Small density differences, large Richardson numbers: buoyancy decides where gypsum deposits in a centifluidic confluence cell

Abstract

The mixing of two aqueous streams in small channels is usually modeled with constant density when the difference in density between the streams is only a few percent or less. In this paper, we investigate whether this holds in a confluence cell where calcium chloride and sodium sulfate meet and form gypsum. A constant density simulation of the reacting flow results in deposition on the floor along the channel centreline. However, in the experiment, gypsum instead forms bands on both side walls, and the deposition bands start further upstream as the flow rate decreases. Dye experiments with density differences between the streams of 0.14 to 2.1\,\%, three channel heights, and 32 flow rates show that the distance at which the dyed stream reaches the opposite side wall is governed by the bulk Richardson number, $Ri=g'H/U^2$, and follows $L/H = 3.31\,Ri^{-0.66}$ over four decades of $Ri$ ($R^2=0.89$). When the two streams' densities match, the dyed stream no longer reaches the opposite wall under most conditions, and in a density-matched reacting experiment, gypsum deposits on the floor, as the constant-density simulation predicts. A small relative density difference is thus not a sufficient condition for neglecting buoyancy: the Richardson number must also be small. For the flow rates typical of centifluidic devices, it often is not.