Flow around a circular pore of a flat and incompressible fluid-membrane

In terms of the steady Stokes approximation, we consider flow fields around a circular pore of a flat and incompressible fluid-membrane, which is surrounded by a three-dimensional fluid. Pore size changes because of the line tension of the pore perimeter and the in-plane stress of the membrane. The pressure difference across the membrane causes a three-dimensional flow through the pore. The dependence of its volumetric flow rate on the difference between the pressure far from the membrane on its one side and that on the other side is found to be the same as obtained previously for a pore of a solid plate. We derive a differential equation for the time evolution of pore size, considering the viscosity of the surrounding fluid.