Engineering 2014 (March 26, 2014): 1–16. http://dx.doi.org/10.1155/2014/430309.

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The paper addresses enhanced oil recovery in chalk and sandstone rocks by CO2 injection, with different wettability, porosity, and permeability as well as injection rate and flooding conditions. Results indicate that an increase in Bond number has a positive effect on oil recovery whereas for capillary number, there is a limit in which recovery is improving. This limit is estimated when the pressure drop by viscous force is approximately equal to the threshold balance between capillary and gravity forces. A dimensionless group is proposed that combines the effect of capillarity, injection rate, permeability, and CO2 diffusion on the oil recovery. Recovery from all experiments in this study and reported data in the literature shows a satisfactory relationship with the proposed group.

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WALTER, J., A. V. SALSAC, and D. BARTHÈS-BIESEL. "Ellipsoidal capsules in simple shear flow: prolate versus oblate initial shapes." Journal of Fluid Mechanics 676 (April 4, 2011): 318–47. http://dx.doi.org/10.1017/s0022112011000486.

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The large deformations of an initially-ellipsoidal capsule in a simple shear flow are studied by coupling a boundary integral method for the internal and external flows and a finite-element method for the capsule wall motion. Oblate and prolate spheroids are considered (initial aspect ratios: 0.5 and 2) in the case where the internal and external fluids have the same viscosity and the revolution axis of the initial spheroid lies in the shear plane. The influence of the membrane mechanical properties (mechanical law and ratio of shear to area dilatation moduli) on the capsule behaviour is investigated. Two regimes are found depending on the value of a capillary number comparing viscous and elastic forces. At low capillary numbers, the capsule tumbles, behaving mostly like a solid particle. At higher capillary numbers, the capsule has a fluid-like behaviour and oscillates in the shear flow while its membrane continuously rotates around its deformed shape. During the tumbling-to-swinging transition, the capsule transits through an almost circular profile in the shear plane for which a long axis can no longer be defined. The critical transition capillary number is found to depend mainly on the initial shape of the capsule and on its shear modulus, and weakly on the area dilatation modulus. Qualitatively, oblate and prolate capsules are found to behave similarly, particularly at large capillary numbers when the influence of the initial state fades out. However, the capillary number at which the transition occurs is significantly lower for oblate spheroids.

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AlQuaimi, B. I., and W. R. Rossen. "Capillary Desaturation Curve for Residual Nonwetting Phase in Natural Fractures." SPE Journal 23, no. 03 (February 5, 2018): 788–802. http://dx.doi.org/10.2118/189448-pa.

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Summary The displacement of a nonwetting phase by a wetting phase is characterized by the capillary number. Different forms of capillary number have been used in the literature for flow in porous media. A capillary number for a single rock fracture has been defined in the literature, using the mean aperture to characterize the trapping and mobilization in a fracture. We propose a new capillary-number definition for fractures that incorporates geometrical characterization of the fracture, dependent on the force balance on a trapped ganglion. The new definition is validated with laboratory experiments using five distinctive model fractures. The model fractures are made of glass plates, with a wide variety of hydraulic apertures, degrees of roughness, and correlation lengths of the roughness. The fracture surfaces were characterized in detail and statistically analyzed. The aperture distribution of each model fracture was represented as a 2D network of pore bodies connected by throats. The hydraulic aperture of each model fracture was measured experimentally. Capillary desaturation curves (CDCs) were generated experimentally using water/air in forced imbibition. The transparent nature of the system permits us to determine the residual air saturation as a function of pressure gradient from the captured images. The residual nonwetting saturation/capillary-number relationship obtained from different fractures varying in aperture and roughness can be represented approximately by a single curve in terms of the new definition of the capillary number. They do not fit a single trend using the conventional definition of the capillary number.

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LAC, ETIENNE, and J. D. SHERWOOD. "Motion of a drop along the centreline of a capillary in a pressure-driven flow." Journal of Fluid Mechanics 640 (November 2, 2009): 27–54. http://dx.doi.org/10.1017/s0022112009991212.

