Abstract Rheological behaviors of a droplet moving in the micro-channel with a linear obstacle off the channel axis are investigated numerically by employing Volume of Fluid methods. Five different hydrodynamic patterns of the rheological behaviors of the droplet have been observed. The effects of the length ratio L of the mother droplet to the linear obstacle on the critical capillary number of the droplet breakup have been particularly studied. When L is less than a critical value Lmin, the larger the droplet is, the smaller the critical capillary number Cacr is; when L is greater than Lmin, the larger the droplet is, the greater Cacr is. The curve of Cacr as a function of L has a minimum point at Lmin, which means that the droplet with L = Lmin could be broken up most easily. This is caused by the competition of the enhancing (positive) factors and the hindering (negative) factors on the droplet breakup, which has been analyzed carefully in this paper. When other parameters are fixed, it is very interesting to find out that the change of the obstacle length does not change the value of Lmin, which is fixed to 0.66 for the conditions discussed in this paper. The results obtained here might enlighten potential applications for the design of the micro-channel with obstacles and the packing rings in columns.

中文翻译：

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障碍物长度对直线微通道中液滴不对称破碎的影响

摘要 采用流体体积法数值研究了液滴在微通道中移动的流变行为，该微通道具有远离通道轴的线性障碍物。已经观察到液滴流变行为的五种不同流体动力学模式。特别研究了母液滴与线性障碍物的长度比 L 对液滴破裂的临界毛细管数的影响。当L小于临界值Lmin时，液滴越大，临界毛细管数Cacr越小；当L大于Lmin时，液滴越大，Cacr越大。作为 L 函数的 Cacr 曲线在 Lmin 处有一个最小值点，这意味着 L = Lmin 的液滴最容易破碎。这是由于液滴破裂的增强（积极）因素和阻碍（消极）因素的竞争引起的，本文对此进行了仔细分析。当其他参数固定时，很有趣的发现障碍物长度的变化并没有改变Lmin的值，本文讨论的条件固定为0.66。这里获得的结果可能会启发设计带有障碍物的微通道和柱中的填料环的潜在应用。