DEFORMATION OF LIQUID CAPSULES ENCLOSED BY ELASTIC MEMBRANES IN SIMPLE SHEAR-FLOW - LARGE DEFORMATIONS AND THE EFFECT OF FLUID VISCOSITIES

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Rey nolds numbers using a boundary-element method. The surface of the caps ule is discretized into quadratic triangular elements that form an evo lving unstructured grid. The elastic membrane tensions are expressed i n terms of the surface deformation gradient, which is evaluated from t he position of the grid points. Compared to an earlier formulation tha t uses global curvilinear coordinates, the triangular-element formulat ion suppresses numerical instabilities due to uneven discretization an d thus enables the study of large deformations and the investigation o f the effect of fluid viscosities. Computations are performed for caps ules with spherical, spheroidal, and discoidal unstressed shapes over an extended range of the dimensionless shear rate and for a broad rang e of the ratio of the internal to surrounding fluid viscosities. Resul ts for small deformations of spherical capsules are in quantitative ag reement with the predictions of perturbation theories. Results for lar ge deformations of spherical capsules and deformations of non-spherica l capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially sph erical capsules deform into steady elongated shapes whose aspect ratio s increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed fo r any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymm etric capsules subject to a stagnation-point flow. When the sheer rate is sufficiently high and the viscosity ratio is sufficiently low, liq uid drops exhibit continuous elongation leading to breakup. Axisymmetr ic capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of caps ules in shear flow, large elastic tensions develop at large deformatio ns and prevent continued elongation, stressing the importance of the v orticity of the incident flow. The long-time behaviour of deformed cap sules depends strongly on the unstressed shape. Oblate capsules exhibi t unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sp hericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinni ng behaviour.