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The deformation of a drop as it flows along the axis of a circular capillary in low Reynolds number pressure-driven flow is investigated numerically by means of boundary integral computations. If gravity effects are negligible, the drop motion is determined by three independent parameters: the size a of the undeformed drop relative to the radius R of the capillary, the viscosity ratio λ between the drop phase and the wetting phase and the capillary number Ca, which measures the relative importance of viscous and capillary forces. We investigate the drop behaviour in the parameter space (a/R, λ, Ca), at capillary numbers higher than those considered previously. If the fluid flow rate is maintained, the presence of the drop causes a change in the pressure difference between the ends of the capillary, and this too is investigated. Estimates for the drop deformation at high capillary number are based on a simple model for annular flow and, in most cases, agree well with full numerical results if λ ≥ 1/2, in which case the drop elongation increases without limit as Ca increases. If λ < 1/2, the drop elongates towards a limiting non-zero cylindrical radius. Low-viscosity drops (λ < 1) break up owing to a re-entrant jet at the rear, whereas a travelling capillary wave instability eventually develops on more viscous drops (λ > 1). A companion paper (Lac & Sherwood, J. Fluid Mech., doi:10.1017/S002211200999156X) uses these results in order to predict the change in electrical streaming potential caused by the presence of the drop when the capillary wall is charged.

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Enad, J. G., M. Fournier, and G. C. Sieck. "Oxidative capacity and capillary density of diaphragm motor units." Journal of Applied Physiology 67, no. 2 (August 1, 1989): 620–27. http://dx.doi.org/10.1152/jappl.1989.67.2.620.

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Motor units in the cat diaphragm (DIA) were isolated in situ by microdissection and stimulation of C5 ventral root filaments. Motor units were classified based on their isometric contractile force responses and fatigue indexes (FI). The muscle fibers belonging to individual units (i.e., the muscle unit) were identified using the glycogen-depletion method. Fibers were classified as type I or II based on histochemical staining for myofibrillar adenosine triphosphatase (ATPase) after alkaline preincubation. The rate of succinate dehydrogenase (SDH) activity of each fiber was determined using a microphotometric procedure. The location of capillaries was determined from muscle cross sections stained for ATPase after acid (pH = 4.2) preincubation. The capillarity of muscle unit fibers was determined by counting the number of capillaries surrounding fibers and by calculating the number of capillaries per fiber area. A significant correlation was found between the fatigue resistance of DIA units and the mean SDH activity of muscle unit fibers. A significant correlation was also observed between DIA unit fatigue resistance and both indexes of muscle unit fiber capillarity. The mean SDH activity and mean capillary density of muscle unit fibers were also correlated. We conclude that DIA motor unit fatigue resistance depends, at least in part, on the oxidative capacity and capillary density of muscle unit fibers.

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28

Mathieu-Costello, Odile, Peter J. Agey, Richard B. Logemann, Richard W. Brill, and Peter W. Hochachka. "Capillary–fiber geometrical relationships in tuna red muscle." Canadian Journal of Zoology 70, no. 6 (June 1, 1992): 1218–29. http://dx.doi.org/10.1139/z92-169.

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The aim of this study was to examine the size and geometry of the capillary network in tuna red muscle, one of the most aerobic muscles in fish. Deep red muscle of 1.5- to 2-kg skipjack tuna, Katsuwonus pelamis, was perfusion fixed in situ, processed for electron microscopy, and analyzed by morphometry. Fiber cross-sectional area was 560 ± 30 (SE) μm2 in the samples. Capillary length per fiber volume was 4143 ± 242 (SE) mm−2 and mitochondrial volume density 28.5 ± 1.0 (SE) %. Indexes of capillarity such as average number of capillaries around a fiber, capillary length and surface per fiber volume, and capillary surface per fiber surface were high for a fish muscle. In fact, the size of the capillary–fiber interface (i.e., capillary to fiber surface) at a given mitochondrial volume per fiber was not significantly different in tuna red muscle compared with rat soleus muscle. However, calculation of mitochondrial respiratory rates in tuna red muscle yielded a substantially lower value (approximately 1/20th) compared with muscles of mammals. Besides the possible effect of differences in operating temperatures and (or) mitochondrial function(s) in fish compared with mammals, this suggests that the large capillary–fiber interface in tuna may be related to functions other than oxygen delivery per se, such as substrate and (or) heat transfer between capillaries and muscle fiber.

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29

He, Xiansong, Yi Liu, and Wangqing Wu. "A General and Efficient Approach for the Dual-Scale Infiltration Flow Balancing in In Situ Injection Molding of Continuous Fiber Reinforced Thermoplastic Composites." Polymers 13, no. 16 (August 12, 2021): 2689. http://dx.doi.org/10.3390/polym13162689.

