Near-Critical Binary Fluid Mixture Research Articles

Thermo-osmosis of a near-critical binary fluid mixture: A general formulation and universal flow direction.

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.

Effects of the preferential adsorption in a near-critical binary fluid mixture on dynamics of a droplet

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.

Isothermal transport of a near-critical binary fluid mixture through a capillary tube with the preferential adsorption

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.

Suppression of viscosity enhancement around a Brownian particle in a near-critical binary fluid mixture

Abstract

Drag coefficient of a rigid spherical particle in a near-critical binary fluid mixture, beyond the regime of the Gaussian model

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 ( $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}_{d}$ ) is experimentally shown to depend approximately linearly on the correlation length of the composition fluctuation far from the particle ( $\unicode[STIX]{x1D709}_{\infty }$ ), 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 $\unicode[STIX]{x1D709}_{\infty }$ . This spatial inhomogeneity, not considered in the previous theoretical studies, can influence the dependence of $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}_{d}$ on $\unicode[STIX]{x1D709}_{\infty }$ . 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 $\unicode[STIX]{x1D709}_{\infty }$ becomes larger, the dependence of $\unicode[STIX]{x0394}\unicode[STIX]{x1D6FE}_{d}$ on $\unicode[STIX]{x1D709}_{\infty }$ becomes distinctly gradual and close to the linear dependence.

Osmotic Effects on Dynamics of a Colloidal Rigid Sphere in a Near-Critical Binary Fluid Mixture

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 concent...

Onset of convection in a near-critical binary fluid mixture driven by concentration gradient

A linear stability analysis is conducted for the onset of natural convection driven by a concentration gradient in a horizontal layer of a near-critical binary fluid mixture. The problem is regarded as a limiting case of double-diffusive convection. The governing equations for small perturbations after normal-mode expansion are solved numerically with finite difference discretization to obtain the critical concentration Rayleigh number. It is found that, when the height of the fluid layer is small, the initial density stratification is negligible and the theoretical criterion developed under Boussinesq approximation with the modified Rayleigh number is accurate even extremely close to the critical point. However, for a large height, the initial density stratification makes the fluid layer become more unstable, and deviations from theoretical predictions are observed. We further propose a method to estimate these deviations, which can be used to check the applicability of the theoretical criterion. As the second part of the study, we apply the criterion to interpret the onset of convection for a transient problem: a near-critical binary fluid mixture confined in a two-dimensional cavity submitted to concentration increases at the bottom wall. The numerical results demonstrate four typical behaviours of the concentration boundary layer: onset of convection, collapse of the concentration boundary layer, return to stability, and remaining stable. Comparisons between numerical results and the stability criterion are made, where consistencies are found except for the behaviour of return to stability. We attribute the inconsistency to the existence of lateral walls, whose stabilizing effect is strong when the return to stability happens.

Osmotic Suppression of Positional Fluctuation of a Trapped Particle in a Near-Critical Binary Fluid Mixture in the Regime of the Gaussian Model

Suppose a spherical colloidal particle surrounded by a near-critical binary fluid mixture in the homogeneous phase. The particle surface usually preferentially attracts one component of the mixture...

Erratum: “Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture within the Regime of the Gaussian Model” [J. Phys. Soc. Jpn. 85, 044401 (2016)

Erratum: “Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture within the Regime of the Gaussian Model” [J. Phys. Soc. Jpn. 85, 044401 (2016)

Undulation Amplitude of a Fluid Membrane in a Near-Critical Binary Fluid Mixture Calculated beyond the Gaussian Model Supposing Weak Preferential Attraction

