A deterministic model for bubble propagation through simple and cascaded loops of microchannels in power-law fluids

Abstract

This paper investigates the path selection of bubbles suspended in different power-law carrier liquids in microfluidic channel networks. A finite volume-based numerical method is used to analyze the two-dimensional incompressible fluid flow in microchannels, while the volume of fluid method is used to capture the gas–liquid interface. To instill the influences of shear thinning, Newtonian, and shear-thickening fluids, the range of power-law indices (n) is varied from 0.3 to 1.5. We have validated our numerical model with the available literature data in good agreement. We have investigated the nonlinearity in the hydrodynamic resistance which arises due to single-phase non-Newtonian fluid flow. The path selection of a bubble in power-law fluids is examined from the perspective of velocity distribution and bubble deformation. We have found that the bubble indeed goes to the channel with a higher flow rate for all power-law fluids, but interestingly it did not always take the shorter route channel at a junction for n = 0.3. Our results suggest that long channels need not be more resistant for every fluid and that the longest arm becomes the least resistant resulting in the bubble leading into the long arm at a junction for shear-thinning fluid. We have proposed a deterministic model that enables predicting the second bubble path in a single bubble system for any location of the first bubble. We believe that the present study results will help design future generation microfluidic systems for efficient drug delivery and biomedical and biochemical applications.