InterPore2026

Multistep Injection Protocols in Immiscible and Partially Miscible Hele–Shaw Flows: Coupled Hydrodynamic and Thermodynamic Effects

20 May 2026, 10:05

1h 30m

Poster Presentation (MS05) Physics of multiphase flow in diverse porous media Poster

Speaker

Ms Mousumi Mondal (Indian Institute of Technology Guwahati)

Description

Interfacial instabilities are ubiquitous in nature and often give rise to fascinating patterns. One such hydrodynamic instability is viscous fingering [1], which occurs when a more viscous fluid is displaced by a less viscous one in a porous medium. Also, when a fluid mixture enters the spinodal region (where the second derivative of the free energy is negative), the mixture becomes thermodynamically unstable and undergoes phase separation [2], which leads to the spontaneous formation and growth of compositionally distinct regions. Previously, a study by Deki et al. [3] examined the effects of phase separation on viscous fingering in radial Hele–Shaw flows under continuous injection, with the injected concentration lying in the spinodal region. We numerically investigate how multistep injection protocols, implemented through a prescribed time variation of the injected concentration in the spinodal as well as the binodal region, influence the coupled hydrodynamic and thermodynamic effects in immiscible and partially miscible radial Hele –Shaw flows. The dynamics are described with a diffuse–interface Hele–Shaw–Cahn–Hilliard model yielding coupled governing equations for flow and concentration [3]. To solve the system numerically, the continuity and momentum equations are reformulated into the well-known stream function–vorticity formulation, and the resulting Poisson equation is solved using a hybrid pseudospectral method combined with higher-order compact finite differences [4,5]. The concentration equation is discretized using a sixth-order compact scheme and advanced in time employing an explicit third-order Runge–Kutta method with a CFL-based adaptive time step.

In this study, we consider a range of injection protocols which includes continuous, one-step, two-step, three-step, four-step, and linear injection. For continuous injection, we set the nondimensional injected concentration to $c_i=1$. For one-step through four-step injections, we consider various combinations of injected concentrations while keeping the total injected volume, $V_{\mathrm{inj}}=\int_{0}^{t} c(\tau) d\tau$, fixed at $0.5$. For linear injection, we impose $c_i=t$. We find that multistep injection enables control over the displacement outcome. Prescribed stepwise variations in the injection rate drive the system into distinct regimes, either enhancing viscous fingering or suppressing fingering while triggering or delaying phase separation in the system. Such protocol-based control can be used to target a desired sweep efficiency, mixing level, or resulting interfacial patterns with direct relevance to injection-driven displacement processes in porous media such as enhanced oil recovery and groundwater remediation.