Dynamics of a nonspherical capsule in general flow. (English) Zbl 1390.76948
Summary: The dynamics of a capsule in general flows is studied analytically and numerically. The capsule is modeled as a liquid-filled drop enclosed by a membrane. We adapted the Keller-Skalak (KS) theory and Skotheim-Secomb model to the case of general flow, the governing equations are derived. It is found that when viscosity ratio \(\lambda = 1\), the capsule dynamics in general flows is controlled by two dimensionless parameters, the ratio of vorticity to strain rate of the flow and the ratio of the elastic force to fluid stress. In the literature, the transition between swinging (SW) and tumbling (TU) is always one way (TU to SW). As far as we know, it is the first time that the TU-SW-TU transition has been identified, i.e., the transition may also transfer from SW to TU after the transition (TU to SW) occurs under some circumstances. The possible mechanism is that the rotation of the flow suppresses the deformation along the vorticity direction of the capsule. The shape dynamics of a capsule is studied in detail and the rheology of dilute capsule suspension is also investigated briefly.
MSC:
| 76Z05 | Physiological flows |
| 76M28 | Particle methods and lattice-gas methods |
| 92C35 | Physiological flow |
Keywords:
deformable particle; capsule dynamics; lattice Boltzmann; general flow; fluid structure interactionReferences:
| [1] | Abkarian, M.; Faivre, M.; Viallat, A., Swinging of red blood cells under shear flow, Phys Rev Lett, 98, 18, 188302, (2007) |
| [2] | Bagchi, P.; Kalluri, R. M., Dynamic rheology of a dilute suspension of elastic capsules: effect of capsule tank-treading, swinging and tumbling, J Fluid Mech, 669, 498-526, (2011) · Zbl 1225.76287 |
| [3] | Kessler, S.; Finken, R.; Seifert, U., Swinging and tumbling of elastic capsules in shear flow, J Fluid Mech, 605, 207-226, (2008) · Zbl 1154.76021 |
| [4] | Cordasco, D.; Bagchi, P., Intermittency and synchronized motion of red blood cell dynamics in shear flow, J Fluid Mech, 759, 472-488, (2014) |
| [5] | de Loubens, C.; Deschamps, J.; Boedec, G.; Leonetti, M., Stretching of capsules in an elongation flow, a route to constitutive law, J Fluid Mech, 767, R3, (2015) |
| [6] | Sui, Y.; Chen, X.; Chew, Y.; Roy, P.; Low, H., Numerical simulation of capsule deformation in simple shear flow, Comput Fluids, 39, 2, 242-250, (2010) · Zbl 1242.76280 |
| [7] | Sui, Y.; Low, H.; Chew, Y.; Roy, P., A front-tracking lattice Boltzmann method to study flow-induced deformation of three-dimensional capsules, Comput Fluids, 39, 3, 499-511, (2010) · Zbl 1242.76281 |
| [8] | Ye, H.; Huang, H.; Lu, X.-Y., Numerical study on dynamic sorting of a compliant capsule with a thin shell, Comput Fluids, 114, 110-120, (2015) · Zbl 1390.76787 |
| [9] | Skotheim, J.; Secomb, T., Red blood cells and other nonspherical capsules in shear flow: oscillatory dynamics and the tank-treading-to-tumbling transition, Phys Rev Lett, 98, 7, 078301, (2007) |
| [10] | Keller, S. R.; Skalak, R., Motion of a tank-treading ellipsoidal particle in a shear flow, J Fluid Mech, 120, 27-47, (1982) · Zbl 0503.76142 |
| [11] | Barthes-Biesel, D., Motion of a spherical microcapsule freely suspended in a linear shear flow, J Fluid Mech, 100, 04, 831-853, (1980) · Zbl 0456.76038 |
| [12] | Barthes-Biesel, D.; Rallison, J., The time-dependent deformation of a capsule freely suspended in a linear shear flow, J Fluid Mech, 113, 251-267, (1981) · Zbl 0493.76129 |
| [13] | Chang, K.; Olbricht, W., Experimental studies of the deformation of a synthetic capsule in extensional flow, J Fluid Mech, 250, 587-608, (1993) |
| [14] | Ramanujan, S.; Pozrikidis, C., Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities, J Fluid Mech, 361, 117-143, (1998) · Zbl 0921.76058 |
| [15] | Wang, Z.; Sui, Y.; Spelt, P. D.; Wang, W., Three-dimensional dynamics of oblate and prolate capsules in shear flow, Phys Rev E, 88, 5, 053021, (2013) |
| [16] | Sui, Y.; Chew, Y.; Roy, P.; Cheng, Y.; Low, H., Dynamic motion of red blood cells in simple shear flow, Phys Fluids, 20, 11, 112106, (2008) · Zbl 1182.76730 |
| [17] | Gao, T.; Hu, H. H.; Ponte Castañeda, P., Dynamics and rheology of elastic particles in an extensional flow, J Fluid Mech, 715, 573-596, (2013) · Zbl 1284.76379 |
