Drag Coefficient of a Rigid Spherical Particle in a Near-Critical Binary Fluid Mixture

2013

J. Phys. Soc. Jpn.

Self Cite

We consider a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids, and assume that the membrane outside the domain is a two-dimensional near-critical binary fluid mixture. The membrane viscosity outside the domain is assumed to be uniform, irrespective of the local composition, and to be the same as that of the domain. Using the Gaussian free-energy functional, we show that the drag coefficient of the domain can be decreased by the preferential attraction between the domain and a component of the mixture, unlike that of a rigid sphere in a three-dimensional near-critical binary fluid mixture studied recently.

“…As in the model H, 22,31,32) we can use Eq. (2.1) to derive where the superscript ''T'' indicates the transposition.…”

Section: Dynamicsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Drag Coefficient of a Raftlike Domain Embedded in a Fluid Membrane Being a Near-Critical Binary Mixture

2013

J. Phys. Soc. Jpn.

Self Cite

“…The correlation length of the mixture is much smaller than the the domain size. Thus, the domain dynamics can be regarded as independent of the critical concentration fluctuation [40][41][42], which is remarkable at length scales smaller than the correlation length. The preferential attraction between the domain component and one component of the mixture is caused by a short-ranged interaction.…”

Section: Introductionmentioning

confidence: 99%

Drag Coefficient of a Circular Inclusion in a Near-Critical Binary Fluid Membrane

Tani

2018

J. Phys. Soc. Jpn.

Self Cite

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. *

Drag coefficient of a liquid domain with distinct viscosity in a fluid membrane

Tani

2017

J. Fluid Mech.

We calculate the drag coefficient of a circular liquid domain in a flat fluid membrane surrounded by three-dimensional fluids on both sides. The coefficient of a rigid disk is well known, while that of a circular liquid domain is also well known when the membrane viscosity inside the domain equals the one outside the domain. As the ratio of the former viscosity to the latter increases to infinity, the drag coefficient of a liquid domain should approach that of the disk of the same size in the same ambient viscosities. This approach has not yet been shown explicitly, however. When the ratio is not unity, the continuity of the stress makes the velocity gradient discontinuous across the domain perimeter in the membrane. On the other hand, the velocity gradient is continuous in the ambient fluids, whose velocity field should agree with that of the membrane as the spatial point approaches the membrane. This means that we need to assume dipole singularity along the domain perimeter in solving the governing equations unless the ratio is unity. In the present study, we take this singularity into account and obtain the drag coefficient of a liquid domain as a power series with respect to a dimensionless parameter, which equals zero when the ratio is unity and approaches unity when the ratio tends to infinity. As the parameter increases to unity, the sum of the series is numerically shown to approach the drag coefficient of the disk.