arXiv subjects

Ivan C. Christov

Publications and source records attributed to Ivan C. Christov.

At least 19 recordsLinked to original sources

arXiv2026

Variational Acoustics

Many variational principles for acoustics have appeared in the literature, often introduced in an \textit{ad hoc} manner by picking and choosing terms in a Lagrangian density to yield a desired governing partial differential equation. In this chapter, we show that such guesswork is unnecessary, as the governing equations of acoustics can be derived systematically from the primitive Lagrangians of classical continuum mechanics. Furthermore, we note that using Eulerian coordinates is not the only way to derive variational principles in acoustics. To this end, we review the construction of an action in the Lagrangian frame for compressible nondissipative fluids. We explore the consequences of material relabeling symmetry and the associated pseudomomentum balance, together with the boundary and jump conditions it implies. Via perturbation expansions, we show how to recover the equations of linear acoustics from each variational principle, the material frame yielding in addition the second-order acoustic energy balance. We show how weakly nonlinear approximations with variational structure emerge in each frame, in both cases for a general barotropic fluid, with the nonlinearity carried by the fluid's parameter $B/A$ and the perfect-gas results recovered as a special case.

physics.flu-dyn↗

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↗

arXiv2026

Flow in a porous non-axisymmetric annular conduit: Coupling wall compliance and peristalsis

Coenen \textit{et al.}\ (\textit{J. Fluid Mech.}, vol.~921, 2021, p.~R2) developed a reduced-order model of peristaltic pumping in non-axisymmetric annular conduits with rigid walls, in the context of periarterial space (PAS) flows. \textit{In vivo} studies show that the PAS's outer wall undergoes significant displacement due to flow within and that the penetrating PASs form a porous pathway. To account for these biomechanical aspects, we revisit the problem of flow in an eccentric annular conduit and incorporate porous drag and two-way-coupled fluid--structure interaction between the compliant outer wall and the cerebrospinal fluid flow within. A Darcy--Brinkman term in the axial momentum equation accounts for drag due to the porous medium. We account for changes in hydraulic resistance due to peristalsis and compliant-wall displacements perturbatively, thereby reducing the problem to a single nonlinear partial differential equation for the axial pressure. This reduced-order model allows us to build a mechanistic understanding of flow through a porous penetrating PAS and enables parametric studies. For small-amplitude peristaltic waves, analytical solutions are possible.

physics.flu-dyn↗

arXiv2026

A fluid--peridynamic structure model of deformation and damage of microchannels

Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not been addressed. To this end, we explore fluid--structure interaction in microchannels whose compliant top wall is governed by a nonlocal mechanical theory capable of simulating both deformation and material failure. We develop a one-dimensional model by coupling viscous flow under the lubrication approximation to a state-based peridynamic formulation of an Euler--Bernoulli beam. The peridynamic formulation enables the wall to be modeled as a genuinely nonlocal beam, and the integral form of its equation of motion remains valid whether the deformation field is smooth or contains discontinuities. Through the proposed computational model, we explore the steady and time-dependent behaviors of this fluid--peridynamic structure interaction. We rationalize the wave and damping dynamics observed in the simulations through a dispersion (linearized) analysis of the coupled system, finding that, with increasing nonlocal influence, wave propagation exhibits a clear departure from classical behavior, characterized by a gradual suppression of the phase velocity. The main contribution of our study is to outline the potential failure scenarios of the microchannel's soft wall under the hydrodynamic load of the flow. Specifically, we find a dividing curve in the space spanned by the dimensionless Strouhal number (quantifying unsteady inertia of the beam) and the compliance number (quantifying the strength of the fluid--structure coupling) separating scenarios of potential failure during transient conditions from potential failure at the steady load.

cs.CE↗

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↗

arXiv2025

Experimental investigation of the flow rate--pressure drop relation of a viscoelastic Boger fluid in a deformable channel

