A new understanding of patterns in fluid flow

(a) A fluid of blue color that is enclosed by a less viscous fluid. (b) VF observed during experiments. (c) Mathematically, VF is shown in black. (d) A persistent phenomenon that was observed in experiments. (e) A mathematically observed persistent phenomenon. Credit: Tokyo University of Agriculture and TechnologyThrough a combination experiment and numerical simulation, scientists have discovered the viscous fingering of an annular rings. This is where the 'fingers" in a fluid with finite volume grow radially. They have shown that the VF in an annular rings is a persistent phenomenon.Their results were published in the Journal of Fluid Mechanics, April 6, 2021.A less viscous fluid can move in a viscous media while a more viscous fluid is in porous media. This causes the interface between them to become unstable and forms finger shapes. This VF has been studied since the 1950s as a fluid dynamics problem. The VF can be divided into two types: radially or rectilinearly."The interface of two semi-infinite domains with different viscosities has been studied historically. Recent research has focused on VF at the interface between two fluids of finite volume. This is because it is relevant to chromatography and groundwater contamination. VFs formed by finite volume fluids with linear geometry have so far been mainly studied through numerical simulation. However, VFs that are formed in finite volumes fluids with radial geometry have not been studied either numerically or experimentally. Dr. Nagatsu is Associate Professor at the Department of Chemical Engineering, Tokyo University of Agriculture and Technology. This is due to the difficulty in solving the governing equations numerically and the complexity of creating finiteness through experiments.The integrated analysis and numerical simulation of VF in finite volume fluids with radial geometry were achieved by the research team (see Figure). The experiments were conducted in a Hele Shaw cell, which is an experimental apparatus that mimics porous medium flows. Simulation is performed using the module of COMSOL Multiphysics (TPDL), which uses the Darcy law in two phases."Our team discovered that the VF in an annular ring is a permanent phenomenon, contrary to the transient nature seen with VF in a slice. (see Figure). New fingers may cease to appear after a while, but due to the radial spreading area for VF, a finite amount of fingers remain at a later date. Nagatsu explains that VF can only be observed if the finite layer is larger than some value."Our results show that VF in an annular ring has a dramatically different dynamic than those of radial and rectilinear fluids with one fluid sandwiched between layers. In fact, annular VF is caused by groundwater contamination and enhanced oil-recovery. Nagatsu says that our findings will allow us to predict such processes with high accuracy."Explore more A new study could revise a 60 year-old theory concerning flowing viscous fluidsFurther information: Vandita Sharma et. al., Viscous fingering of a miscible annular ring. Journal of Fluid Mechanics (2021). Journal Information: Journal of Fluid Mechanics Vandita Singh et al., Viscous fingering of a miscible annular ring. (2021). DOI: 10.1017/jfm.2021.124Tokyo University of Agriculture and Technology