1,066 research outputs found
Numerical approximation of a phase-field surfactant model with fluid flow
Modelling interfacial dynamics with soluble surfactants in a multiphase
system is a challenging task. Here, we consider the numerical approximation of
a phase-field surfactant model with fluid flow. The nonlinearly coupled model
consists of two Cahn-Hilliard-type equations and incompressible Navier-Stokes
equation. With the introduction of two auxiliary variables, the governing
system is transformed into an equivalent form, which allows the nonlinear
potentials to be treated efficiently and semi-explicitly. By certain subtle
explicit-implicit treatments to stress and convective terms, we construct first
and second-order time marching schemes, which are extremely efficient and
easy-to-implement, for the transformed governing system. At each time step, the
schemes involve solving only a sequence of linear elliptic equations, and
computations of phase-field variables, velocity and pressure are fully
decoupled. We further establish a rigorous proof of unconditional energy
stability for the first-order scheme. Numerical results in both two and three
dimensions are obtained, which demonstrate that the proposed schemes are
accurate, efficient and unconditionally energy stable. Using our schemes, we
investigate the effect of surfactants on droplet deformation and collision
under a shear flow, where the increase of surfactant concentration can enhance
droplet deformation and inhibit droplet coalescence
Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities
 In this work, we present a hydrodynamics coupled phase-field surfactant model with variable densities. Two scalar auxiliary variables are introduced to transform the original free energy functional into an equivalent form, and then a new thermodynamically consistent model can be obtained. In this model, evolutions of two phase-field variables are described by two Cahn-Hilliard-type equations, and the fluid flow is dominated by incompressible Navier-Stokes equation. The finite difference method on staggered grid is used to solve the above model. Then a classical droplet rising case and a droplet merging case are used to validate our model. Finally, we study the effect of surfactants on droplet deformation and merging. A more prolate profile of droplet is observed under a higher surfactant bulk concentration, which verifies the effect of surfactant in reducing the interfacial tension. Increases in surface Peclet number and initial surfactant bulk concentration can enhance the non-uniformity of surfactant distribution around the interface, which will arise the Marangoni force. The Marangoni force acts as an additional repulsive force to delay the droplet merging.Cited as: Zhu, G., Li, A. Interfacial dynamics with soluble surfactants: A phase-field two-phase flow model with variable densities. Advances in Geo-Energy Research, 2020, 4(1): 86-98, doi: 10.26804/ager.2020.01.0
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