Stationary shapes of deformable particles moving at low Reynolds numbers
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We introduce an iterative solution scheme in order to calculate stationary shapes of deformable elastic capsules which are steadily moving through a viscous fluid at low Reynolds numbers. The iterative solution scheme couples hydrodynamic boundary integral methods and elastic shape equations to find the stationary axisymmetric shape and the velocity of an elastic capsule moving in a viscous fluid governed by the Stokes equation. We use this approach to systematically study dynamical shape transitions of capsules with Hookean stretching and bending energies and spherical resting shape sedimenting under the influence of gravity or centrifugal forces. We find three types of possible axisymmetric stationary shapes for sedimenting capsules with fixed volume: a pseudospherical state, a pear-shaped state, and buckled shapes. Capsule shapes are controlled by two dimensionless parameters, the Föppl-von-Kármán number characterizing the elastic properties and a Bond number characterizing the driving force. For increasing gravitational force the spherical shape transforms into a pear shape. For very large bending rigidity (very small Föppl-von-Kármán number) this transition is discontinuous with shape hysteresis. The corresponding transition line terminates, however, in a critical point, such that the discontinuous transition is not present at typical Föppl-von-Kármán numbers of synthetic capsules. In an additional bifurcation, buckled shapes occur upon increasing the gravitational force.
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- 6.R. Clift, J. Grace, M. Weber, Bubbles, Drops, and Particles (Academic Press, New York, 1978)Google Scholar
- 21.G.K. Batchelor, An introduction to fluid dynamics (Cambridge University Press, Cambridge, 2000)Google Scholar
- 22.A. Libai, J. Simmonds, The Nonlinear Theory of Elastic Shells (Cambridge University Press, Cambridge 1998)Google Scholar
- 23.C. Pozrikidis, Modeling and Simulation of Capsules and Biological Cells (CRC Press, Boca Raton, 2003)Google Scholar
- 26.L. Landau, E. Lifshitz, Theory of Elasticity (Pergamon, New York, 1986)Google Scholar
- 27.J. Happel, H. Brenner, Low Reynolds Number Hydrodynamics: With Special Applications to Particulate Media (Martinus Nijhoff Publishers, The Hague, 1983)Google Scholar
- 28.C. Pozrikidis, Boundary Integral and Singularity Methods for Linearized Viscous Flow (Cambridge University Press, Cambridge, 1992)Google Scholar