1,451 research outputs found
A hybrid lattice Boltzmann and finite difference method for two-phase flows with soluble surfactants
A hybrid method is developed to simulate two-phase flows with soluble
surfactants. In this method, the interface and bulk surfactant concentration
equations of diffuse-interface form, which include source terms to consider
surfactant adsorption and desorption dynamics, are solved in the entire fluid
domain by the finite difference method, while two-phase flows are solved by a
lattice Boltzmann color-gradient model, which can accurately simulate binary
fluids with unequal densities. The flow and interface surfactant concentration
fields are coupled by a modified Langmuir equation of state, which allows for
surfactant concentration beyond critical micelle concentration. The capability
and accuracy of the hybrid method are first validated by simulating three
numerical examples, including the adsorption of bulk surfactants onto the
interface of a stationary droplet, the droplet migration in a constant
surfactant gradient, and the deformation of a surfactant-laden droplet in a
simple shear flow, in which the numerical results are compared with theoretical
solutions and available literature data. Then, the hybrid method is applied to
simulate the buoyancy-driven bubble rise in a surfactant solution, in which the
influence of surfactants is identified for varying wall confinement, Eotvos
number and Biot number. It is found that surfactants exhibit a retardation
effect on the bubble rise due to the Marangoni stress that resists interface
motion, and the retardation effect weakens as the Eotvos or Biot number
increases. We further show that the weakened retardation effect at higher Biot
numbers is attributed to a decreased non-uniform effect of surfactants at the
interface
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
Influence of surfactants on the electrohydrodynamic stretching of water drops in oil
In this paper we present experimental and numerical studies of the
electrohydrodynamic stretching of a sub-millimetre-sized salt water drop,
immersed in oil with added non-ionic surfactant, and subjected to a suddenly
applied electric field of magnitude approaching 1 kV/mm. By varying the drop
size, electric field strength and surfactant concentration we cover the whole
range of electric capillary numbers () from 0 up to the limit of drop
disintegration. The results are compared with the analytical result by Taylor
(1964) which predicts the asymptotic deformation as a function of . We
find that the addition of surfactant damps the transient oscillations and that
the drops may be stretched slightly beyond the stability limit found by Taylor.
We proceed to study the damping of the oscillations, and show that increasing
the surfactant concentration has a dual effect of first increasing the damping
at low concentrations, and then increasing the asymptotic deformation at higher
concentrations. We explain this by comparing the Marangoni forces and the
interfacial tension as the drops deform. Finally, we have observed in the
experiments a significant hysteresis effect when drops in oil with large
concentration of surfactant are subjected to repeated deformations with
increasing electric field strengths. This effect is not attributable to the
flow nor the interfacial surfactant transport
Phase field modelling of surfactants in multi-phase flow
A diffuse interface model for surfactants in multi-phase flow with three or
more fluids is derived. A system of Cahn-Hilliard equations is coupled with a
Navier-Stokes system and an advection-diffusion equation for the surfactant
ensuring thermodynamic consistency. By an asymptotic analysis the model can be
related to a moving boundary problem in the sharp interface limit, which is
derived from first principles. Results from numerical simulations support the
theoretical findings. The main novelties are centred around the conditions in
the triple junctions where three fluids meet. Specifically the case of local
chemical equilibrium with respect to the surfactant is considered, which allows
for interfacial surfactant flow through the triple junctions
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