We calculate the mean square amplitude of the shape fluctuation -- an equal-time correlation -- of an almost planar fluid membrane immersed in a near-critical binary fluid mixture. One fluid component is usually preferentially attracted by the membrane, and becomes more concentrated around it because of the near criticality. This generates osmotic pressure, which influences the amplitude. The amplitude is also affected by the reversible dynamics of the mixture, which moves with the membrane. By assuming the Gaussian free-energy functional and weak preferential attraction, the author previously showed that a new term is added to the restoring force of the membrane and tends to suppress the amplitude. Not assuming both of them, but still focusing on modes with wavelength longer than the correlation length, we here calculate the amplitude of a tensionless membrane. First, within the Gaussian model, we solve the governing equations to show that, for long wavelength, the additional term becomes predominant, although decreased hydrodynamic effects make its numerical factor approximately half that of the previous result. The change in the term turns out not to be monotonic with the wavelength, which is mainly caused by the change in the induced mass. Second, assuming the critical composition far from the membrane, we calculate the amplitude beyond the regime of the Gaussian model. The result coincides roughly with the corresponding result in the Gaussian model if the correlation length is interpreted as one close to the membrane.

Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture within the Regime of the Gaussian Model

The position of a colloidal particle trapped in an external field thermally fluctuates at equilibrium. As is well known, the ambient fluid is not a simple heat bath and the particle mass appears to increase, which influences the mean square velocity of the particle. In this study, we suppose that the particle is surrounded by a binary fluid mixture in the homogeneous phase near, but not too close to, the critical point. Usually, one component is preferably attracted by the particle surface, and the resultant adsorption layer becomes significant because of the near-criticality. When the particle fluctuates in this situation, its mean square displacement should also be influenced by the ambient fluid because the adsorption layer does not follow the particle motion totally. We calculate the influence in a simple case, where a rigid spherical particle fluctuates with a small amplitude and its surface attracts one component weakly. We utilize the hydrodynamics in the limit of no dissipation to examine the contribution from the ambient mixture to the equal-time correlation, which is shown to be reduced by an additional stress, including osmotic pressure.

Relaxation rate of the shape fluctuation of a fluid membrane immersed in a near-critical binary fluid mixture.

We consider the two-time correlation of the shape fluctuation of a fluid membrane immersed in a near-critical binary fluid mixture. Usually one component of the mixture is preferably attracted by the membrane. Adsorption layers, where the preferred component is more concentrated, are generated on both sides of the membrane significantly because of the near-criticality. The resultant gradient of the local mass-density difference between the two components generates additional stress, including the osmotic pressure, to influence the membrane motion. Assuming the mixture to be in the homogeneous phase near, but not too close to, the demixing critical point, we use the Gaussian free-energy functional to calculate the relaxation rate for a wavelength much longer than the correlation length of the mixture. Our calculation supposes weak preferential attraction and weak dependence of the mixture viscosity on the mass-density difference, and is performed within the linear approximation with respect to the undulation amplitude. It is shown for small wave number that the additional stress makes the relaxation more rapid independently of whether the preferred component is more viscous or not and that the relaxation rate can be regarded as proportional to the wave number even for a tensionless membrane. This linear dependence comes from the balance between the frictional force due to the mixture viscosity and the restoring force of the adsorption layer.

Effective Viscosity of a Near-Critical Binary Fluid Mixture with Colloidal Particles Dispersed Dilutely under Weak Shear

We consider a spherical liquid droplet immersed in a near-critical binary fluid mixture whose components interact with the droplet slightly unequally. Assuming uniform viscosity of the mixture, we use the Gaussian free-energy functional to calculate the pressure and velocity fields occurring when a weak linear shear flow is imposed far from the droplet. These fields in the limit of infinite droplet viscosity give those for a rigid sphere. Using these fields, we calculate the effective viscosity emerging when identical droplets or rigid spheres are dilutely dispersed in the mixture.

Drag Coefficient of a Spherical Droplet Immersed in a Near-Critical Binary Fluid Mixture

We consider a spherical liquid droplet immersed in a near-critical binary fluid mixture. A weak preferential attraction is assumed between the droplet and one of the two mixture components, and the difference in the viscosity is neglected between the mixture components. Using the Gaussian free-energy functional, we calculate the drag coefficient of a droplet. Whether it is increased or decreased by the preferential attraction turns out to depend on the bulk correlation length and the ratio of the viscosity of the surrounding mixture to that of the droplet.