We study the steady flow-induced deformation between an incompressible non-Newtonian fluid and a three-dimensional (3D) deformable channel. Specifically, we provide a comprehensive experimental--theoretical framework for such flows of constant-viscosity viscoelastic (i.e., Boger) fluids, which allows us to quantify the influence of the fluid's viscoelasticity on the flow rate--pressure drop ($q-Δp$) relation. For a flow-rate-controlled regime and weakly viscoelastic flow, we find excellent agreement between the theoretical prediction and experimental results, specifically providing an experimental demonstration of how both wall compliance and fluid viscoelasticity decrease the pressure drop. To definitively demonstrate the coupled effect of wall compliance and fluid viscoelasticity (change of cross-sectional area and curving of streamlines), we perform experiments in an equivalent rigid channel, showing that both the Boger fluid and a viscosity-matched Newtonian fluid have the same pressure drop. Thus, the experimentally verified theory for the $q-Δp$ relation of weakly viscoelastic flows of Boger fluids in compliant channels can now be used for the design of microfluidics and soft hydraulic systems operating with complex fluids.

physics.flu-dyn↗

arXiv2025

Asymptotic Behavior of a Buoyant Jet Regime inside a Carbon-dioxide Ejector

Ejectors are used in various engineering systems, including steam and vapor compression cycles. Optimizing the performance of ejectors requires understanding and analysis of multiphase and turbulent flow structures associated with their internal flow fields. This approach yields higher fidelity but at a high computational cost. Lower-fidelity one-dimensional (1D) models offer lower computational costs; however, 1D models are often empirical and provide limited understanding of the internal flow fields, overlooking possibilities of optimization. Ejector flows can be categorized into four regimes: Regime 1 (R1), which is compressibility dominated; Regime 2 (R2), which is interface instability driven; Regime 3 (R3), which is buoyancy dominated; and Regime 4 (R4), which is a wall-bounded turbulent jet expansion. Among these, the buoyancy-dominated regime is the most complex and least understood. This work discusses an approach to develop a reduced-order model utilizing a self-similarity framework to capture the internal flow field of the jet within the buoyancy-dominated regime under quasi-steady, compressible, and isothermal flow conditions, where density variations arise only from mixing. The density variation is captured through the Favre-averaging approach. The model captures the expansion of a central jet influenced by momentum diffusivity and a constant streamwise pressure gradient. Interaction of the central jet with the cylindrical wall induces a counterflow annular wall jet due to the combined effects of negative radial density gradients and shear stress imposed by the wall. Initially, the discussion focuses on flow topology inside the ejector, followed by the self-similarity methodology and implementation of asymptotic analysis. Finally, the resemblance...

physics.flu-dyn↗

arXiv2025

Hierarchical Bayesian inference for uncertainty quantification of thermal grease rheology

Rheologically complex soft solids such as thermal greases consist of filler particles within a polymer matrix. These materials find applications in improving the conformity of solid-solid contacts and enhancing heat transfer. Complex soft solids exhibit a transient non-Newtonian rheological response, including thixotropy and viscoelasticity. Previously, stress relaxation and buildup in sheared commercial thermal greases were successfully captured using a nonlinear elasto-visco-plastic (NEVP) model and a thixo-elasto-visco-plastic (TEVP). However, the previous model calibration methods ignored parameter uncertainty, providing only single values of the rheological parameters, and did not quantitatively address the chosen model's identifiability from the data or credibility of the calibration. We address these limitations via hierarchical Bayesian inference, accounting for uncertainties arising from epistemic and aleatoric sources. Importantly, the hierarchical approach allows us to assimilate experiments measuring the stress responses at various startup shear rates by allowing the models' parameters to vary across different shear rates. Then, a global distribution and the associated uncertainty are obtained by pooling. We also propagate uncertainties to the transient shear stress response predicted by the models. Overall, we demonstrate that the chosen NEVP and TEVP models are identifiable from rheometric startup data. However, for the TEVP model, the uncertainty of the parameters is lower (narrower distributions) when higher shear rates are used for inference.

