A front-tracking method for viscous, incompressible, multi-fluid flows
Journal of Computational Physics
Variational problems and partial differential equations on implicit surfaces
Journal of Computational Physics
Transport and diffusion of material quantities on propagating interfaces via level set methods
Journal of Computational Physics
An Eulerian Formulation for Solving Partial Differential Equations Along a Moving Interface
Journal of Scientific Computing
A finite element method for surface diffusion: the parametric case
Journal of Computational Physics
Numerical simulation of anisotropic surface diffusion with curvature-dependent energy
Journal of Computational Physics
Journal of Computational Physics
Diffusion on a curved surface coupled to diffusion in the volume: Application to cell biology
Journal of Computational Physics
A front-tracking method for computation of interfacial flows with soluble surfactants
Journal of Computational Physics
An immersed boundary method for interfacial flows with insoluble surfactant
Journal of Computational Physics
Journal of Computational Physics
A conservative SPH method for surfactant dynamics
Journal of Computational Physics
A hybrid numerical method for interfacial fluid flow with soluble surfactant
Journal of Computational Physics
A diffuse-interface method for two-phase flows with soluble surfactants
Journal of Computational Physics
Short note: A note on pressure accuracy in immersed boundary method for Stokes flow
Journal of Computational Physics
Hi-index | 31.45 |
Many physical problems arising in biological or material sciences involve solving partial differential equations in deformable interfaces or complex domains. For instance, the surfactant (an amphiphilic molecular) which usually favors the presence in the fluid interface may couple with the surfactant soluble in one of bulk domains through adsorption and desorption processes. Thus, it is important to accurately solve coupled surface-bulk convection-diffusion equations especially when the interface is moving. In this paper, we first rewrite the original bulk concentration equation in an irregular domain (soluble region) into a regular computational domain via the usage of the indicator function so that the concentration flux across the interface due to adsorption and desorption processes can be termed as a singular source in the modified equation. Based on the immersed boundary formulation, we then develop a new conservative scheme for solving this coupled surface-bulk concentration equations which the total surfactant mass is conserved in discrete sense. A series of numerical tests has been conducted to validate the present scheme. As an application, we extend our previous work [M.-C. Lai, Y.-H. Tseng, H. Huang, An immersed boundary method for interfacial flows with insoluble surfactant, J. Comput. Phys. 227 (2008) 7279-7293] to the soluble case. The effects of solubility of surfactant on drop deformations in a quiescent and shear flow are investigated in detail.