Coupled Heat and Mass Transfer in Binary Mixtures at Supercritical Pressures

This chapter enters the first part of this thesis, where a relaxation problem is studied and coupled heat and mass transfer exists through cross-diffusion effects. This chapter is devoted to reporting the mass piston effect induced by the cross-boundary mass flux in a binary mixture under supercritical pressures. Mass piston effect is driven by three cooperative or competing mechanisms: boundary velocity, Dufour effect, and concentration variation. A traveling-wave theory is developed to represent the amplitudes of the acoustic wave and the wave’s propagation. Furthermore, in the energy balance analysis, the modified energy and temperature efficiencies measuring the capabilities of the mass piston effect in terms of energy transfer and thermalization are derived.

This chapter also belongs to the first part of this thesis, where a diffusion problem is studied and coupled heat and mass transfer exists through cross-diffusion effects. The steady-state responses of an enclosed binary mixture subjected to transcritical temperature differences under supercritical pressures are numerically simulated to study the coexistence of liquid-like and gas-like states and the influences of the concentration gradient. It is found that the steady state is strongly nonlinear in state variables and physical properties. The Soret effect induces the concentration gradient, and the low heat conducting nature of gas-like state compared to the liquid-like one gives rise to the pressure drop. As the critical pressure is approached and the temperature difference is enlarged, the profiles of state variables own growing nonlinearities. Under near-critical conditions, the concentration gradient has deep effects on the relative variations of density and pressure. Therefore, it plays a vital role in buoyancy flows and transient phenomena like the piston effect.

This chapter enters the second part of this thesis, where a hydrodynamic instability problem is studied and coupled heat and mass transfer exists through cross-diffusion effects. In this chapter, theoretical tools are implemented to study the Rayleigh-Bénard instability in a binary mixture at supercritical pressures, which is characterized by gravity-related effects and cross-diffusion effects with positive separation ratio. Analytical criteria are derived for ideal stress-free boundary conditions, and an unusual oscillatory instability is discovered. Analyses regarding the origin of oscillatory instability reveal that it requires a sufficiently large stabilizing concentration gradient and the total diffusivity rate of concentration is less than that of temperature, where the stabilizing concentration gradient is a result of gravity-related effects. Discussions concerning the relative importance of gravity-related effects reveal that for the reference fluid under near-critical states, gravity-related effects become dominate when the thickness of fluid layer is at the centimeter level.

This chapter also belongs to the second part of this thesis. Based on the previous chapter, this chapter investigates the bifurcation around the onset threshold, with special attention paid to the conditions of finite-amplitude (FA) instability. The coupled heat and mass transfer exists through cross-diffusion effects. By means of weakly nonlinear analysis and a series of numerical simulations, the nonlinear dynamics of Rayleigh-Bénard (RB) convection near the stability threshold is studied for a binary mixture at supercritical pressures. This chapter confirms the near-threshold RB convection is deeply influenced by a FA instability mechanism, which requires a large enough stabilizing concentration gradient. The underlying mechanism of FA instability is attributed to the buoyancy-release mechanism of convective motions. Mathematically, this chapter also provides the bifurcation diagrams near the stability threshold.

This chapter enters the third part of this thesis, where a cavity flow problem is studied and coupled heat and mass transfer exists through temperature-dependent boundary reactions. For a supercritical solvent–solute system, as a critical end point (CEP) is approached, the solubility becomes sensitive to temperature variations. By virtue of this phenomenon, a conceptual model is proposed to combine extraction and crystal growth. CO2-naphthalene is chosen as the reference system. Theoretical optimizations suggest that the newly defined pseudo-CEPs are favorable reference states, especially those close to the lower CEP. The temperature at the bottom wall should be higher than that at the top one to offset the stabilizing concentration gradient due to gravity and initiate double-diffusive convection in the cooperative regime. Numerical simulations confirm that the performance of the current model operating at the optimized reference state is better than the previous experimental results in terms of crystal growth rates. The conceptual model provides an efficient configuration for coupled extraction and crystal growth apparatuses.

In this thesis, fundamental transport phenomena and related effects in binary mixtures at supercritical pressures are explored, where coupled heat and mass transfer exists via cross-diffusion effects or temperature-dependent boundary reactions. The main conclusions are summarized as in this chapter.