微型管中液滴流动的三维数值模拟

NUMERICAL SIMULATION OF DROPLET FLOW IN A THREE DIMENSIONAL MICROFLUIDIC DEVICES

对于微型设备中的低雷诺数流动,毛细力和黏性力起主导作用．应用相场方法,引入自由能泛函,研究了二相流体在微型管中流动问题及表面浸润现象,并给出了微型管中二相流体的无量纲输运方程．针对方形微管道,利用差分法给出了输运方程的数值求解方法．最后,模拟了方形直管中的液滴流动和变形的过程,并给出了液滴前后压力差与其它主要物理参数之间的变化关系．结果表明,压力差随液滴半径增大而增加,而随毛细管系数的增大而减小．

For low Reynolds number flow in a micro-fluidic device, the capillary and viscous stresses are more important than the inertial forces, as is characteristic of the micro-fluidic devices. Based on the free energy function, a phase-field method is applied for the two-phase flow in a micro-fluidic device and the interaction of the fluid components with a wall. The transport equations of dimensionless form for the two-phase flow are obtained. To solve the transport equations for a micro-fluidic square pipe, a numerical method is proposed using the finite difference m^thod. The numerical simulation of the flow and the deformation of a droplet in a cubic pipe is carried out, and the effects of the capillary number and the drop radius on the deformation and the additional pressure drop ahead of and behind the droplet are studied. The simulations show that the additional pressure drop increases with the droplet size, and decreases with the capillary number.