Numerical modeling of the behavior of an elastic capsule in a microchannel flow: The initial motion

Microcapsule mechanics: from stability to function

Microcapsules are reviewed with special emphasis on the relevance of controlled mechanical properties for functional aspects. At first, assembly strategies are presented that allow control over the decisive geometrical parameters, diameter and wall thickness, which both influence the capsule's mechanical performance. As one of the most powerful approaches the layer-by-layer technique is identified. Subsequently, ensemble and, in particular, single-capsule deformation techniques are discussed. The latter generally provide more in-depth information and cover the complete range of applicable forces from smaller than pN to N. In a theory chapter, we illustrate the physics of capsule deformation. The main focus is on thin shell theory, which provides a useful approximation for many deformation scenarios. Finally, we give an overview of applications and future perspectives where the specific design of mechanical properties turns microcapsules into (multi-)functional devices, enriching especially life sciences and material sciences.

Micro-capsules in shear flow

This paper deals with flow-induced shape changes of elastic capsules. The state of the art concerning both theory and experiments is briefly reviewed starting with dynamically induced small deformation of initially spherical capsules and the formation of wrinkles on polymerized membranes. Initially non-spherical capsules show tumbling and tank-treading motion in shear flow. Theoretical descriptions of the transition between these two types of motion assuming a fixed shape are at odds with the full capsule dynamics obtained numerically. To resolve the discrepancy, we expand the exact equations of motion for small deformations and find that shape changes play a dominant role. We classify the dynamical phase transitions and obtain numerical and analytical results for the phase boundaries as a function of viscosity contrast, shear and elongational flow rate. We conclude with perspectives on time-dependent flow, on shear-induced unbinding from surfaces, on the role of thermal fluctuations and on applying the concepts of stochastic thermodynamics to these systems.

Inertial migration of an elastic capsule in a Poiseuille flow

The inertial migration of a two-dimensional elastic capsule in a Poiseuille flow was studied over the Reynolds number range 1 ≤ Re ≤ 100. The lateral migration velocity, slip velocity, and the deformation and inclination angle of the capsule were investigated by varying the lateral position, Reynolds number, capsule-to-channel size ratio (λ), membrane stretching coefficient (ϕ), and membrane bending coefficient (γ). During the initial transient motion, the lateral migration velocity increased with increasing Re and λ, but decreased with increases in ϕ, γ, and the lateral distance from the wall. On the other hand, the deformation of the capsule increased and the inclination angle became smaller as Re, ϕ, γ, and the distance from the wall decreased. The initial behavior of the capsule was influenced by variation in the initial lateral position (y(0)), but the equilibrium position of the capsule was not affected by such variation. The balance between the wall effect and the shear gradient effect determined the equilibrium position. As Re increased, the equilibrium position initially shifted closer to the wall and then moved toward the channel center. A peak in the equilibrium position was observed near Re = 30 for λ = 0.1, and the peak shifted to higher Re as λ increased. Depending on the lateral migration velocity, the equilibrium position moved toward the centerline for larger λ, but moved toward the wall for larger ϕ and γ.

Modeling performance of a two-dimensional capsule in a microchannel flow: long-term lateral migration

The long-term lateral migration of a two-dimensional elastic capsule in a microchannel is studied numerically in this paper. The numerical method combines a finite volume technique for solving the fluid problem with a front tracking technique for capturing and tracking the capsule membrane. The capsule is modeled as a liquid medium enclosed by a thin membrane which has linear elastic properties. The capsule, whose initial shape is circle and which starts from a near-center position or a near-wall position, experiences tilting and membrane tank-treading, and migrates laterally when moving along the surrounding flow. The lateral migration demonstrates the existence of lift effect of surrounding flow on moving capsule. Before capsule approaches to the microchannel centerline closely, lower membrane dilation modulus and lower viscosity ratio tend to result in faster lateral migration. The initial position also influences the performance behavior of capsule, despite the lateral migration of capsule is a quasisteady process. Small difference in capsule behavior when capsule is not near to the microchannel centerline might lead to significant difference in capsule behavior when capsule approaches closely to the centerline. When capsules are near to microchannel wall, the effect of the wall on capsule behavior might dominate, leading to relatively faster lateral migration. When capsules are not far from microchannel centerline, the effect of the nonlinearity of Poiseuille flow might dominate, resulting in relatively slower lateral movement. When capsules are located closely to the centerline, they behave differently, where the reason still remains poorly understood and it will be one of our future studies. The comparison between the capsule behavior from the present simulation and that by the migration law proposed by Coupier [Phys. Fluids 20, 111702 (2008)] shows that the behavioral agreement for near-wall capsule is better than that for near-center capsule, and the best agreement occurs to the near-wall capsule with intermediate membrane dilation modulus and highest viscosity ratio.