arXiv subjects

Shrihari D. Pande

Publications and source records attributed to Shrihari D. Pande.

6 recordsLinked to original sources

arXiv2026

Theory and simulation of elastoinertial rectification of oscillatory flows in two-dimensional deformable rectangular channels

Oscillatory flows in compliant confinements underpin processes ranging from physiological transport in blood vessels and airways to flow control and pumping in soft microfluidic devices. To understand the fundamental physics behind such processes, we study how hydrodynamic forces induce deformation at the fluid--solid interface in a slender two-dimensional (2D) channel bounded below by a rigid bottom surface and above by a slender elastic layer. The nonlinear coupling between flow and deformation, along with the attendant geometric asymmetry caused by flow-induced deformation, produces a streaming effect (a nonzero cycle-average despite time-periodic forcing). Surprisingly, flow inertia provides another nonlinear coupling, tightly connected to deformation, that enhances streaming, termed "elastoinertial rectification" by Zhang and Rallabandi [J. Fluid Mech. 996, A16 (2024)]. We adapt the latter theory of how two-way coupled fluid--structure interaction (FSI) produces streaming to a 2D rectangular configuration, specifically taking care to capture the deformations of the nearly incompressible slender elastic layer via the combined foundation model of Chandler and Vella [Proc. R. Soc. A 476, 20200551 (2020)]. We put this elastoinertial rectification theory to a stringent test against direct numerical simulations performed using a stabilized, conforming arbitrary Lagrangian--Eulerian FSI formulation, implemented via the open-source computing platform FEniCS. We examine the axial variation of the cycle-averaged pressure as a function of key dimensionless groups of the problem: the Womersley number and the elastoviscous number. Assuming a small compliance number, we find excellent agreement between a perturbative calculation based on elastoinertial rectification theory and the simulations for both the leading-order and cycle-averaged pressure and deformation across a range of conditions.

physics.flu-dyn↗

arXiv2025

Reciprocal theorem for calculating the flow rate of oscillatory channel flows

We demonstrate the use of the Lorentz reciprocal theorem in obtaining corrections to the steady flow rate due to flow oscillations in rigid channels. Starting from the unsteady Stokes equations, we derive the suitable reciprocity relation, assuming all quantities can be expressed as time-harmonic phasors. The auxiliary problem is the steady Hagen--Poiseuille flow solution, from which the reciprocal theorem allows us to calculate the first-order correction in the Womersley number to the steady flow rate in a straight rigid channel. We also consider nonuniform channels, specifically with variable height in the flow-wise direction, in which case the flow rate correction provides the leading-order effect of the interplay between the oscillations of the fluid flow and the given shape of the channel.

physics.flu-dyn↗

arXiv2025

Oscillatory flows in three-dimensional deformable microchannels

Deformable microchannels emulate a key characteristic of soft biological systems and flexible engineering devices: the flow-induced deformation of the conduit due to slow viscous flow within. Elucidating the two-way coupling between oscillatory flow and deformation of a three-dimensional (3D) rectangular channel is crucial for designing lab- and organ-on-a-chip microsystems and eventually understanding flow-structure instabilities that can enhance mixing and transport. To this end, we determine the axial variations of the primary flow, pressure, and deformation for Newtonian fluids in the canonical geometry of a slender (long) and shallow (wide) 3D rectangular channel with a deformable top wall under the assumption of weak compliance and without restriction on the oscillation frequency (\textit{i.e.}, on the Womersley number). Unlike rigid conduits, the pressure distribution is not linear with the axial coordinate. To validate this prediction, we design a PDMS-based experimental platform with a speaker-based flow-generation apparatus and a pressure acquisition system with multiple ports along the axial length of the channel. The experimental measurements show good agreement with the predicted pressure profiles across a wide range of the key dimensionless quantities: the Womersley number, the compliance number, and the elastoviscous number. Finally, we explore how the nonlinear flow-deformation coupling leads to self-induced streaming (rectification of the oscillatory flow). Following Zhang and Rallabandi (\textit{J.\ Fluid Mech.}, vol.~996, 2024, A16), we develop a theory for the cycle-averaged pressure based on the primary problem's solution, and we validate the predictions for the axial distribution of the streaming pressure against the experimental measurements.

