Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31100
Capsule-substrate Adhesion in the Presence of Osmosis by the Immersed Interface Method

Authors: P.G. Jayathilake, B.C. Khoo, Zhijun Tan


A two-dimensional thin-walled capsule of a flexible semi-permeable membrane is adhered onto a rigid planar substrate under adhesive forces (derived from a potential function) in the presence of osmosis across the membrane. The capsule is immersed in a hypotonic and diluted binary solution of a non-electrolyte solute. The Stokes flow problem is solved by the immersed interface method (IIM) with equal viscosities for the enclosed and surrounding fluid of the capsule. The numerical results obtained are verified against two simplified theoretical solutions and the agreements are good. The osmotic inflation of the adhered capsule is studied as a function of the solute concentration field, hydraulic conductivity, and the initial capsule shape. Our findings indicate that the contact length shrinks in dimension as capsule inflates in the hypotonic medium, and the equilibrium contact length does not depend on the hydraulic conductivity of the membrane and the initial shape of the capsule.

Keywords: Fluid Mechanics, mass transfer, osmosis, Capsule-substrate adhesion, Immersed interface method

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1334


[1] T. A. Springer, "Traffic signals on endothelium for lymphocyte recirculation and leukocyte emigration," Annu. Rev. Physiol., vol. 57, pp. 827-872, 1995.
[2] D. B. Khismatullin and G. A. Truskey, "A 3D numerical study of the effect of channel height on leukocyte deformation and adhesion in parallel plate flow chambers," Microvasc. Res., vol. 68, pp. 188-202, 2004.
[3] C. Dong and X. X. Lei, "Biomechanics of cell rolling: shear flow, cellsurface adhesion, and cell deformability," J. Biomech., vol. 33, pp. 35- 43, 2000.
[4] V. Pappu, S. K. Doddi and P. Bagchi, "A computational study of leukocyte adhesion and its effect on flow pattern in microvessels," J. Theor. Biol., vol. 254, pp. 483-498, 2008.
[5] V. Pappu and P. Bagchi, "3D computational modeling and simulation of leukocyte rolling adhesion and deformation," Comput. Biol. Med., vol. 38, pp. 738-753, 2008.
[6] K. T. Wan and K. K. Liu, "Contact mechanics of a thin-walled capsule adhered onto a rigid planar substrate," Med. Biol. Eng. Comput., vol. 39, pp. 605-608, 2001.
[7] R. M. Servuss and W. Helfrich, "Mutual adhesion of lecithin membranes at ultralow tensions," J. Phys., vol. 50, pp. 809-827, 1989.
[8] K. D. Tachev, J. K. Angarska, K. D. Danov, and P. A. Kralchevsky, "Erythrocyte attachment to substrates: determination of membrane tension and adhesion energy," Colloid. Surface B., vol. 19, pp. 61-80, 2000.
[9] J. J. Foo, V. Chan, and K. K. Liu, "Contact deformation of liposome in the presence of osmosis," Ann. Biomed. Eng., vol. 31, pp. 1279-1286, 2003.
[10] J. J. Foo, V. Chan, and K. K. Liu, "Coupling bending and shear effects on liposome deformation," J. Biomech., vol. 39, pp. 2338-2343, 2006.
[11] K. K. Liu and K. T. Wan, "New model to characterize cell-substrate adhesion in the presence of osmosis," Med. Biol. Eng. Comput., vol. 38, pp. 690-691, 2000.
[12] K. K. Liu, V. Chan, and Z. Zhang, "Capsule-sunstrate contact deformation: determination of adhesion energy," Med. Biol. Eng. Comput., vol. 40, pp. 491-495, 2002a.
[13] K. K. Liu, H. G. Wang, K. T. Wan, T. Liu, and T. Zhang, "Characterizing capsule-substrate adhesion in presence of osmosis," Colloid. Surface B., vol. 25, pp. 293-298, 2002b.
[14] C. S. Peskin, "Numerical analysis of blood flow in the heart," J. Comput. Phys., vol. 25, pp. 220-252, 1977.
