Numerical simulation of breakup of a viscous drop in simple shear flow through a volume-of-fluid method

Abstract

A spherical drop, placed in a second liquid of the same density, is subjected to shearing between parallel plates. The subsequent flow is investigated numerically with a volume-of-fluid ͑VOF͒ method. The scheme incorporates a semi-implicit Stokes solver to enable computations at low Reynolds number. Our simulations compare well with previous theoretical, numerical, and experimental results. For capillary numbers greater than the critical value, the drop deforms to a dumbbell shape and daughter drops detach via an end-pinching mechanism. The number of daughter drops increases with the capillary number. The breakup can also be initiated by increasing the Reynolds number.

Three-Dimensional Lattice Boltzmann Simulation of Two-Phase Flow Containing a Deformable Body with a Viscoelastic Membrane

“…It is seen that for low G, the body slightly deforms and the shapes are ellipsoidal, but for high G, they become slender and sigmoidal owing to its large deformation. These shapes are similarly observed for a viscous liquid drop under simple shear flows, in which the effect of the interfacial tension is considered [22,29,30]. In the case of a liquid drop, however, the drop continues to deform and eventually breaks up as the shear rate becomes larger, whereas the body evolves to a steady shape without disintegration.…”

Influence of viscoelasticity on drop deformation and orientation in shear flow. Part 2: Dynamics

“…The dimensionless parameters are the viscosity ratio based on total viscosities λ = η d /η m , the capillary number Ca = R 0γ η m /Γ whereγ is the shear rate, a Reynolds number based on the matrix liquid Re = ργR 2 0 /η m , a Weissenberg number per fluid W e =γτ , and a retardation parameter per fluid β = η s /η. Alternatively, the Deborah numbers are The two in-house volume-of-fluid (VOF) codes used in this paper are described in detail in [34,41], and reconstructs the interface position from the values of a VOF function which represents the volume fraction of one of the fluids in each grid cell. The surface tension force is computed as a body force in the momentum equation, Γκ S nδ S , where κ S denotes the mean curvature of the surface, n is the normal and δ S is a delta function on the interface.…”

Hemodynamic Assessment of Pre- and Post-operative Aortic Coarctation from MRI

“…Our embedded boundary Navier-Stokes solver uses a fractional step method [14] that computes in a first step an intermediate velocity field, using the nonlinear advection-diffusion equation for velocity, and then projects the intermediate velocity onto the field of divergence free and tangent to the vessel boundary vector fields. For the velocity advection we use second-order upwind, Van-Leer slope limiting methods, while for the diffusion force components we use a semi-implicit approach as in [15] which is first order accurate and unconditionally stable in 3D. We solve the pressure projection Poisson equation using an efficient implicit multi-grid preconditioned conjugate gradient solver.…”