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In situ injection molding of continuous fiber reinforced thermoplastic composites is challenged by unbalanced dual-scale infiltration flow due to the pronounced capillary effect. In this paper, a general and efficient approach was proposed for dual-scale infiltration flow balancing based on numerical simulation. Specifically, Stokes and Brinkman equations were used to describe the infiltration flow in inter- and intra-fiber bundles. In particular, capillary pressure drop was integrated in the Brinkmann equation to consider the capillary effect. The infiltration flow front is tracked by the level set method. Numerical simulation and experimental results indicate that the numerical model can accurately demonstrate the unbalanced infiltration flow in inter- and intra-fiber bundles caused by the changes of the injection rate, the resin viscosity, the injection rate, the fiber volume fraction and the capillary number. In addition, the infiltration flow velocity in inter- and intra-fiber bundles can be efficiently tuned by the capillary number, which is mainly determined by the injection rate for a specified resin system. The optimal capillary numbers obtained by simulation and experiment are 0.022 and 0.026, which are very close to each other. Finally, one-dimensional in situ injection molding experiments with constant injection pressure were conducted to prepare fiber reinforced polymerized cyclic butylene terephthalate composite laminate with various flow rates along the infiltration direction. The experimental results confirmed that the lowest porosity and the highest interlaminar shear strength of the composite can only be obtained with the optimized capillary number, which is basically consistent with the simulation results.

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30

Plyley, Michael J., Barbara J. Olmstead, and Earl G. Noble. "Time course of changes in capillarization in hypertrophied rat plantaris muscle." Journal of Applied Physiology 84, no. 3 (March 1, 1998): 902–7. http://dx.doi.org/10.1152/jappl.1998.84.3.902.

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The time course of angiogenesis during hypertrophy of the rat plantaris muscle was studied by using a unilateral, synergistic ablation model. Animals ( n = 6/group) were euthanized 2, 5, 7, 15, 21, and 30 days postmyectomy. Sections from both the hypertrophied and contralateral muscles were simultaneously stained for capillaries and muscle fiber type. Mean fiber cross-sectional area (FA) and various indexes of capillarity were determined by using a video analysis system. The capillary supply to individual fibers, assessed as the FA supplied per capillary contact, remained unchanged until day 21 (compared with day 2) and exhibited a significant increase at day 30. Analysis of the time course of capillary development on the basis of the number of capillary contacts per fiber, and of hypertrophy on the basis of FA, yielded half-lives of 10.1 and 11.2 days, respectively. It was concluded that angiogenesis during muscle overload is tightly coupled to the changes in FA, which could suggest that the two processes are initiated and/or driven by some common factor(s).

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31

Zoccoli, Giovanna, Maria Luisa Lucchi, Emanuela Andreoli, Veronique Bach, Tullia Cianci, Pierluigi Lenzi, and Carlo Franzini. "Brain Capillary Perfusion during Sleep." Journal of Cerebral Blood Flow & Metabolism 16, no. 6 (November 1996): 1312–18. http://dx.doi.org/10.1097/00004647-199611000-00028.

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Brain capillary perfusion was evaluated in the different states of the wake–sleep cycle—quiet wakefulness (QW), quiet sleep (QS), and active sleep (AS)—in rats. The extent of the perfused capillary network was determined by intravascular distribution of a fluorescent marker, Evans blue (EB); it remained unchanged across the three behavioral conditions, QW, QS, and AS. The anatomical network was assessed by alkaline phosphatase (AP) endothelial staining, which is known to underestimate the number of existing capillaries. The resulting number of AP profiles were, therefore, significantly lower than the number of EB profiles, but the percentage of AP-stained capillaries that were perfused (96%) was also unchanged across the behavioral conditions. The results indicate that no capillary recruitment accompanies the wake–sleep cycle. Capillary surface area is a relevant factor in determining exchanges across the blood–brain barrier. In the absence of capillary recruitment (relative constancy of the surface area), the CBF changes during sleep should preferentially affect flow-limited with respect to diffusion-limited transport.

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32

Schulkes, R. M. S. M. "The evolution of capillary fountains." Journal of Fluid Mechanics 261 (February 25, 1994): 223–52. http://dx.doi.org/10.1017/s0022112094000327.