[15] N. A. N-Dri, W. Shyy, and R. Tran-Son-Tay, "Computational modeling of cell adhesion and movement using a continuum-Kinetics Approach," Biophys. J., vol. 85, pp. 2273-2286, 2003.
[16] S. Jadhav, K.Y. Chan, K. Konstantinos, and C. D. Eggleton, "Shear modulation of intercellular contact area between two deformable cells colliding under flow," J. Biomech., vol. 40, pp. 2891-2897, 2007.
[17] R. J. LeVeque and Z. Li, "The immersed interface method for elliptic equations with discontinuous coefficients and singular sources," SIAM J. Numer. Anal., vol. 31, pp. 1019-1044, 1994.
[18] Z. Li and M-C. Lai, "The immersed interface method for the Navier- Stokes equations with singular forces," J. Comput. Phys., vol. 171, pp. 822-842, 2001.
[19] M-C. Lai and H. C. Tseng, "A simple implementation of the immersed interface methods for Stokes flows with singular forces," Comput. Fluids., vol. 37, pp. 99-106, 2008.
[20] D. V. Le, B. C. Khoo, and J. Peraire, "An immersed interface method for viscous incompressible flows involving rigid and flexible boundaries," J. Comput. Phys., vol. 220, pp. 109-138, 2006.
[21] L. Lee and R. J. LeVeque, "An immersed interface method for the incompressible Navier-Stokes equations," SIAM J. Sci. Comput., vol. 25, pp. 832-856, 2003.
[22] R. J. LeVeque and Z. Li, "Immersed interface methods for Stokes flow with elastic boundaries or surface tension," SIAM J. Sci. Comput., vol. 18, pp. 709-735, 1997.
[23] Z. Li, "An overview of the immersed interface method and its applications," Taiwan. J. Math., vol. 7, pp. 1-49, 2003.
[24] M. N. Linnick and H. F. Fasel, "A high-order immersed interface method for simulating unsteady incompressible flows on irregular domains," J. Comput. Phys., vol. 204, pp. 157-192, 2005.
[25] Z. Tan, D. V. Le, Z. Li, K. M. Lim, and B. C. Khoo, "An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane," J. Comput. Phys., vol. 227, pp. 9955-9983, 2008.
[26] S. Xu and Z. J. Wang, "An immersed interface method for simulating the interaction of a fluid with moving boundaries," J. Comput. Phys., vol. 216, pp. 454-493, 2006.
[27] A. T. Layton, "Modeling water transport across elastic boundaries using an explicit jump method," SIAM J. Sci. Comput., vol. 28, pp. 2189-2207, 2006.
[28] O. Kedem and A. Katchalsky, "Thermodynamics Analysis of the Permeability of Biological Membranes to Non-electrolytes," Biochim. Biophys. Acta, vol. 27, pp. 229-246, 1958.
[29] Z. Li, X. Wan, K. Ito, and S. R. Lubkin, "An augmented approach for the pressure boundary condition in a stokes flow," Commun. Comput. Phys., vol. 5, pp. 874-885, 2006.
[30] Z. Li and K. Ito, "The Immersed Interface Method: Numerical solutions of PDEs involving interfaces and irregular domains," USA, 2006.
[31] P. G. Jayathilake, Z.-J. Tan, B. C. Khoo, and N. E. Wijeysundera, "Deformation and osmotic swelling of an elastic membrane capsule in Stokes flows by the immersed interface method," Chem. Eng. Sci, to be published, 2009.
[32] I. Contat and C. Misbah, "Dynamics and similarity laws for adhering vesicles in haptotaxis," Phys. Rev. Lett., vol. 83, pp. 235-238, 1999.
[33] Y. Liu, L. Zhaing, X. Wang, and W. K. Liu, "Coupling of Navier- Stokes equations with protein molecular dynamics and its application to hemodynamics," Int. J. Numer. Meth. Fl., vol. 46, pp. 1237-1252, 2004.
[34] J. Zhang, P.C. Johnson, and A.S. Popel, "Red blood cell aggregation and dissociation in shear flows simulated by lattice Boltzmann method," J. Biomech., vol. 41, pp. 47-55, 2008.
[35] C. X. Wang, L. Wang, and C.R. Thomas, "Modelling the mechanical properties of single suspension-cultured tomato cells," Ann. Bot- London, vol. 93, pp. 443-453, 2004.
[36] D. Zinemanas, A. Nir, "Osmophoretic motion of deformable particles," Int. J. Multiphas. Flow, vol. 21, pp. 787-800, 1995.