Dynamics of a Viscous Droplet in Return Bends of Microfluidic Channels

Return bends are frequently encountered in microfluidic systems. In this study, a three-dimensional spectral boundary element method for interfacial dynamics in Stokes flow has been adopted to investigate the dynamics of viscous droplets in rectangular return bends. The droplet trajectory, deformation, and migration velocity are investigated under the influence of various fluid properties and operational conditions, which are depicted by the Capillary number, viscosity ratio, and droplet size, as well as the dimensions of the return bend. While the computational results provide information for the design of return bends in microfluidic systems in general, the computational framework shows potential to guide the design and operation of a droplet-based microfluidic delivery system for cell seeding.

Steady Stokes flow of a non-Newtonian Reiner-Rivlin fluid streaming over an approximate liquid spheroid

The investigation is carried out to study steady Stokes axisymmetrical Reiner-Rivlin streaming flow over a fixed viscous droplet, and this droplet to be deformed sphere in shape. As boundary conditions, vanishing of radial velocities, continuity of tangential velocities and shear stresses at the droplet surface are used. The very common configuration of approximate sphere governed by polar equation $\tilde{r} =a[1 +\alpha_m \vartheta_m(\zeta)]$ has been considered for the study to $o(\varepsilon)$ describing the distortion. Based on the Stokes approximation, an analytical investigation is achieved in the orthogonal curve linear framework in an unbounded region of a Reiner-Rivlin fluid. In constraining cases, some earlier noted outcomes are obtained. Also, the yielded outcomes for the drag have been compared with solution existing in the literature. Further, the change for both force and pressure are evaluated with deflection w.r.t. the parameters of interest and shown through table and graphs.