Numerical simulation of mass transfer in circulating drops
Numerical simulation of mass transfer in circulating drops
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DOI：
10.1016/j.ces.2010.01.021
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发表时间：
2010-05
影响因子：
4.7
通讯作者：
S. Ubal;C. Harrison;P. Grassia;W. J. Korchinsky
中科院分区：
文献类型：
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作者：
S. Ubal;C. Harrison;P. Grassia;W. J. Korchinsky
对循环液滴的传质过程进行了数值模拟，并将其应用于液-液萃取。选取了丙酮-甲醇-苯多元三元体系的模拟参数。通过液滴流函数的截断伽辽金表示来估计液滴环流模式。采用麦克斯韦-斯蒂芬理论，结合热力学修正，得到了多组分传质的费克扩散系数。通过两种不同的数值方法求解控制传质的对流扩散方程：有限差分格式(使用交替方向隐式方法)和有限元格式。两个方案之间取得了良好的一致。给出了雷诺数(Re=30)和选择的Peclet数(Pe=100、1000和10000，从而深入了解增加Peclet数的影响)的模拟结果。将全对流扩散方程的数值模拟与刚性液滴模式(即无环流)的预报以及Uribe-Ramirez和Korchinsky发展的半解析边界层模式的预报进行了比较。对于体积质量分数的结果表明，刚性液滴模型的预测发展太慢，而边界层模型的预测发展得比数值模拟快得多。对液滴中选定单个位置质量分数演化的对流扩散模拟结果表明，距离液滴表面和/或液滴轴线最近的流线上的点演化最快，而离液滴内部停滞点最近的流线上的点演化最慢。在选定的时间，整个液滴的成分浓度等值线图证实了这一点，这支持这样一种图景，即质量分数沿着单独的流线大致均匀，但质量从流线扩散到流线。
Numerical simulations of mass transfer are performed for a circulating liquid drop with applications in liquid–liquid extraction. Simulation parameters are chosen for a multi-component ternary system acetone–methanol–benzene. The drop circulation pattern is estimated via a truncated Galerkin representation of the drop streamfunction. Fickian diffusivities for multi-component mass transfer are obtained via Maxwell–Stefan theory with thermodynamic corrections. The advection–diffusion equations governing mass transfer are solved via two distinct numerical methods: a finite difference scheme (using the alternating direction implicit method) and a finite element scheme. Good agreement was obtained between both schemes. Simulation results are presented for a Reynolds number (Re=30) and for a selection of Peclet numbers (Pe=100, 1000 and 10000, thereby giving insight into the effects of increasing Peclet number). The numerical simulations of the full advection–diffusion equations are compared against predictions of a rigid drop model (i.e. without circulation) and also against predictions of a semi-analytical boundary layer model developed by Uribe-Ramirez and Korchinsky. Results for bulk mass fractions reveal that the rigid drop model predictions evolve too slowly, while the boundary layer model predictions evolve much more quickly than the numerical simulations. Advection–diffusion simulation results for the evolution of mass fractions at selected individual locations in the drop show that points on streamlines nearest to the drop surface and/or drop axis evolve fastest, while those closest to the drop internal stagnation point evolve slowest. Corroborated by contour plots of component concentrations throughout the drop at selected times, this supports a picture whereby mass fractions become roughly uniform along individual streamlines, but mass is transferred diffusively from streamline to streamline.