Competition Between Thermophoretic Separation and Thermal Convective Mixing

In binary fluid systems under temperature differences, thermophoretic separation and thermal convective mixing are two key mechanisms that affect the processes of transport. The thermophoretic effect, also known as the Soret effect, describes the migration behavior of molecules in the fluid with temperature gradient. Thermophilic and thermophobic molecules tend to migrate to regions of higher and lower temperature. Thermal convective mixing is triggered by a Rayleigh-B{\'e}nard-type hydrodynamics instability as a macroscopic flow caused by buoyancy induced by temperature differences, promoting the mixing of different components within the fluid. There is a competition between the separation caused by thermophoresis and the mixing produced by convection. A dimensionless number, namely Soret-Rayleigh number $S_R$, which is the ratio of dimensionless Soret factor $S_T$ and Rayleigh numbers $Ra$, is introduced to quantitatively describe this competition. The impact of different $S_R$ and Rayleigh numbers $Ra$ on the concentration field is studied by energy-conserving dissipative particle dynamics (eDPD). The results indicate that the components separation exhibits a non-monotonic variation with $Ra$ increase. For a specific $S_R$, there exists an optimal $Ra$ that achieves the lowest separation at long time scales. This result will have potential implications for the design and application of micro-mixers.