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

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.

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

We calculate the drag coefficient of a rigid spherical particle in an incompressible binary fluid mixture. A weak preferential attraction is assumed between the particle surface and one of the fluid components, and the difference in the viscosity between the two components is neglected. Using the Gaussian free-energy functional and solving the hydrodynamic equation explicitly, we can show that the preferential attraction makes the drag coefficient larger as the bulk correlation length becomes longer. The dependence of the deviation from the Stokes law on the correlation length, when it is short, turns out to be much steeper than the previous estimates.

Interfacial roughness in a near-critical binary fluid mixture: X-ray reflectivity and near-specular diffuse scattering

Measurements are presented of the X-ray specular reflectivity and near-specular diffuse scattering of the interface in a near-critical mixture of hexane and perfluorohexane. A lineshape analysis of the scattered intensity at each temperature yields values for the interfacial tension and interfacial width. The temperature variation of the tension and width so-obtained are consistent with current understanding of this interface, which holds that there is, firstly, an intrinsic width over which the fluid density varies smoothly from one coexistence composition to the other, and, secondly, that the interface acquires an additional and larger statistical interfacial width as a result of capillary fluctuations.

Testing the Lorentz–Lorenz relation in the near-critical binary fluid mixture isobutyric acid and water

The refractive index in each phase of the binary fluid mixture isobutyric acid and water was measured at temperatures below the system’s upper consolute point. This data was combined with existing density data to test the Lorentz–Lorenz relation in a near-critical binary fluid mixture. The Lorentz–Lorenz relation is verified within experimental error (0.5%) when the volume change on mixing the components is taken into account. The density coexistence curve data is reanalyzed to determine the critical exponent β and amplitude B. By allowing the order parameter to be a definition of the volume fraction that includes volume loss on mixing, a very symmetric coexistence curve is obtained which can be described by simple scaling with β=0.326±0.003 and B=1.565±0.021. This exponent agrees with theoretical predictions while the amplitude, when combined with existing turbidity data, confirms two-scale-factor universality. The amplitude obtained by analyzing the coexistence curve when the refractive index is the order parameter also combines with turbidity data to confirm two-scale-factor universality, but does not require knowledge of the volume loss on mixing or the composition dependence of the refractive index.

Turbidity in the binary fluid mixture methanol-cyclohexane.

The turbidity of a near-critical binary fluid mixture, methanol-cyclohexane, has been carefully measured above its (upper) critical consolute point. These measurements covered the reduced temperature region ${10}^{\mathrm{\ensuremath{-}}5}$${10}^{\mathrm{\ensuremath{-}}2}$ and allowed theoretical predictions for the critical exponents \ensuremath{\nu} and \ensuremath{\gamma} to be verified. The amplitude ${\ensuremath{\xi}}_{0}$ of the correlation length was also determined to be 3.24\ifmmode\pm\else\textpm\fi{}0.2 A\r{} while ${\ensuremath{\tau}}_{0}$ was (6.9\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}6}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$. Our result for ${\ensuremath{\xi}}_{0}$ is compared with other experimental determinations, and when combined with ${\ensuremath{\tau}}_{0}$ and coexistence curve data, is used to determine the ratio R=${\ensuremath{\xi}}_{0}$(${B}^{2}$/${k}_{B}$${T}_{c}$${\ensuremath{\chi}}_{0}$${)}^{1/}$ ${3=0.71}_{5}$\ifmmode\pm\else\textpm\fi{}${0.02}_{4}$ which is consistent with the prediction 0.65--0.67 from two-scale-factor universality.

Impurity effects in a near-critical binary-fluid mixture

Impurity effects in a near-critical binary-fluid mixture