cond-mat.soft↗

arXiv2025

Correlations for the Interphase Drag in the Two-Fluid Model of Gas--Liquid Flows through Packed-Bed Reactors

Experiments conducted by NASA measured the pressure drop due to gas--liquid flow through a packed-bed reactor under microgravity conditions. From these experiments, we develop correlations for the gas--liquid $f_{gl}$ interphase drag in a two-fluid model (TFM). We use an Ergun-type closure for liquid--solid drag. Then, under a 1D flow assumption, $f_{gl}$ is the only unknown in the TFM. Using a data-driven approach, we determine $f_{gl}$ and correlate it (via composite fits) with the liquid and gas Reynolds numbers, $Re_{l}$ and $Re_{g}$, respectively, and the Suratman number $Su_{l}$. To validate the proposed $f_{gl}(Re_{l},Re_{g},Su_{l})$ closure, we perform two-dimensional transient simulations at microgravity conditions using ANSYS Fluent and employing an Euler--Euler formulation. We find good agreement between the simulations based on the proposed $f_{gl}$ closure and the experimental data.

physics.flu-dyn↗

arXiv2024

Series solutions for clamped peridynamic beams using fourth-order eigenfunctions

We propose an analytical approach to solving nonlocal generalizations of the Euler--Bernoulli beam. Specifically, we consider a version of the governing equation recently derived under the theory of peridynamics. We focus on the clamped--clamped case, employing the natural eigenfunctions of the fourth derivative subject to these boundary conditions. Static solutions under different loading conditions are obtained as series in these eigenfunctions. To demonstrate the utility of our proposed approach, we contrast the series solution in terms of fourth-order eigenfunctions to the previously obtained Fourier sine series solution. Our findings reveal that the series in fourth-order eigenfunctions achieve a given error tolerance (with respect to a reference solution) with ten times fewer terms than the sine series. The high level of accuracy of the fourth-order eigenfunction expansion is due to the fact that its expansion coefficients decay rapidly with the number of terms of the series, one order faster than the Fourier series in our examples.

physics.class-ph↗

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↗

arXiv2024

Sixth-order parabolic equation on an interval: Eigenfunction expansion, Green's function, and intermediate asymptotics for a finite thin film with elastic resistance

A linear sixth-order partial differential equation (PDE) of ``parabolic'' type describes the dynamics of thin liquid films beneath surfaces with elastic bending resistance when deflections from the equilibrium film height are small. On a finite domain, the associated sixth-order eigenvalue problem is self-adjoint for the boundary conditions corresponding to a thin film in a closed trough, and the eigenfunctions form a complete orthonormal set. Using these eigenfunctions, we derive the Green's function for the governing sixth-order PDE on a finite interval and compare it to the known infinite-line solution. Further, we propose a Galerkin spectral method based on the constructed sixth-order eigenfunctions and their derivative expansions. The system of ordinary differential equations for the time-dependent expansion coefficients is solved by standard numerical methods. The numerical approach is applied to versions of the governing PDE with a second-order spatial derivative (in addition to the sixth-order one), which arises from gravity acting on the film. In the absence of gravity, we demonstrate the self-similar intermediate asymptotics of initially localized disturbances on the film surface, at least until the disturbances ``feel'' the finite boundaries, and show that the derived Green's function is an attractor for such solutions. In the presence of gravity, we use the proposed Galerkin numerical method to demonstrate that self-similar behavior persists, albeit for shortened intervals of time, even for large values of the gravity-to-bending ratio.\\[1mm]

math.NA↗

arXiv2024

Flow rate-pressure drop relations for shear-thinning fluids in deformable configurations: theory and experiments

