Numerical study on the effect of viscoelasticity on pressure drop and film thickness for a droplet flow in a confined microchannel

The prediction of pressure drop for a droplet flow in a confined microchannel is presented using FE-FTM (Finite Element - Front Tracking Method). A single droplet is passing through 5:1:5 contraction - straight narrow channel - expansion flow domain. The pressure drop is investigated especially when the droplet flows in the straight narrow channel. We explore the effects of droplet size, capillary number (Ca), viscosity ratio (chi) between droplet and medium, and fluid elasticity represented by the Oldroyd-B constitutive model on the excess pressure drop (Delta p(+)) against single phase flow. The tightly fitted droplets in the narrow channel are mainly considered in the range of 0.001 <= Ca <= 1 and 0.01 <= chi <= 100. In Newtonian droplet/Newtonian medium, two characteristic features are observed. First, an approximate relation Delta p(+)similar to chi is observed for chi >= 1. The excess pressure drop necessary for droplet flow is roughly proportional to chi. Second, Delta p(+) seems inversely proportional to Ca, which is represented as Delta p(+)similar to Ca-m with negative in irrespective of chi. In addition, we observe that the film thickness (delta(f)) between droplet interface and channel wall decreases with decreasing Ca, showing delta(f)similar to Ca-n with positive n independent of chi. Consequently, the excess pressure drop (Delta p(+)) is strongly dependent on the film thickness (delta(f)). The droplets larger than the channel width show enhancement of Delta p(+), whereas the smaller droplets show no significant change in Delta p(+). Also, the droplet deformation in the narrow channel is affected by the flow history of the contraction flow at the entrance region, but rather surprisingly Delta p(+) is not affected by this flow history. Instead, Delta p(+) is more dependent on delta(f) irrespective of the droplet shape. As for the effect of fluid elasticity, an increase in delta(f) induced by the normal stress difference in viscoelastic medium results in a drastic reduction of Delta p(+).