16 research outputs found
A cut finite element method for coupled bulk-surface problems on time-dependent domains
In this contribution we present a new computational method for coupled
bulk-surface problems on time-dependent domains. The method is based on a
space-time formulation using discontinuous piecewise linear elements in time
and continuous piecewise linear elements in space on a fixed background mesh.
The domain is represented using a piecewise linear level set function on the
background mesh and a cut finite element method is used to discretize the bulk
and surface problems. In the cut finite element method the bilinear forms
associated with the weak formulation of the problem are directly evaluated on
the bulk domain and the surface defined by the level set, essentially using the
restrictions of the piecewise linear functions to the computational domain. In
addition a stabilization term is added to stabilize convection as well as the
resulting algebraic system that is solved in each time step. We show in
numerical examples that the resulting method is accurate and stable and results
in well conditioned algebraic systems independent of the position of the
interface relative to the background mesh
Phase-field modeling droplet dynamics with soluble surfactants
Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence
Surfactant-dependent contact line dynamics and droplet spreading on textured substrates: derivations and computations
We study spreading of a droplet, with insoluble surfactant covering its
capillary surface, on a textured substrate. In this process, the
surfactant-dependent surface tension dominates the behaviors of the whole
dynamics, particularly the moving contact lines. This allows us to derive the
full dynamics of the droplets laid by the insoluble surfactant: (i) the moving
contact lines, (ii) the evolution of the capillary surface, (iii) the
surfactant dynamics on this moving surface with a boundary condition at the
contact lines and (iv) the incompressible viscous fluids inside the droplet.
Our derivations base on Onsager's principle with Rayleigh dissipation
functionals for either the viscous flow inside droplets or the motion by mean
curvature of the capillary surface. We also prove the Rayleigh dissipation
functional for viscous flow case is stronger than the one for the motion by
mean curvature. After incorporating the textured substrate profile, we design a
numerical scheme based on unconditionally stable explicit boundary updates and
moving grids, which enable efficient computations for many challenging examples
showing significant impacts of the surfactant to the deformation of droplets.Comment: 35 pages, 6 figure
On diffuse interface modeling and simulation of surfactants in two-phase fluid flow
An existing phase-field model of two immiscible fluids with a single soluble
surfactant present is discussed in detail. We analyze the well-posedness of the
model and provide strong evidence that it is mathematically ill-posed for a
large set of physically relevant parameters. As a consequence, critical
modifications to the model are suggested that substantially increase the domain
of validity. Carefully designed numerical simulations offer informative
demonstrations as to the sharpness of our theoretical results and the qualities
of the physical model. A fully coupled hydrodynamic test-case demonstrates the
potential to capture also non-trivial effects on the overall flow