The gas-driven displacement of a viscous liquid from a confined geometry is a classical class of problems in interfacial fluid dynamics. This process also features in a variety of practical applications, including the operation of a fuel cell, the subsurface storage of carbon dioxide or hydrogen, and even the squeezing of ketchup out of a bottle. In all of these scenarios, the compression of the gas provides the driving force and the viscosity of the liquid provides the resistance. However, both the amount of compression and the amount of resistance are typically coupled to the amount of liquid that has been displaced. Here, we show that the tight coupling of these basic mechanical ingredients leads to surprising behavior, even in the simplest of settings. We study the impact of gas compression on gas-liquid displacement in capillary tubes and Hele-Shaw cells using laboratory experiments, minimal mathematical models, linear stability analysis, and fully nonlinear numerical simulations. We show that a steady rate of squeezing can generate a strongly unsteady flow and we identify a new dimensionless parameter, the compressibility number, that controls the evolution of the flow. We show that increasing the compressibility number can trigger a sudden flow transition in a capillary tube and can systematically delay the onset -- and decrease the ultimate severity -- of viscous fingering in a Hele-Shaw cell.
Christopher W. MacMinn - Compression-driven gas-liquid displacement
Professor Christopher MacMinn is a Professor of Engineering Science at the University of Oxford and leads the Poromechanics Lab, an interdisciplinary research group that brings together engineers, physicists, mathematicians, and earth scientists. His work focuses on the mechanics of fluids and soft materials, particularly how fluids flow through and deform porous materials such as soils, biological tissues, gels, and subsurface rock formations.
Professor MacMinn earned his SB, SM, and PhD in Mechanical Engineering from the Massachusetts Institute of Technology (MIT), where he worked with Ruben Juanes on the fluid mechanics of geological carbon dioxide sequestration. He later held a postdoctoral position at Yale University where he worked with John Wettlaufer and Eric Dufresne, researching the deformation of porous and granular materials.
His research combines mathematical modeling with laboratory experiments to address challenges in energy, environmental science, soft materials, and biomedical engineering. Recent work from his group has advanced understanding of fluid-driven deformation, gas migration in soft materials, carbon storage, and multiphase flow in porous media.
To read more about him please check out his webpage.