Semi-analytic solutions for elastic capsules in 2D flow
نویسندگان
چکیده
Elastic capsules occur in nature in the form of cells and vesicles and are manufactured for biomedical applications. They are widely modeled but there are few analytical results. In this paper, complex variable techniques are used to derive semi-analytic solutions for the steady-state response and timedependent evolution of elastic capsules in 2D Stokes flow. This provides a complete picture of the steady response of initially circular capsules in canonical linear strain and shear flows as a function of the capillary number Q. The analysis is complemented by spectrally accurate numerical simulations of the time-dependent evolution. An imposed nonlinear strain that models the far-field velocity in Taylor’s four roller mill is found to lead to cusped steady shapes at a critical capillary number Qc. Numerical simulation of the time-dependent evolution for Q > Qc shows the development of finite-time cusp singularities. The dynamics immediately prior to cusp formation are asymptotically self-similar, and the similarity exponents are predicted analytically and confirmed numerically. This appears to be the first example of finite-time singularity formation in fluid flow with elastic interfaces.
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تاریخ انتشار 2011