Hybrid Simulation of Miscible Mixing with Viscous Fingering

Abstract

By modeling mass transfer phenomena, we simulate solids and liquids dissolving or changing to other substances. We also deal with the very small-scale phenomena that occur when a fluid spreads out at the interface of another fluid. We model the pressure at the interfaces between fluids with Darcy's Law and represent the viscous fingering phenomenon in which a fluid interface spreads out with a fractal-like shape. We use hybrid grid-based simulation and smoothed particle hydrodynamics (SPH) to simulate intermolecular diffusion and attraction using particles at a computable scale. We have produced animations showing fluids mixing and objects dissolving.

A Particle-based Dissolution Model using Chemical Collision Energy

“…(c)) the sampling density does not affect the dissolution process, even when the sampling is nonhomogeneous. In (d) we demonstrate the result when using previous methods (Wojtan et al, 2007;Shin et al, 2010). All the images are taken from the same frame with the same initial conditions.…”

“…It is easy to tell that ρ s = ∑ j m s W (x s − x j , h) originates from the basic SPH density calculation in Equation 1. j is the object particle within the solute neighbourhood h. The volume mass m vs must be updated in each frame due to the changing shape of the object during dissolution. Figure 1 demonstrates sampling independence by using different sampling resolutions, as well as non-homogeneous sampling resolutions, and compare these against previous dissolution methods ( Wojtan et al, 2007;Shin et al, 2010). This property is further discussed in Section 4.2.…”

“…In previous methods (Wojtan et al, 2007;Shin et al, 2010) shape alteration of a dissolving object was achieved using mass transfer. Both methods used level-sets to represent the solute, causing the dissolution result to be largely affected by the grid resolution.…”

“…We also evaluate this example using two different sampling resolutions in order to demonstrating that the dissolution results are equivalent. We calculated the percentage of the volume difference at each frame of both spheres: with our method, this reaches a maximum of 3.4% of the sphere volume, while with the method of (Wojtan et al, 2007;Shin et al, 2010) the low sampled sphere dissolves completely before the high sampled sphere halves in size. The adhesion method of (Akinci et al, 2013) is used to ensure the fluid realistically adheres to the sides of the sphere.…”

“…Their focus was on simulating the dispersed bubble flow -the dissolution model was approximated by generating offsets of a level-set representation of the solute, which had little relationship with actual dissolution behaviour. (Shin et al, 2010) simulated solids dissolving in liquids by modelling solid mass transfer. They treated the solvent and solution as different fluids, and used multiple level-sets to track mixing surfaces which needed to be updated whenever the reactions and interactions occurredan expensive but necessary step.…”