In this work, we numerically investigate the deformation and breakup of a droplet flowing along the centerline of a microfluidic non-orthogonal intersection junction. The relevant boundary data of the velocity field is numerically computed by solving the depth-averaged Brinkman equation via a self-consistent integral equation using the boundary element method. The effect of the capillary number, droplet size, intersection angle, and ratio of outlet channel width to inlet channel width on maximum droplet deformation are studied. We study droplet deformation for the capillary numbers in the range of 0.08-0.3 and find that the maximum droplet deformation scales with the capillary number with power law with an exponent 1.10. We also investigate the effect of droplet size and intersection angle on the maximum droplet deformation and observe that the droplet deformation is proportional to droplet volume and square root of intersection angle, respectively. In continue, we study the droplet breakup phenomenon in an orthogonal intersection junction. By increasing the capillary number, the deformation of a droplet traveling in the cross-junction region becomes larger, until the droplet shape is no longer observed and droplet breakup takes place at a critical value of capillary number. We present a phase diagram for droplet breakup as a function of undeformed droplet radius.

中文翻译：

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非正交截面中液滴变形和液滴破碎的数值研究

在这项工作中，我们数值研究了沿微流体非正交交叉点中心线流动的液滴的变形和破裂。速度场的相关边界数据是通过使用边界元方法通过自洽积分方程求解深度平均 Brinkman 方程来数值计算的。研究了毛细管数、液滴尺寸、交叉角和出口通道宽度与入口通道宽度的比率对最大液滴变形的影响。我们研究了毛细管数在 0.08-0.3 范围内的液滴变形，发现最大液滴变形与毛细管数成比例，幂律为 1.10。我们还研究了液滴尺寸和交叉角对最大液滴变形的影响，并观察到液滴变形分别与液滴体积和交叉角的平方根成正比。接下来，我们研究了正交交叉结中的液滴破裂现象。通过增加毛细管数，在交叉连接区域中移动的液滴变形变大，直到不再观察到液滴形状并且液滴破裂发生在毛细管数的临界值。我们提出了液滴破裂的相图，作为未变形液滴半径的函数。通过增加毛细管数，在交叉连接区域中移动的液滴变形变大，直到不再观察到液滴形状并且液滴破裂发生在毛细管数的临界值。我们提出了液滴破裂的相图，作为未变形液滴半径的函数。通过增加毛细管数，在交叉连接区域中移动的液滴变形变大，直到不再观察到液滴形状并且液滴破裂发生在毛细管数的临界值。我们提出了液滴破裂的相图，作为未变形液滴半径的函数。