A Variable Density and Viscosity Solver for Acoustic Streaming

Acoustofluidics, the merger of acoustics and microfluidics, has shown significant promise for lab-on-a-chip applications. Fluid response in acoustofluidic systems is characterized by a harmonic component and a time-averaged acoustic streaming component. Typical numerical models either consider fluid-only systems or assume the immersed objects (e.g., bubbles, cells, particles, etc.) to have same density/viscosity as the surrounding fluid.), which omits interesting physics concerning acoustic response of variable density and viscosity media.



We present a numerical formulation that considers spatially and temporally varying density and viscosity in an acoustofluidic system. Using a perturbation approach, we split the problem into a harmonic first-order and a second-order acoustic streaming system. The former is a hyperbolic system solved using a sparse direct solver while the latter resembles a steady low-Mach Stokes system, with forcing terms arising from the first-order solution. The second-order system is solved using the FGMRES solver with a matrix-free implementation and a projection method-based preconditioner. In both first- and second-order systems, we achieve O(2) accuracy. Furthermore, we adapt the variable viscosity and density formulation to model rigid immersed objects in acoustofluidic flows via a Brinkman penalization method and provide the details of implementation within the open-source Immersed Boundary Adaptive Mesh Refinement (IBAMR) framework.