We provide an experimental framework to measure the flow rate--pressure drop relation for Newtonian and shear-thinning fluids in two common deformable configurations: (\textit{i}) a rectangular channel and (\textit{ii}) an axisymmetric tube. Using the Carreau model to describe the shear-dependent viscosity, we identify the key dimensionless rheological number, $Cu$, which characterizes shear thinning, and we show that our experiments lie within the power-law regime of shear rates. To rationalize the experimental data, we derive the flow rate-pressure drop relation taking into account the two-way-coupled fluid-structure interaction between the flow and its compliant confining boundaries. We thus identify the second key dimensionless number, $α$, which characterizes the compliance of the conduit. We then compare the theoretical flow rate-pressure drop relation to our experimental measurements, finding excellent agreement between the two. We further contrast our results for shear-thinning and Newtonian fluids to highlight the influence of $Cu$ on the flow rate-pressure drop relation. Finally, we delineate four distinct physical regimes of flow and deformation by mapping our experimental flow rate-pressure drop data for Newtonian and shear-thinning fluids into a $Cu-α$ plane.

physics.flu-dyn↗

arXiv2023

Hydrodynamics of bubble flow through a porous medium with applications to packed bed reactors

Gas-liquid flows through packed bed reactors (PBRs) are challenging to predict due to the tortuous flow paths that fluid interfaces must traverse. Experiments at the International Space Station showed that bubble and pulse flows are predominately observed under microgravity conditions, while the trickle and spray flows observed under terrestrial conditions are not present in microgravity. To understand the physics behind the former experiments, we simulate bubble flow through a PBR for different packing-particle-diameter-based Weber numbers and under different gravity conditions. We demonstrate different pore-scale mechanisms, such as capillary entrapment, buoyancy entrapment, and inertia-induced bubble displacement. Then, we perform a quantitative analysis by introducing new dynamic scales, dependent upon the evolving gas-liquid interfacial area, to understand the dynamic trade-offs between the inertia, capillary, and buoyancy forces on a bubble passing through a PBR. This analysis leads us to define new dimensionless Weber-like numbers that delineate bubble entrapment from bubble displacement.

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↗

arXiv2023

Multi-bounce resonances in the interaction of walking droplets

Discrete dynamical models of walking droplets ("walkers") have allowed swift numerical experiments revealing heretofore unobserved quantum statistics and related behaviors in a classical hydrodynamic system. We present evidence that one such model of walking droplets exhibits the empirically elusive $n$-bounce resonances that are traditionally seen in the scattering of solitary waves governed by covariant nonlinear field theories with polynomial self-interaction. A numerical investigation of the chosen model of interacting walking droplets reveals a fractal structure of resonances in the velocity in--velocity out diagram, much like the usual maps constructed for collisions of solitary waves. We suggest avenues for further theoretical analysis of walker collisions, which may connect this discrete model to the field-theoretic setting, as well as directions towards new experimental realizations $n$-bounce resonances.

nlin.CD↗

arXiv2023

Data-driven rheological characterization of stress buildup and relaxation in thermal greases

Thermal greases, often used as thermal interface materials, are complex paste-like mixtures composed of a base polymer in which dense metallic (or ceramic) filler particles are dispersed to improve the heat transfer properties of the material. They have complex rheological properties that impact the performance of the thermal interface material over its lifetime. We perform rheological experiments on thermal greases and observe both stress relaxation and stress buildup regimes. This time-dependent rheological behavior of such complex fluid-like materials is not captured by steady shear-thinning models often used to describe these materials. We find that thixo-elasto-visco-plastic (TEVP) and nonlinear-elasto-visco-plastic (NEVP) constitutive models characterize the observed stress relaxation and buildup regimes respectively. Specifically, we use the models within a data-driven approach based on physics-informed neural networks (PINNs). PINNs are used to solve the inverse problem of determining the rheological model parameters from the dynamic response in experiments. This training data is generated by startup flow experiments at different (constant) shear rates using a shear rheometer. We validate the ``learned'' models by comparing their predicted shear stress evolution to experiments under shear rates not used in the training datasets. We further validate the learned TEVP model by solving a forward problem numerically to determine the shear stress evolution for an input step-strain profile. Meanwhile, the NEVP model is further validated by comparison to a steady Herschel--Bulkley fit of the material's flow curve.

cond-mat.soft↗