論文

We consider a rigid spherical particle immersed in a binary non-electrolyte fluid mixture which lies in the one-phase region near the demixing critical point. Mixture components differently interact with the particle surface, which generates preferential adsorption of one component onto the surface. The resultant inhomogeneity in composition, significant owing to the near criticality, causes particle motion under an imposed temperature gradient, i.e., thermophoresis. Using hydrodynamics based on a coarse-grained free-energy density, we calculate the thermophoretic mobility of the particle, far from which the critical composition is assumed. As expected from the recently predicted direction of thermoosmosis of a mixture, our numerical results show that the particle moves toward the colder side in a mixture near the upper consolute point and toward the warmer side in a mixture near the lower consolute point regardless of which mixture component is adsorbed onto the surface. This property, stemming from the requirement of the free-energy density for describing the phase separation, should hold in general and be able to be examined experimentally.

A large amount of binary fluid mixture in the homogeneous phase near the demixing critical point can include a small spherical droplet of a third fluid-component confined by a sharp interface. Conversely, a droplet consisting of the mixture can be immersed in the third fluid-component. In either of the situations, we assume that the third component attracts one mixture component more than the other via short-range interactions. The adsorption layer, enriched with the preferred component, appears on the mixture side of the interface and can thicken significantly because of large susceptibility. The preferential adsorption affects flows, causing the drag coefficient to deviate. We use the hydrodynamics based on a coarse-grained free-energy functional to calculate the deviation, while neglecting the weak singularity of mixture viscosity. When the mixture lies inside the droplet, the ratio of the deviation changes nonmonotonically as the ratio of the ambient viscosity to the droplet viscosity increases. When the mixture lies outside, the deviation ratio increases with the viscosity ratio and can be considerably larger for a droplet than for a rigid sphere. Then, if a composition gradient is imposed, a force-free droplet undergoes diffusiophoresis, whose mobility can be considerably larger in magnitude than that of a rigid sphere. These results can be utilized in future applications in the droplet microfluidics. We also discuss probable power-law dependences of the drag coefficient and the mobility on the reduced temperature. The suggested power for the mobility is connected with the universal order-parameter profile in the surface critical behavior.

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point, and study its transport through a capillary tube linking two large reservoirs. We assume that short-range interactions cause preferential adsorption of one component onto the tube's wall. The adsorption layer can become much thicker than the molecular size, which enables us to apply hydrodynamics based on a coarse-grained free-energy functional. For transport processes induced by gradients of the pressure, composition, and temperature along a cylindrical tube, we obtain the formulas of the Onsager coefficients to extend our previous results on isothermal transport, assuming the critical composition in the middle of each reservoir in the reference equilibrium state. Among the processes, we focus on thermo-osmosis - mass flow due to a temperature gradient. We explicitly derive a formula for the thermal force density, which is nonvanishing in the adsorption layer and causes thermo-osmosis. This formula for a near-critical binary fluid mixture is an extension of the conventional formula for a one-component fluid, expressed in terms of local excess enthalpy. We predict that the direction of thermo-osmotic flow of a mixture near the upper (lower) consolute point is the same as (opposite to) that of the temperature gradient, irrespective of which component is adsorbed on the wall. Our procedure would also be applied to dynamics of a soft material, whose mesoscopic inhomogeneity can be described by a coarse-grained free-energy functional.

We assume that a binary fluid mixture, lying in the one-phase region near the demixing critical point, contains a Brownian particle trapped by a harmonic potential. A mixture component, preferred by the particle surface via a short-range interaction, concentrates near the surface to generate a thick adsorption layer. This layer, deformed by particle motion, increases the effective mass and restoring force, thereby reducing the equal-time correlation of the fluctuations of the particle position and that of the particle velocity. We calculate these fluctuation amplitudes using the reversible part of hydrodynamics on the basis of the free-energy density of a local functional theory, which is known to describe the critical properties well. The effects of the preferential adsorption are negligible when the stiffness of the trapping potential is sufficiently large. A typical stiffness below which the effects emerge is largely determined by the strength of preferential adsorption and shifts toward larger stiffness as the adsorption is stronger. Plots of the fluctuation amplitudes against the stiffness are approximately independent of the deviation of the temperature from the critical temperature. These properties should facilitate future experimental studies on this phenomenon.

We assume that two parallel plates are immersed in a binary fluid mixture lying in the one-phase region near the demixing critical point and that the surface of each plate attracts the mixture components differently via short-range interactions. It is known that the composition inhomogeneity caused by the difference can induce a force exerted on the plate at equilibrium. In the present study, we investigate how a temperature gradient imposed vertically on the plates changes the induced force by calculating the composition profile subject to the Soret effect. Numerically solving the derived differential equation, we show that a temperature gradient within the critical regime can change the force distinctly from its equilibrium value and can make the force direction opposite to the one at equilibrium.