| [18] | Dupin, M. M.; Halliday, I.; Care, C. M.; Alboul, L.; Munn, L. L., Modeling the flow of dense suspensions of deformable particles in three dimensions, Phys Rev E, 75, 6, 066707, (2007) |
| [19] | Finken R., Seifert U.. Wrinkling of microcapsules in shear flow. arXiv preprint cond-mat/06015892006. |
| [20] | Walter, A.; Rehage, H.; Leonhard, H., Shear induced deformation of microcapsules: shape oscillations and membrane folding, Colloid Surf A, 183, 123-132, (2001) |
| [21] | Barthès-Biesel, D., Capsule motion in flow: deformation and membrane buckling, Comptes Rendus Physique, 10, 8, 764-774, (2009) |
| [22] | Fischer, T. M., Shape memory of human red blood cells, Biophys J, 86, 5, 3304-3313, (2004) |
| [23] | Bagchi, P.; Kalluri, R. M., Dynamics of nonspherical capsules in shear flow, Phys Rev E, 80, 1, 016307, (2009) |
| [24] | Finken, R.; Kessler, S.; Seifert, U., Micro-capsules in shear flow, J Phys, 23, 18, 184113, (2011) |
| [25] | Noguchi, H., Dynamic modes of microcapsules in steady shear flow: effects of bending and shear elasticities, Phys Rev E, 81, 5, 056319, (2010) |
| [26] | Noguchi, H., Swinging and synchronized rotations of red blood cells in simple shear flow, Phys Rev E, 80, 2, 021902, (2009) |
| [27] | Vlahovska, P.; Young, Y.-N.; Danker, G.; Misbah, C., Dynamics of a non-spherical microcapsule with incompressible interface in shear flow, J Fluid Mech, 678, 221-247, (2011) · Zbl 1241.76473 |
| [28] | Cordasco, D.; Yazdani, A.; Bagchi, P., Comparison of erythrocyte dynamics in shear flow under different stress-free configurations, Phys Fluids, 26, 4, 041902, (2014) |
| [29] | Peng, Z.; Mashayekh, A.; Zhu, Q., Erythrocyte responses in low-shear-rate flows: effects of non-biconcave stress-free state in the cytoskeleton, J Fluid Mech, 742, 96-118, (2014) |
| [30] | Yazdani, A. Z.; Bagchi, P., Phase diagram and breathing dynamics of a single red blood cell and a biconcave capsule in dilute shear flow, Phys Rev E, 84, 2, 026314, (2011) |
| [31] | Deschamps, J.; Kantsler, V.; Segre, E.; Steinberg, V., Dynamics of a vesicle in general flow, Proc Nat Acad Sciences, 106, 28, 11444-11447, (2009) · Zbl 1203.76005 |
| [32] | Jeffery, G. B., The motion of ellipsoidal particles immersed in a viscous fluid, Proc R Soc London A, 102, 161-179, (1922) · JFM 49.0748.02 |
| [33] | Roscoe, R., On the rheology of a suspension of viscoelastic spheres in a viscous liquid, J Fluid Mech, 28, 02, 273-293, (1967) · Zbl 0145.46304 |
| [34] | Sui, Y.; Chew, Y.-T.; Roy, P.; Low, H.-T., A hybrid method to study flow-induced deformation of three-dimensional capsules, J Comput Phys, 227, 12, 6351-6371, (2008) · Zbl 1160.76028 |
| [35] | Gao, T.; Hu, H. H.; Castañeda, P. P., Shape dynamics and rheology of soft elastic particles in a shear flow, Phys Rev Lett, 108, 5, 058302, (2012) |
| [36] | Lebedev, V.; Turitsyn, K.; Vergeles, S., Dynamics of nearly spherical vesicles in an external flow, Phys Rev Lett, 99, 21, 218101, (2007) |
| [37] | Kaoui, B.; Farutin, A.; Misbah, C., Vesicles under simple shear flow: elucidating the role of relevant control parameters, Phys Rev E, 80, 6, 061905, (2009) |
| [38] | Wang, Z.; Shi, D.; Zhang, A., Three-dimensional lattice Boltzmann simulation of bubble behavior in a flap-induced shear flow, Comput Fluids, 123, 44-53, (2015) · Zbl 1390.76777 |
| [39] | Yu, D.; Girimaji, S. S., Multi-block lattice Boltzmann method: extension to 3d and validation in turbulence, Physica A, 362, 1, 118-124, (2006) |
| [40] | Guo, Z.; Zheng, C.; Shi, B., Discrete lattice effects on the forcing term in the lattice Boltzmann method, Phys Rev E, 65, 4, 046308, (2002) · Zbl 1244.76102 |
| [41] | Zou, Q.; He, X., On pressure and velocity boundary conditions for the lattice Boltzmann bgk model, Phys Fluids, 9, 6, 1591-1598, (1997) · Zbl 1185.76873 |
| [42] | Kessler, S.; Finken, R.; Seifert, U., Elastic capsules in shear flow: analytical solutions for constant and time-dependent shear rates, Eur Phys J E:, 29, 4, 399-413, (2009) |
| [43] | Batchelor, G., The stress system in a suspension of force-free particles, J Fluid Mech, 41, 03, 545-570, (1970) · Zbl 0193.25702 |
| [44] | Huang, H.; Yang, X.; Krafczyk, M.; Lu, X.-Y., Rotation of spheroidal particles in Couette flows, J Fluid Mech, 692, 369-394, (2012) · Zbl 1250.76172 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
