Migration of a viscoelastic drop in a ratchet microchannel

We numerically investigate the deformation and migration of a viscoelastic droplet in a ratchet microchannel, a phenomenon that occurs in many practical applications and involves rich physics due to the associated complex geometry and non-Newtonian nature of the fluid. The numerical method required to handle viscoelastic fluid is also extremely challenging, especially when the Weissenberg number, a dimensionless relaxation time related to the viscoelastic fluids, is high. In the present study, we incorporate a log-conformation stabilization method that overcomes this numerical problem and examine the shape transition dynamics of a viscoelastic droplet for a wide range of parameters, including the wavelength and type of the ratchet, Weissenberg number, and Reynolds number. The droplet dynamics in a ratchet microchannel is compared to that in a straight channel. The presence of the ratchet section causes a distinct stress distribution in the viscoelastic droplet, which significantly influences the residence period, the shape of the droplet in the microchannel, and shape recovery dynamics when flowing out of the channel.