Drag Coefficient of a Liquid Domain in a Fluid Membrane

Abstract

We calculate the drag coefficient of a circular liquid domain in a flat fluid membrane, which is surrounded by threedimensional fluids, by using the Stokes approximation. Taking into account the difference between the membrane viscosities inside and outside the domain, we obtain an integral equation involving a parameter, which is defined as unity minus the ratio of the latter viscosity to the former. We solve the equation up to the linear order with respect to the parameter to calculate the drag coefficient numerically. Its derivative with respect to the domain viscosity, evaluated when there is no difference between the membrane viscosities, is shown to almost vanish.

Drag Coefficient of a Liquid Domain in a Fluid Membrane Almost as Viscous as the Domain

“…10, while general cases were studied in ref. 9. We set the Cartesian coordinate system so that the xy plane coincides with the membrane and so that the origin is at the domain center.…”

“…5,6) Large circular raftlike domains can also be observed in artificial membranes. 7,8) In the author's previous work, 9) we considered a flat incompressible fluid membrane surrounded by incompressible 3D fluids on both sides (Fig. 1).…”

Drag Coefficient of a Liquid Domain in a Fluid Membrane Surrounded by Confined Three-Dimensional Fluids

“…This tricky problem arises irrespective of the existence of the walls, but has not been considered in previous studies including the present author's for unconfined surroundings. 7,8) In this paper, we correct the errors in Refs. 7 and 8, and study the effects of confined surroundings.…”

“…The present author previously studied the drag coefficient of a liquid domain in a flat fluid membrane surrounded by 3D fluids occupying semi-infinite spaces on both sides, taking into account a possible difference between the membrane viscosities inside and outside the domain. 7,8) In some practical situations, however, the 3D fluid cannot be considered to occupy a semi-infinite space because the container wall is close to the membrane, for example. In fact, in Ref.…”

Hydrodynamic Effect on Concentration Fluctuation in a Two-Component Fluid Membrane with a Spherical Shape

“…It is known that the diffusion coefficient of a disk having radius A in a fluid membrane is almost proportional to k B T =ð AÞ when A is much larger than = , and to k B T lnf =ð AÞg= when A is much smaller than = . [30][31][32][33][34] The diffusion coefficient of a spherical rigid body in a 3D fluid also has the power dependence, while that of a disk in a purely 2D fluid also has the logarithmic dependence, derived by means of Oseen's approximation. 23,35) Thus, the motion of an object in a fluid membrane is considered to cause significant flow in the surrounding 3D fluids if it is much larger than = , but negligible flow if it is much smaller than = .…”