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In this paper we consider the dynamics of a growing capillary fountain. We assume that at some time t = 0 an inviscid incompressible fluid is ejected vertically upwards through a circular nozzle. The subsequent dynamics of the resulting fountain is studied numerically using the boundary-element technique. The rate at which fluid is discharged from the nozzle and the Bond number (a measure of gravitational and surface tension forces) are the parameters that govern the dynamics of the fountain. For small discharge rates the fountain assumes the form of a slowly growing sessile drop, with dynamic effects not modifying the shape of the drop significantly. For large discharge rates we find that close to the symmetry axis a region develops with a high curvature. This strongly curved region results in a physical instability which can take on one of two forms: either a liquid drop is ejected from the free surface or the capillary surface entrains a bubble. For intermediate values of the discharge rate we find that fluid lobes develop which fall over the side of the nozzle. A number of experimental results are also presented showing the evolution of water fountains for different Bond numbers and discharge rates. Some of our numerical predictions are confirmed by the experimental results.

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33

Dyck, P. J., S. Hansen, J. Karnes, P. O'Brien, H. Yasuda, A. Windebank, and B. Zimmerman. "Capillary number and percentage closed in human diabetic sural nerve." Proceedings of the National Academy of Sciences 82, no. 8 (April 1, 1985): 2513–17. http://dx.doi.org/10.1073/pnas.82.8.2513.

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34

Reddy, Shravanthi, P. Randall Schunk, and Roger T. Bonnecaze. "Dynamics of low capillary number interfaces moving through sharp features." Physics of Fluids 17, no. 12 (December 2005): 122104. http://dx.doi.org/10.1063/1.2140691.

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35

Hsueh, Ching, Carmen Lucía Moraila Martínez, Frédéric Doumenc, Miguel A. Rodríguez-Valverde, and Béatrice Guerrier. "Self-assembly in drying complex fluid at low capillary number." Chemical Engineering and Processing: Process Intensification 68 (June 2013): 64–68. http://dx.doi.org/10.1016/j.cep.2012.07.006.

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36

Kamiya, Akira, Shinya Takeda, and Masahiro Shibata. "Optimum capillary number for oxygen delivery to tissue in man." Bulletin of Mathematical Biology 49, no. 3 (May 1987): 351–61. http://dx.doi.org/10.1007/bf02460125.

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37

Kamotani, Y., S. Ostrach, and J. P. Kizito. "Experimental free coating flows at high capillary and Reynolds number." Experiments in Fluids 27, no. 3 (August 3, 1999): 235–43. http://dx.doi.org/10.1007/s003480050348.

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38

Ponce F., Ranena V., Vladimir Alvarado, and Marcio S. Carvalho. "Water-alternating-macroemulsion reservoir simulation through capillary number-dependent modeling." Journal of the Brazilian Society of Mechanical Sciences and Engineering 39, no. 10 (August 12, 2017): 4135–45. http://dx.doi.org/10.1007/s40430-017-0885-7.

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39

KAMIYA, A., S. TAKEDA, and M. SHIBATA. "Optimum capillary number for oxygen delivery to tissue in man." Bulletin of Mathematical Biology 49, no. 3 (1987): 351–61. http://dx.doi.org/10.1016/s0092-8240(87)80029-0.

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40

SCHLEIZER, ANTHONY D., and ROGER T. BONNECAZE. "Displacement of a two-dimensional immiscible droplet adhering to a wall in shear and pressure-driven flows." Journal of Fluid Mechanics 383 (March 25, 1999): 29–54. http://dx.doi.org/10.1017/s0022112098003462.

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The dynamic behaviour and stability of a two-dimensional immiscible droplet subject to shear or pressure-driven flow between parallel plates is studied under conditions of negligible inertial and gravitational forces. The droplet is attached to the lower plate and forms two contact lines that are either fixed or mobile. The boundary-integral method is used to numerically determine the flow along and dynamics of the free surface. For surfactant-free interfaces with fixed contact lines, the deformation of the interface is determined for a range of capillary numbers, droplet to displacing fluid viscosity ratios, droplet sizes and flow type. It is shown that as the capillary number or viscosity ratio or size of the droplet increases, the deformation of the interface increases and above critical values of the capillary number no steady shape exists. For small droplets, and at low capillary numbers, shear and pressure-driven flows are shown to yield similar steady droplet shapes. The effect of surfactants is studied assuming a fixed amount of surfactant that is subject to convective–diffusive transport along the interface and no transport to or from the bulk fluids. Increasing the surface Péclet number, the ratio of convective to diffusive transport, leads to an accumulation of surfactant at the downstream end of the droplet and creates Marangoni stresses that immobilize the interface and reduce deformation. The no-slip boundary condition is then relaxed and an integral form of the Navier-slip model is used to examine the effects of allowing the droplet to slip along the solid surface in a pressure-driven flow. For contact angles less than or equal to 90°, a stable droplet spreads along the wall until a steady shape is reached, when the droplet translates across the wall at a constant velocity. The critical capillary number is larger for these droplets compared to those with pinned contact lines. For contact angles greater than 90°, the wetted area between a stable droplet and the wall decreases until a steady shape is reached. The critical capillary number for these droplets is less than that for pinned droplets. Above the critical capillary number the droplet completely detaches for a contact angle of 120°, or part of it is pinched off leaving behind a smaller attached droplet for contact angles less than or equal to 90°.

