A binary fluid in a one-phase state, where the two fluid components mix uniformly, near its critical point is confined within a system comprising two large containers of binary mixture connected by a sufficiently long capillary tube. The composition and pressure within both containers are set to their critical-point values, while the temperatures of the reservoirs are adjusted to slightly different values.

Distribution of "thermal force density," which is normalized by a characteristic force density, of the tube as a unit, within the capillary tube as a function of the distance from the tube’s central axis, which is normalized by the radius of the tube as a unit. Positive values represent forces in the same direction as the temperature gradient, while negative values represent forces in the opposite direction. NEMP refers to a binary fluid wherein phase separation occurs when the temperature decreases, and LW refers to one where phase separation occurs when the temperature increases.

Fluid flow within confined spaces, such as capillary tubes or porous membranes under the influence of thermodynamic forces like pressure or temperature gradients plays a crucial role in material separation and microfluidics. Specifically, when a temperature gradient is applied to a fluid within a narrow tube, a “thermal force” arises near the tube’s surface owing to fluid inhomogeneity at the solid-liquid interface, initiating flow within the tube. Despite being a fundamental topic in nonequilibrium physics, the physical mechanism underlying this phenomenon remains poorly understood.

In this study, we theoretically analyzed the flow behavior of a binary fluid, such as a mixture of water and oil, near the critical point^* of phase separation, where two states with different compositions coexist, within a capillary tube using hydrodynamic principles. As a result, we made theoretical predictions as explained below. In such systems, one of the two fluid components is selectively adsorbed at the solid-liquid interface. The thickness of this adsorption layer (depicted as the yellow layer in Fig. 1) increases as the system approaches the critical point. Our findings, illustrated in Fig. 2, reveal that within this adsorption layer, "thermal force" is generated in the same or opposite direction as the temperature gradient. The direction depends on whether phase separation occurs when the temperature decreases or increases, respectively, regardless of the mixture’s microscopic characteristics. Therefore, our theory would apply to any binary fluids. This force drives mass flow in the binary fluid, aligning with or opposing the temperature gradient accordingly.

Experimental validation of this prediction and its application to waste separation would be important future research topics.

 

^*Critical point: The temperature and the composition at which phase separation begins to occur.

Yabunaka, S. et al., Thermo-Osmosis of a Near-Critical Binary Fluid Mixture: A General Formulation and Universal Flow Direction, Physical Review E, vol.109, issue 6, 2024, 064610, 19p.

Paper URL: https://doi.org/10.1103/PhysRevE.109.064610

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