Low Reynolds number motion of a droplet in shear flow including wall effects

Computation of multiphase systems with phase field models

“…We plot the contour of φ = 0 only. The observed deformation increases in accordance with the predictions in [29,30] without any appreciable change in the orientation.…”

“…The convergence of the results under grid refinement is evident. The drop shape is ellipsoidal with the major axis converging to an angle of 45 o as Ca decreases, just as predicted by the analytic results [29,30]. Moreover, the contours −0.9 and 0.9 describing the interface are well behaved since they stay parallel throughout the computation.…”

“…We choose the droplet radius to be 35 grid points which is large enough to avoid effects due to the finite interfacial width and the presence of the walls [30]. We see from Figure 2 that the deformation parameters obtained from simulations with different capillary numbers Ca and Re = 0.01, P e = 100 (error bars) correspond well with the theoretical predictions of (35).…”

“…This is a classical problem that was solved analytically for sharp interfaces and small deformations in the creeping flow approximation for unbounded domain by Taylor [29] and in the presence of two walls by Shapira and Haber [30]. The drop will assume the shape of an ellipsoid with a deformation that depends on the capillary number and the viscosity ratio.…”

Microconfined equiviscous droplet deformation: Comparison of experimental and numerical results

“…Only a few studies were conducted including the effects of two parallel walls on the behavior of single droplets. [21][22][23][24] For instance, using an integral solution, Shapira and Haber calculated a first-order correction for wall effects that took into account the deviation from sphericity and the drag force acting upon a droplet in confined shear flow. 21 It was shown for equal viscosities that the obtained deformation parameter matched experimental results quite well.…”