Effects of obstacle lengths on the asymmetric breakup of a droplet in a straight microchannel

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.