We consider a binary fluid mixture, which lies in the one-phase region near the demixing critical point. Short-range interactions between the mixture components and a solid surface in contact with the mixture can make the mixture composition inhomogeneous significantly near the surface. This inhomogeneity has been shown to cause various phenomena by using the renormalized local functional theory. In its free-energy density, the order-parameter field is coarse-grained without rescaled and only the most singular part is specified. In the present study, on the basis of the crossover theory, we introduce a square-gradient term to the free-energy density of the extended non-random two-liquid model, which includes more than the most singular part. Thanks to similarity between the renormalized local functional theory and the crossover theory, the relationship between the two free-energy densities can be clarified. Supposing a mixture of nitroethane and 3-methylpentane and a mixture of 2,6-lutidine and water, we use the proposed free-energy density to calculate the inhomogeneous composition profile numerically. The free-energy density also enables us to calculate excess densities of entropy and enthalpy, unlike that of the renormalized local functional theory. We also find that the magnitude of the thermal force density, which is induced by a temperature gradient to cause flow in thermoosmosis, can depend on the calculation procedures significantly.

We study isothermal transport of a binary fluid mixture, which lies in the homogeneous phase near the demixing critical point, through a capillary tube. A short-range interaction is assumed between each mixture component and the tube's wall surface, which usually attracts one component more than the other. The resulting preferential adsorption becomes significant owing to large osmotic susceptibility. The mixture flowing out of the tube is rich in the preferred component when flow is driven by the pressure difference between the reservoirs. When flow is driven by the mass-fraction difference, the total mass flow occurs in the presence of the preferential adsorption. These phenomena can be regarded as cross-effects linked by the reciprocal relation. The latter implies that diffusioosmosis arises from the free energy of the bulk of the mixture not involving the surface potential, unlike usual diffusioosmosis far from the critical point. We also study these phenomena numerically by using the hydrodynamics based on the coarse-grained free-energy functional, which was previously obtained to reveal near-critical static properties, and using material constants that were previously obtained in some experimental studies. Influence of the critical enhancement of the transport coefficients is found to be negligible because of off-critical composition in the tube. It is also shown that the conductance, or the total mass flow rate under a given mass-fraction difference, can change non-monotonically with the temperature. The change is well expected to be large enough to be detected experimentally.

© 2017 Cambridge University Press. 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.

© 2018 The Physical Society of Japan. We calculate the drag coefficient of a circular liquid domain, which is placed 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 a significant composition gradient outside the domain, which 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 markedly decreases 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 secondly 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.

©2018 The Physical Society of Japan. When a rigid spherical particle is put in a binary fluid mixture lying in the homogeneous phase near the demixing critical point, one of the fluid components is expected to be significantly concentrated around the particle because it is attracted preferentially by the particle surface. The resultant gradient of the mixture composition causes an additional pressure including osmotic pressure. We study how this pressure changes the particle motion by using the Gaussian free-energy functional for the mixture and assuming a correlation length much smaller than the particle size. The drag coefficient in this situation was calculated in the regime of sufficiently weak preferential attraction in a previous study [R. Okamoto, Y. Fujitani, and S. Komura, J. Phys. Soc. Jpn. 82, 084003 (2013)]. We here devise a new procedure beyond the regime to calculate the drag coefficient and the long-time tail of the velocity correlation of the particle. Our results cannot be explained totally by effective enlargement of the particle due to the layer rich in the preferred component.

We consider the Brownian motion of a rigid spherical particle in a binary fluid mixture, which lies in the homogeneous phase near the demixing critical point, assuming that neither component is more attracted by the particle surface. In a recent study, it was experimentally shown that the self-diffusion coefficient first decreases and then reaches a plateau as the critical point is approached. The decrease should reflect the critical enhancement of the viscosity, while the plateau was interpreted as representing the suppression of the enhancement due to the shear around the particle. To examine this interpretation, we take into account the local shear rate to calculate the dependence of the drag coefficient on the particle speed, and then utilize a Langevin equation to calculate the self-diffusion coefficient.

The drag coefficient of a rigid spherical particle deviates from Stokes law when it is put into a near-critical fluid mixture in the homogeneous phase with the critical composition. The deviation is experimentally shown to depend approximately linearly on the correlation length of the composition fluctuation far from the particle , and is suggested to be caused by the preferential adsorption between one component and the particle surface. In contrast, the dependence was shown to be much steeper in the previous theoretical studies based on the Gaussian free-energy density. In the vicinity of the particle, especially when the adsorption of the preferred component makes the composition strongly off-critical, the correlation length becomes very small as compared with. This spatial inhomogeneity, not considered in the previous theoretical studies, can influence the dependence of on. To examine this possibility, we here apply a renormalized local functional theory, describing the preferential adsorption in terms of the surface field. This theory was previously proposed to explain the interaction of walls immersed in a (near-)critical binary fluid mixture. The free-energy density in this theory, coarse-grained up to the local correlation length, has a very complicated dependence on the order parameter, as compared with the Gaussian free-energy density. Still, a concise expression of the drag coefficient, which was derived in one of the previous theoretical studies, turns out to be valid in the present formulation. We show that, as becomes larger, the dependence of on becomes distinctly gradual and close to the linear dependence.

We consider placing a rigid spherical particle into a binary fluid mixture in the homogeneous phase near the demixing critical point. The particle surface is assumed to have a short-range interaction with each mixture component and to attract one component more than the other. Owing to large osmotic susceptibility, the adsorption layer, where the preferred component is more concentrated, can be of significant thickness. This causes a particle motion under an imposed composition gradient. Thus, diffusiophoresis emerges from a mechanism which has not been considered so far. We calculate how the mobility depends on the temperature and particle size.

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