PHYSICAL REVIEW FLUIDS 7, 044001 (2022) Nanoparticles impact on miscible viscous fingering with absorbing boundary condition at inlet Anoop Kumar 1, 2 and Manoranjan Mishra 1 , * 1 Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar-140001, Punjab, India 2 Department of Mathematics, Government College Barwala (Panchkula), 134118, Haryana, India (Received 30 July 2021; accepted 17 March 2022; published 4 April 2022) The addition of nanoparticles in fluids significantly influences the fluid’s viscosity and can be helpful to control viscosity-driven instability. In this work, we analyze how such nanoparticles modulate viscosity and impact miscible viscous fingering (VF) dynamics. We consider the flow configuration such that the Hele-Shaw cell is initially filled with a viscous fluid and then displaces it with other viscous fluid-carrying nanoparticles through the inlet boundary, which corresponds to the absorbing boundary condition. A closed- form solution of base-state flow using the Laplace-transform method is obtained, which overcomes the discrepancy of the base-state solution known in the form of an infinite series as available in the literature. Due to the time-dependency and nonmonotonic nature of the base state, nonmodal linear stability analysis in the self-similar domain is used to determine the onset time of instability. In this work, the effects of various governing flow parameters such as nanoparticles diffusive coefficient (α np ), effective log-mobility ratio (R), and deposition rate of nanoparticles (Da dep ) on the instability are studied. Our finding suggests that the onset occurs early with increasing Da dep for α np > 1, whereas such onset time is a nonmonotonic function of Da dep for smaller values of α np . In addition, our results indicate that the onset time is a nonmonotonic function of α np for the smaller value of Da dep , whereas such onset time is an increasing function of α np for the larger value of Da dep . Further, nonlinear simulations are performed using COMSOL MULTIPHYSICS, and the nonmonotonic nature on the onset of instability for different α np is observed which is in good agreement with the linear stability analysis results. The present investigation removes various inconsistencies in the literature about the impact of the nanoparticles on VF with the quasi-steady-state approximation. DOI: 10.1103/PhysRevFluids.7.044001 I. INTRODUCTION In porous media, instability is often observed at the fluid-fluid interface when a less viscous fluid displaces a more viscous fluid, known as viscous fingering (VF) instability [1,2]. Conversely, when a more viscous fluid displaces a less viscous fluid, the fluid-fluid interface remains stable. In this work, we assume fluids are miscible and incompressible. In addition, fluid-fluid displacement is considered rectilinear. VF is significantly observable in various displacement processes such as in enhanced oil recovery [2], chromatography separation techniques [3], CO 2 sequestration in the underground reservoir [4,5], and contaminant transport in aquifers [6], to name a few. A Hele-Shaw cell is commonly used in the laboratory to study such interfacial phenomena in the miscible displacement process. In most experiments, the Hele-Shaw cell is first filled with one fluid and displaces it with another fluid through the inlet boundary. So in this work, we considered the flow configuration taken by Ghesmat et al. [7] where initially a more viscous fluid filled in the * manoranjan@iitrpr.ac.in 2469-990X/2022/7(4)/044001(20) 044001-1 ©2022 American Physical Society