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.

Nonlinear Phenomena in Microfluidics

“…As bubbles or droplets travel through microfluidic networks composed of channels with constant cross-sectional areas, such as those depicted in Figure , they show nonlinear behaviors. At a junction of two diverging paths, a bubble or droplet will choose the path with the lower hydraulic resistance or, equivalently, the one through which the continuous phase flows more quickly. − The hydraulic resistance is a measure of how difficult it is for a fluid to flow through a channel; it is defined as the ratio between the pressure difference across the channel and the resultant flow rate . The decision of which path to select is local because it depends on the flow rates of the continuous phase through the branches immediately extending from the junction.…”

Formation of Droplets of Shear-Thinning Non-Newtonian Fluids in Asymmetrical Parallelized Microchannels

“…Microfluidics technology has been applied to polymerization reactions due to the advantages of controlling the related process . As the polymerization proceeds, the viscosity and the rheological property of fluids may be changed, and most polymer solutions exhibit shear-thinning property that affects the flow and mixing of fluids in microchannels. , Recently, the droplet and bubble formation and the hydrodynamics of droplets in shear-thinning fluids in microchannels have been studied. − The stability and uniformity of bubbles in shear-thinning fluids have also been investigated, but the liquid–liquid system is different from the gas–liquid system due to the larger pressure drop and the incompressibility of the liquid in microchannels. Microchannels with the asymmetrical structure used in this work are also different from the symmetrical microchannels used in the gas–liquid system.…”