RHEOLOGY AND SHAPE TRANSITIONS OF VESICLES UNDER CAPILLARY-FLOW

We present an analytical description of the rheology and shape of axis ymmetric vesicles flowing down narrow capillaries. The vesicle surface is described by the Helfrich bending energy. We find that the rheolog ical properties of the vesicle are independent of the Helfrich bending energy. The classical Bretherton theory for tense drops can be applie d provided we replace the drop tension with a ''dynamical tension'' di scussed in the text. Darcy's Law is obeyed with an effective permeabil ity which depends on the filling fraction and the dimensions of the ve sicle and the pore. For vesicles with tension, there are two rheologic al regimes. At low applied pressure heads, the vesicle moves very slow ly and violates Darcy's Law. With increasing-pressure gradient, there is a singular point beyond which the rear of the vesicle becomes tensi onless and Darcy's Law is obeyed. This singular point marks a whole se quence of shapes transitions of the vesicle, starting from a spherocyl inder and ending in a Bell shape, similar to those reported for red bl ood cells in the physiological literature.