TY - JOUR

T1 - Drag coefficient of a circular inclusion in a near-critical binary fluid membrane

AU - Tani, Hisasi

AU - Fujitani, Youhei

N1 - Publisher Copyright:
Copyright © 2018, The Authors. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2018/6/18

Y1 - 2018/6/18

N2 - We calculate the drag coefficient of a circular liquid domain, which is put in a flat fluid membrane composed of a binary fluid mixture lying in the homogeneous phase near the demixing critical point. Assuming a sufficiently small correlation length, we regard the domain dynamics as independent of the critical fluctuation and use the Gaussian free-energy functional for the mixture. Because of the near-criticality, the preferential attraction between the domain component and one of the mixture components generates the composition gradient outside the domain significantly and can affect the drag coefficient. We first consider a domain having the same membrane viscosity as the domain exterior. The drag coefficient is expanded with respect to a dimensionless strength of the preferential attraction. It is numerically shown that the magnitude of the expansion coefficient decreases much as the order of the strength increases and that the first-order term of the series usually gives a good approximation for practical material constants. The effect of the preferential attraction is shown to be able to become significantly large in practice. We second consider cases where the membrane viscosities of the domain interior and exterior are different. The first-order term of the expansion series decreases to approach zero as the domain viscosity increases to infinity. This agrees with previous numerical results showing that the hydrodynamics makes the effect of the preferential attraction negligibly small for a rigid disk.

AB - We calculate the drag coefficient of a circular liquid domain, which is put in a flat fluid membrane composed of a binary fluid mixture lying in the homogeneous phase near the demixing critical point. Assuming a sufficiently small correlation length, we regard the domain dynamics as independent of the critical fluctuation and use the Gaussian free-energy functional for the mixture. Because of the near-criticality, the preferential attraction between the domain component and one of the mixture components generates the composition gradient outside the domain significantly and can affect the drag coefficient. We first consider a domain having the same membrane viscosity as the domain exterior. The drag coefficient is expanded with respect to a dimensionless strength of the preferential attraction. It is numerically shown that the magnitude of the expansion coefficient decreases much as the order of the strength increases and that the first-order term of the series usually gives a good approximation for practical material constants. The effect of the preferential attraction is shown to be able to become significantly large in practice. We second consider cases where the membrane viscosities of the domain interior and exterior are different. The first-order term of the expansion series decreases to approach zero as the domain viscosity increases to infinity. This agrees with previous numerical results showing that the hydrodynamics makes the effect of the preferential attraction negligibly small for a rigid disk.

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M3 - Article

AN - SCOPUS:85094441328

JO - Mathematical Social Sciences

JF - Mathematical Social Sciences

SN - 0165-4896

ER -