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41

CHANG, Yen-Sheng, Chun-Min SHIH,, Yen-Cheng LI, and Cheng-Huang LIN. "Large-Volume Sample Sweeping with a High Theoretical Plate Number Using a Coupled-Capillary in Capillary Electrophoresis." Analytical Sciences 22, no. 4 (2006): 557–61. http://dx.doi.org/10.2116/analsci.22.557.

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42

Aggelopoulos, C. A., and C. D. Tsakiroglou. "The effect of micro-heterogeneity and capillary number on capillary pressure and relative permeability curves of soils." Geoderma 148, no. 1 (November 2008): 25–34. http://dx.doi.org/10.1016/j.geoderma.2008.08.011.

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43

Chang, Tong-Bou, Bai-Heng Shiue, Yi-Bin Ciou, and Wai-Io Lo. "Analytical Investigation into Effects of Capillary Force on Condensate Film Flowing over Horizontal Semicircular Tube in Porous Medium." Mathematical Problems in Engineering 2021 (March 17, 2021): 1–10. http://dx.doi.org/10.1155/2021/6693512.

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A theoretical investigation is performed into the problem of laminar filmwise condensation flow over a horizontal semicircular tube embedded in a porous medium and subject to capillary forces. The effects of the capillary force and gravity force on the condensation heat transfer performance are analyzed using an energy balance approach method. For analytical convenience, several dimensionless parameters are introduced, including the Jakob number Ja, Rayleigh number Ra, and capillary force parameter Boc. The resulting dimensionless governing equation is solved using the numerical shooting method to determine the effect of capillary forces on the condensate thickness. A capillary suction velocity can be obtained mathematically in the calculation process and indicates whether the gravity force is greater than the capillary force. It is shown that if the capillary force is greater than the condensate gravity force, the liquid condensate will be sucked into the two-phase zone. Under this condition, the condensate film thickness reduces and the heat transfer performance is correspondingly improved. Without considering the capillary force effects, the mean Nusselt number is also obtained in the present study as N u ¯ | V 2 ∗ = 0 = 2 R a D a / J a 1 / 2 ∫ 0 π 1 + cos θ 1 / 2 d θ .

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44

Deike, Luc, Stephane Popinet, and W. Kendall Melville. "Capillary effects on wave breaking." Journal of Fluid Mechanics 769 (March 25, 2015): 541–69. http://dx.doi.org/10.1017/jfm.2015.103.

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We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number, $\mathit{Bo}$, and the initial wave steepness, ${\it\epsilon}$, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of $({\it\epsilon},\mathit{Bo})$ is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness ${\it\epsilon}_{c}$ defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as ${\it\epsilon}\sim (1+\mathit{Bo})^{-1/3}$. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter $b$ is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.

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45

Sugihardjo, Sugihardjo. "Capillary Desaturation Curves For Evaluating Surfactant Performance By Core Flooding Experiments." Scientific Contributions Oil and Gas 32, no. 1 (March 17, 2022): 16–20. http://dx.doi.org/10.29017/scog.32.1.828.

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Capillary desaturation curves are normally generated in laboratory scale by means of core flooding experiments to evaluate the surfactant formulations for chemical injection in EOR projects. Low tension surfactant solution is the only liquid that could increase the dimensionless capillary number in order of magnitude of 103. Two types of core samples have been used in core flooding experiments to develop capillary desaturation curves, i.e., generic and standard Classhach core samples. In Addition, VS surfactant and additional alcohols are also used in these experiments. The higher the capillary number could generate a lower the residual oil saturation. Moreover, each rock may have a particular capillary desaturation curve depending on the rock properties. Therefore before implementing chemical injection in a pilot scale, capillary desaturation curve should be developed in laboratory to evaluate the surfactant injection performance.

