Gas displacing liquids from tubes: high capillary number flow of a power law liquid including inertia effects

• Published in: Chemical engineering science 2004-07, Vol.59 (14), p.2969-2982
• Main Authors: Polynkin, A., Pittman, J.F.T., Sienz, J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Bubble; Chemical engineering; Exact sciences and technology; Fluid mechanics; Inertia effects; Non-Newtonian fluids; Numerical analysis; Reactors; Shear thinning
• ISSN: 0009-2509; 1873-4405
• DOI: 10.1016/j.ces.2004.04.029

Computer simulation has been used as a virtual experimental tool to investigate the displacement of a shear thinning Power Law liquid from a cylindrical tube by a gas, in the limit of high capillary number and in the absence of gravity effects. Two scenarios have been considered. In the first, gas enters at a steady rate, and the gas penetration velocity and residual wall layer thickness attain steady values. In the second, a constant gas pressure is applied at the inlet, and the gas penetration rate accelerates as the column of liquid ahead of it becomes shorter. The first set of experiments confirm that the developed wall layer thickness falls with increased degrees of shear thinning and with increased Reynolds Number, and quantifies the latter effect for the first time. The relationship is summarized by a correlation formula for dimensionless layer thickness as a function of Power Law index, n, and an appropriately defined Reynolds group in the range 0.1⩽ n⩽1.0,0.001⩽ Re⩽100. The flow pattern ahead of the gas bubble throughout the range of these experiments was always of the ‘by-pass’ type, consistent with a generalized criterion for the transition between by-pass and re-circulating flow which is derived for a Power Law liquid. In the second set of experiments, where a constant gas inlet pressure is applied, giving accelerating gas penetration, a comparison of layer thickness values at various axial positions, with those obtained at corresponding Reynolds number in steady flow, showed close agreement, though a small discrepancy for the highest Reynolds numbers could indicate some influence of inertia in the accelerating liquid column. At higher Reynolds number, in both steady and accelerating flow, the gas bubble near to the inlet shows a concave region on the axis, with re-circulation in the liquid ahead of it. As the bubble moves down the tube, the radius of this concavity decreases and a steady convex profile is eventually attained, with reversion of the flow to by-pass type. We show that the origin of this is inertial. The results have applications in a number of technologies, including gas-assisted injection moulding of plastics and certain gas liquid reactors.