Time efficient pattern simulation in multiport Hele-Shaw cells using Voronoi tessellations

Controlled fabrication of families of array patterns has been reported in the recent past using spatially varying port locations in multiport Hele-Shaw cells (MPHSC). Numerical simulations of this phenomenon are computationally expensive, requiring the solution of a time-dependent Poisson's equation with temporally varying boundary conditions. In this paper, we propose simulations of crystal-growth Voronoi tessellations to obtain, within engineering accuracy, the final patterns formed in MPHSC and to enable further interesting investigations. Specifically, we investigate situations with large numbers of ports, and situations where ports on a fixed lattice are digitally controlled both in time and space. The fast marching algorithm employed here substantially reduces the time required for simulation. Our predictions are compared to the CFD results and experimental results to demonstrate efficacy and assess conditions under which the proposed crystal-growth Voronoi diagrams model the final state well.