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46

Singh, Rajesh Kumar, Xiaoyi Li, and Kausik Sarkar. "Lateral migration of a capsule in plane shear near a wall." Journal of Fluid Mechanics 739 (December 20, 2013): 421–43. http://dx.doi.org/10.1017/jfm.2013.624.

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AbstractThe migration of a capsule enclosed by an elastic membrane in a wall-bounded linear shear is investigated using a front-tracking method. A detailed comparison with the migration of a viscous drop is presented varying the capillary number (in the case of a capsule, the elastic capillary number) and the viscosity ratio. In both cases, the deformation breaks the flow reversal symmetry and makes them migrate away from the wall. They quickly go through a transient evolution to eventually reach a quasi-steady state where the dynamics becomes independent of the initial position and only depends on the wall distance. Previous analytical theories predicted that for a viscous drop, in the quasi-steady state, the migration and slip velocities scale approximately with the square of the inverse of the drop–wall separation, whereas the drop deformation scales as the inverse cube of the separation. These power law relations are shown to hold for a capsule as well. The deformation and inclination angle of the capsule and the drop at the same wall separation show a crossover in their variation with the capillary number: the capsule shows a steeper variation than that of the drop for smaller capillary numbers and slower variation than the drop for larger capillary numbers. Using the Green’s function of Stokes flow, a semi-analytic theory is presented to show that the far-field stresslet that causes the migration has two distinct contributions from the interfacial stresses and the viscosity ratio, with competing effects between the two defining the dynamics. It predicts the scaling of the migration velocity with the capsule–wall separation, however, matching with the simulated result very well only away from the wall. A phenomenological correlation for the migration velocity as a function of elastic capillary number, wall distance and viscosity ratio is developed using the simulation results. The effects of different membrane hyperelastic constitutive equations – neo-Hookean, Evans–Skalak, and Skalak – are briefly investigated to show that the behaviour remains similar for different equations.

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47

Loizou, Katerina, Voon-Loong Wong, and Buddhika Hewakandamby. "Examining the Effect of Flow Rate Ratio on Droplet Generation and Regime Transition in a Microfluidic T-Junction at Constant Capillary Numbers." Inventions 3, no. 3 (August 10, 2018): 54. http://dx.doi.org/10.3390/inventions3030054.

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The focus of this work is to examine the effect of flow rate ratio (quotient of the dispersed phase flow rate over the continuous phase flow rate) on a regime transition from squeezing to dripping at constant capillary numbers. The effect of the flow rate ratio on the volume of droplets generated in a microfluidic T-junction is discussed, and a new scaling law to estimate their volume is proposed. Existing work on a regime transition reported by several researchers focuses on the effect of the capillary number on regime transition, and the results that are presented in this paper advance the current understanding by indicating that the flow rate ratio is another parameter that dictates regime transition. In this paper, the transition between squeezing and dripping regimes is reported at constant capillary numbers, with a transition region identified between squeezing and dripping regimes. Dripping is observed at lower flow rate ratios and squeezing at higher flow rate ratios, with a transition region between the two regimes at flow rate ratios between 1 and 2. This is presented in a flow regime map that is constructed based on the observed mechanism. A scaling model is proposed to characterise droplet volume in terms of flow rate ratio and capillary number. The effect of flow rate ratio on the non-dimensional droplet volume is presented, and lastly, the droplet volume is expressed in terms of a range of parameters, such as the viscosity ratio between the dispersed and the continuous phase, capillary number, and the geometrical characteristics of the channels.

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48

Hepple, Russell T., Peter J. Agey, Larnelle Hazelwood, Joseph M. Szewczak, Richard E. MacMillen, and Odile Mathieu-Costello. "Increased capillarity in leg muscle of finches living at altitude." Journal of Applied Physiology 85, no. 5 (November 1, 1998): 1871–76. http://dx.doi.org/10.1152/jappl.1998.85.5.1871.

