Dynamics of the hydrodynamic thin film drainage between a capsule and a solid boundary in flow is crucial to adhesion of capsules, and therefore, to the stability and effectiveness of capsule products. Although there have been numerous studies for drops and initially stress-free vesicles, this phenomenon is still not well understood when capsules or preinflated membrane bound particles are involved. Based on the existing theories for drops and vesicles, we have derived scaling theories in a more general way to allow for a non-uniform and non-isotropic tension profile on the membrane, which is usually the case for capsules, and also included the effect of preinflation. These scaling theories were then compared with simulations using a numerical model coupling the boundary integral method for the motion of the fluids and a finite element method for the membrane mechanics. Surprisingly, we find that the only relevant modulus for capsules in the drainage process is the area dilation modulus K s , which is often deemed to be of secondary importance compared to the shear modulus G s or the surface Young's modulus in studies of capsule dynamics. This leads to the fact that the drainage behavior of an initially stress-free capsule is similar to an initially stress-free vesicle, in spite of the additional shear modulus that is present for capsules. We also find that the drainage behavior of a prestressed capsule or a prestressed vesicle is similar to a drop with an immobile interface in a weak flow. C 2014 AIP Publishing LLC. [http://dx.
The adhesion and detachment of a capsule on a solid boundary surface is studied via a combination of scaling theory and numerical simulation and the behavior is compared and contrasted with a vesicle. It is shown that the dominant physical property for both capsules and vesicles is the area dilation modulus K s of the membrane. The nonzero shear modulus G s for capsules increases the resistance to deformation and thus decreases slightly the equilibrium contact radius for an adhered capsule compared to an adhered vesicle. The detachment process in this study is due to an external axisymmetric flow. Unlike a rigid body that must be pulled away without change of shape, capsules (and vesicles) almost always detach dominantly by peeling in which the contact radius decreases but the minimum separation distance does not change until the final moments of detachment. Compared to a vesicle with the same K s , a capsule maintains a more compact shape and is harder to elongate under a given external flow. Hence, the detachment process is slower for capsules compared to vesicles with the same K s .
The body-force-driven motion of a homogeneous distribution of spherically symmetric porous shells in an incompressible Newtonian fluid and the fluid flow through a bed of these shell particles are investigated analytically. The effect of the hydrodynamic interaction among the porous shell particles is taken into account by employing a cell-model representation. In the limit of small Reynolds number, the Stokes and Brinkman equations are solved for the flow field around a single particle in a unit cell, and the drag force acting on the particle by the fluid is obtained in closed forms. For a suspension of porous spherical shells, the mobility of the particles decreases or the hydrodynamic interaction among the particles increases monotonically with a decrease in the permeability of the porous shells. The effect of particle interactions on the creeping motion of porous spherical shells relative to a fluid can be quite significant in some situations. In the limiting cases, the analytical solution describing the drag force or mobility for a suspension of porous spherical shells reduces to those for suspensions of impermeable solid spheres and of porous spheres. The particle-interaction behavior for a suspension of porous spherical shells with a relatively low permeability may be approximated by that of permeable spheres when the porous shells are sufficiently thick.
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