physics.flu-dyn↗

arXiv2024

Pressure drop reduction due to coupling between shear-thinning fluid flow and a weakly deformable channel wall: A reciprocal theorem approach

We employ the Lorentz reciprocal theorem to derive a closed-form expression for the pressure drop reduction due to the coupling between shear-thinning fluid flow and a weakly deformable channel wall in terms of the shear rate and the viscosity function (and its derivative) of the underlying rigid-channel flow. The methodology is applied in parallel to fluids for which the generalized Newtonian viscosity depends on either the shear rate or the shear stress magnitude. When the viscosity model allows for a closed-form solution for the axial velocity profile in a straight and rigid channel, the pressure drop reduction can be evaluated in closed form, which we demonstrate for the power-law and Ellis viscosity models as featured examples and to enable comparisons to previous works. Importantly, the pressure drop reduction under the Ellis model is valid for both small and large Carreau (or Ellis) numbers, and we show that it reduces to the analytical expression under the power-law model for large Carreau (small Ellis) numbers.

physics.flu-dyn↗

arXiv2023

Oscillatory flows in compliant conduits at arbitrary Womersley number

We develop a theory of fluid--structure interaction (FSI) between an oscillatory Newtonian fluid flow and a compliant conduit. We consider the canonical geometries of a 2D channel with a deformable top wall and an axisymmetric deformable tube. Focusing on the hydrodynamics, we employ a linear relationship between wall displacement and hydrodynamic pressure, which has been shown to be suitable for a leading-order-in-slenderness theory. The slenderness assumption also allows the use of lubrication theory, and the flow rate is related to the pressure gradient (and the tube/wall deformation) via the classical solutions for oscillatory flow in a channel and in a tube (attributed to Womersley). Then, by two-way coupling the oscillatory flow and the wall deformation via the continuity equation, a one-dimensional nonlinear partial differential equation (PDE) governing the instantaneous pressure distribution along the conduit is obtained, without \textit{a priori} assumptions on the magnitude of the oscillation frequency (\textit{i.e.}, at arbitrary Womersley number). We find that the cycle-averaged pressure (for harmonic pressure-controlled conditions) deviates from the expected steady pressure distribution, suggesting the presence of a streaming flow. An analytical perturbative solution for a weakly deformable conduit is obtained to rationalize how FSI induces such streaming. In the case of a compliant tube, the results obtained from the proposed reduced-order PDE and its perturbative solutions are validated against three-dimensional, two-way-coupled direct numerical simulations. We find good agreement between theory and simulations for a range of dimensionless parameters characterizing the oscillatory flow and the FSI, demonstrating the validity of the proposed theory of oscillatory flows in compliant conduits at arbitrary Womersley number.

physics.flu-dyn↗

arXiv2022

Flow rate--pressure drop relations for new configurations of slender compliant tubes arising in microfluidics experiments

We investigate the steady-state fluid--structure interaction between a Newtonian fluid flow and a deformable microtube in two novel geometric configurations arising in recent microfluidics experiments. The first configuration is a cylindrical fluidic channel surrounded by an annulus of soft material with a rigid outer wall, while the second one is a cylindrical fluidic channel extruded from a soft rectangular slab of material. In each configuration, we derive a mathematical theory for the nonlinear flow rate--pressure drop relation by coupling lubrication theory for the flow with linear elasticity for the inner tube wall's deformation. Using the flow conduit's axial slenderness and its axisymmetry, we obtain an analytical expression for the radial displacement in each configuration from a plane-strain configuration. The predicted displacement field, and the resulting closed-form flow rate--pressure drop relation, are each validated against three-dimensional direct numerical simulations via SimVascular's two-way-coupled fluid--structure interaction solver, svFSI, showing good agreement. We also show that weak flow inertia can be easily incorporated in the derivation, further improving the agreement between theory and simulations for larger imposed flow rates.

physics.flu-dyn↗