We consider the coupled motion of a passive interface separating two immiscible
fluids of different viscosities. There are several applications where the velocity of the
two fluids is needed everywhere within the domain. Examples include the
transport of bacteria and diffusing substances within a biofilm matrix and the
transport of cations throughout the mucociliary and periciliary layer in the
lung lining. In this investigation, we use a hybrid approach which employs
the boundary integral method to determine the interface velocity and the
method of regularized stokeslets to determine the velocity elsewhere in the
domain.
Our approach capitalizes on the strengths of the two methods, yielding an
intuitive, efficient procedure for determining the velocity of a two-fluid system
throughout the domain. A key feature of the method is the extension to
two-fluid systems with varying viscosity. We describe the results of three
numerical simulations designed to test the numerical method and motivate its
use.
Keywords
two-fluid, boundary integral method, regularized
stokeslets, biofilm
