We investigate the impact of buoyancy on the solute mass transport in an evaporating liquid mixture (non-volatile solute $+$ solvent) confined in a slit perpendicular to the gravity. Solvent evaporation at one end of the slit induces a solute concentration gradient which in turn drives free convection due to the difference between the densities of the solutes and the solvent. From the complete model coupling mass transport and hydrodynamics, we first use a standard Taylor-like approach to derive a one dimensional non-linear advection-dispersion equation describing the solute concentration process for a dilute mixture. We then perform a complete analysis of the expected regimes using both scaling analysis and asymptotic solutions of this equation. The validity of this approach is confirmed using a thorough comparison with the numerical resolution of both the complete model and the 1D advection-dispersion equation. Our results show that buoyancy-driven free convection always impacts solute mass transport at long time scales, dispersing solutes in a steadily increasing length scale along the slit. Beyond this confined drying configuration, our work also provides an easy way for evaluating the relevance of buoyancy on mass transport in any other microfluidic configuration involving concentration gradients.

中文翻译：

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液体二元混合物密闭干燥中的浮力驱动分散

我们研究浮力对蒸发的液体混合物（非挥发性溶质）中溶质传质的影响。 $+$溶剂）限制在垂直于重力的狭缝中。在狭缝的一端的溶剂蒸发引起溶质浓度梯度，由于溶质和溶剂的密度之间的差异，溶质浓度梯度又驱动自由对流。从耦合质量传输和流体动力学的完整模型中，我们首先使用标准的泰勒式方法得出描述稀混合物溶质浓缩过程的一维非线性对流扩散方程。然后，我们使用比例分析和该方程的渐近解对期望的状态进行完整的分析。通过与完整模型和一维对流扩散方程的数值分辨率进行全面比较，可以确认这种方法的有效性。我们的结果表明，浮力驱动的自由对流始终会影响溶质的长时尺度传输，使溶质沿着缝隙以逐渐增加的长度尺度分散。除了这种受限的干燥配置，我们的工作还提供了一种简便的方法来评估在涉及浓度梯度的任何其他微流体配置中，浮力与质量运输的相关性。