RESEARCH

Thermodynamic instability in partially miscible fluids

We are investigating viscous fingering in partially miscible fluids. Unlike miscible and immiscible fluids, partially miscible fluids exhibits the formation of fingers which split into droplets and propagate due to spontaneous convection. During such process, a Korteweg force, which is thermodynamic in nature, is developed due to the chemical potential gradient minimizing the free energy stored at the interface, resulting in ‘Spinodal Decomposition’. The Margules parameter, Ψ which models the intermolecular interactions is shown to have a critical value below which hydrodynamic effects dominate with fingers developing at the interface while above the critical value of Ψ, thermodynamic effects kicks in with droplet formation. We solve the coupled Navier-Stokes-Cahn-Hillard equations and investigate numerically such processes.

Journal of Fluid Mechanics, (2022)

Reactive Viscous Fingering in Porous medium

We focus on studying chemically reactive fronts, specifically the reaction 𝐴 + 𝐵 → 𝐶 in porous media. we determine the stability of reactive displacements in terms of Rb and RC and, dividing the parameter space (Rb ,RC ) into stable and unstable regions for each Péclet number (Pe) and Da. The stable region in the (Rb ,RC ) phase plane contracts with increasing Pe and Da but never disappears; it persists even as Da approaches infinity. Interestingly, we identify a stable region independent of Da near Rb =RC , where there is no stability transition despite changes in the reaction rate. We also explore how viscous fingering impacts reaction properties. For higher viscosity ratios, we report the existence of frozen fingers in this reactive fluid system. Further, we determine a scaling relation to compute onset time for a given Peclet number and viscosity contrast between reactants and product. Our numerical results allow us to understand how instability and chemical reactions interplay to affect the reaction characteristics and the mixing of fluids.

Coupled effect of viscous and gravitational fingering

Linear and nonlinear dynamics of viscous and gravitational fingering in porous media are studied. We show that a gradient in the dynamic viscosity reduces the instability of gravitational fingering. On the other hand, the consequence of density gradient adds up to the viscous fingering instability. We also show that the displacement velocity has no influence on the gravitational fingering in viscosity-matched fluids. Rigorous numerical simulations reveal that depending on the viscosity and density contrasts, and the displacement velocity, a finite slice can feature six different instability modes. We observe viscous fingers induce gravitational fingers and vice-versa, and also a stable displacement.

Adsorbed Solute Dynamics

Our basic goal is to analyze the effect of hydrodynamic instability in separation dynamics. The VF phenomena has a significant effect on the separation of components in liquid hydrodynamic instability. The separation phenomena is based on the retention of the solute on the porous matrix which get affected by the fingering instability. We mathematically model this phenomena to better understand the flow separation dynamics.

Viscous Fingering Dynamics

Miscible viscous fingering (VF) instability is one of the fundamental hydrodynamic instabilities (Saffman-Taylor instability) having various industrial and biological applications. Few of them favours VF, whereas others require stabilization of the VF instability. One such way of stabilization is to create steep concentration gradient giving rise to Korteweg stress. Here we look how such stress controls the VF instability and to use it as a control parameter.

Nonnormality and Transient Growth of the Perturbations

The nonnormality and transient growth of the perturbations are investigated in the context of miscible viscous fingering in porous media. Nonmmodal stability analysis is performed based on the matrizant or propagator matrix method to determine the optimal perturbations. The obtained results capture the physics of the problem more appropriately. Our obtained results are in accordance with direct numerical simulations.

Figure 7(e)_R=2.mp4

Movie displays the temporal evolution of the Kelvin Helmholtz Instability at the interface for Two-layer Flows

Kelvin Helmholtz Instability

When fluid flows through a confined channel, boundary-induced shear effects cause differential velocities across fluid layers, with the velocity profile being slower near the walls and faster in the center. This shear flow can lead to the Kelvin-Helmholtz instability, where differences in flow velocity between layers can trigger wave-like disturbances. Through extensive numerical simulations, we aim to understand and control these instabilities. Our parametric study examines the role of key dimensionless parameters—Reynolds number (Re), Peclet number (Pe), and the logarithmic mobility ratio (R)—in influencing the onset of instability and fluid mixing in such shear-driven flows.

These findings provide an essential foundation for managing shear-induced instabilities, which is vital for various industrial applications, including those requiring high-precision fluid flow control.

Kelvin Helmholtz Instability in Reactive Systems

In reactive channel flows, the interaction between fluids through chemical reactions introduces unique instability mechanisms due to the varying viscosities of reactants and products. In configurations like two-layer and displacement flows, where we consider a simple second-order reaction (A + B → C), the newly formed product can exhibit different viscosity profiles. These changes create complex and potentially unstable flow patterns, influenced by reaction rates, concentration gradients, and flow parameters. Our study serves as a framework for assessing chemo hydrodynamic instabilities, particularly in settings where stability is crucial. In reactive systems, an additional dimensionless parameter, the Damköhler number (Da), quantifies the rate of reaction relative to flow. Larger Da numbers indicate faster reaction rates, further impacting the stability characteristics of these flows.

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