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An increased ratio of muscle capillary to fiber number (capillary/fiber number) at altitude has been found in only a few investigations. The highly aerobic pectoralis muscle of finches living at 4,000-m altitude ( Leucosticte arctoa; A) was recently shown to have a larger capillary/fiber number and greater contribution of tortuosity and branching to total capillary length than sea-level finches ( Carpodacus mexicanus; SL) of the same subfamily (O. Mathieu-Costello, P. J. Agey, L. Wu, J. M. Szewczak, and R. E. MacMillen. Respir. Physiol. 111: 189–199, 1998). To evaluate the role of muscle aerobic capacity on this trait, we examined the less-aerobic leg muscle (deep portion of anterior thigh) in the same birds. We found that, similar to pectoralis, the leg muscle in A finches had a greater capillary/fiber number (1.42 ± 0.06) than that in SL finches (0.77 ± 0.05; P < 0.01), but capillary tortuosity and branching were not different. As also found in pectoralis, the resulting larger capillary/fiber surface in A finches was proportional to a greater mitochondrial volume per micrometer of fiber length compared with that in SL finches. These observations, in conjunction with a trend to a greater (rather than smaller) fiber cross-sectional area in A than in SL finches (A: 484 ± 42, SL: 390 ± 26 μm2, both values at 2.5-μm sarcomere length; P = 0.093), support the notion that chronic hypoxia is also a condition in which capillary-to-fiber structure is organized to match the size of the muscle capillary-to-fiber interface to fiber mitochondrial volume rather than to minimize intercapillary O2diffusion distances.

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Calderón, Andrés J., J. Brian Fowlkes, and Joseph L. Bull. "Bubble splitting in bifurcating tubes: a model study of cardiovascular gas emboli transport." Journal of Applied Physiology 99, no. 2 (August 2005): 479–87. http://dx.doi.org/10.1152/japplphysiol.00656.2004.

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The transport of long gas bubbles, suspended in liquid, through symmetric bifurcations, is investigated experimentally and theoretically as a model of cardiovascular gas bubble transport in air embolism and gas embolotherapy. The relevant dimensionless parameters in the models match the corresponding values for arteries and arterioles. The effects of roll angle (the angle the plane of the bifurcation makes with the horizontal), capillary number (a dimensionless indicator of flow), and bubble volume (or length) on the splitting of bubbles as they pass through the bifurcation are examined. Splitting is observed to be more homogenous at higher capillary numbers and lower roll angles. It is shown that, at nonzero roll angles, there is a critical value of the capillary number below which the bubbles do not split and are transported entirely into the upper branch. The value of the critical capillary number increases with roll angle and parent tube diameter. A unique bubble motion is observed at the critical capillary number and for slightly slower flows: the bubble begins to split, the meniscus in the lower branch then moves backward, and finally the entire bubble enters the upper branch. These findings suggest that, in large vessels, emboli tend to be transported upward unless flow is unusually strong but that a more homogeneous distribution of emboli occurs in smaller vessels. This corresponds to previous observations that air emboli tend to lodge in the upper regions of the lungs and suggests that relatively uniform infarction of tumors by gas embolotherapy may be possible.

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50

Yu, Yuan, Haihu Liu, Yonghao Zhang, and Dong Liang. "Color-gradient lattice Boltzmann modeling of immiscible two-phase flows on partially wetting surfaces." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 3 (December 28, 2017): 416–30. http://dx.doi.org/10.1177/0954406217749616.

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A zero-interfacial-force condition is derived and implemented to improve the wetting boundary scheme for a lattice Boltzmann color-gradient model. This new wetting boundary scheme is validated by two static problems, i.e. a droplet resting on a flat surface and a cylindrical surface, and one dynamic problem, i.e. the capillary filling in a two-dimensional channel. In these simulations, we observe that non-physical mass transfer is suppressed and spurious velocities become smaller. Meanwhile, accurate results including dynamic contact line movement are achieved for a broad range of contact angles. The model is then applied to study the displacement of immiscible fluids in a two-dimensional channel. Both the displacement velocity and the change rate of finger length are found to exhibit a linear dependence on the contact angle at the viscosity ratio of unity. The displacement velocity decreases but the change rate of finger length increases with increasing capillary number, while the displacement velocity tends to be constant, i.e. two-thirds of the maximum inlet velocity, at high viscosity ratios or low capillary numbers. In contrast to the displacement velocity, the change rate of finger length is negligible at high viscosity ratios or low capillary numbers, where the finger length is in an equilibrium state, while the equilibrium finger length itself is smaller at a higher viscosity ratio or a lower capillary number.

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Journal articles on the topic 'Capillary number'

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