arXiv subjects

Evgeniy Boyko

Publications and source records attributed to Evgeniy Boyko.

18 recordsLinked to original sources

arXiv2026

Understanding the Theory--Experiment Discrepancy in Pressure Drop of Dilute Polymer Solutions in Channel Flows

For decades researchers have experimentally observed that the flow of dilute viscoelastic polymer solutions through contraction or contraction--expansion channels yields results at odds with theory and simulations. In particular, the experimentally reported pressure drops are larger than those of generalized Newtonian reference fluids with the same shear viscosity, while constitutive models, such as Oldroyd-B and FENE-P, predict smaller pressure drops under conditions of low Reynolds numbers and stable flow at small Weissenberg ($Wi$) or Deborah ($De$) numbers. This apparent contradiction between experiments and theory has been a long-standing puzzle in the field. Here, we characterize the properties of dilute viscoelastic polymer solutions and employ two distinct types of pressure-sensing systems, conventional recessed pressure taps and flush-mounted diaphragm sensors, to systematically measure pressure drops across channels of different geometrical configurations. These measurements yield qualitative agreement with theoretical predictions across all geometries if the largest relaxation time is adopted for the analysis of the flow. Our results indicate that the apparent discrepancies mentioned above can be attributed to improper interpretation of the measurements and to mismatches between experimental conditions and assumptions made in the theoretical and numerical studies, which include hole pressure effects, the choice of relaxation time of the fluid, and the presence of experimental flow instabilities. For quantitative improvements, our results suggest the use of continuum-level constitutive models containing more realistic microscopic features of polymer solutions.

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

Viscoelastic flow of an Oldroyd-B fluid through a slowly varying contraction-expansion channel: pressure drop and elastic stress relaxation

Viscoelastic fluid flows in narrow non-uniform geometries are ubiquitous in various engineering applications and physiological flow systems. For such flows, one of the key interests is understanding how fluid viscoelasticity affects the flow rate-pressure drop relation, which remains not fully understood. We analyze the flow of the Oldroyd-B fluid in slowly varying contraction-expansion channels, commonly referred to as constrictions. Unlike most previous theoretical studies focusing on contracting channels, we consider a constriction geometry and present a theory for calculating the elastic stresses and flow rate-pressure drop relation at low and high Deborah ($De$) numbers. We apply lubrication theory and consider the ultra-dilute limit, in which the velocity approximates a parabolic and Newtonian profile. This results in a one-way coupling between the velocity and elastic stresses, allowing us to derive closed-form expressions for the elastic stresses and pressure drop for arbitrary values of $De$. We validate our theoretical predictions with numerical simulations, finding excellent agreement. We identify the physical mechanisms governing the pressure drop behavior and compare our results for the constriction with previous predictions for the contraction. At low $De$, the pressure drop in the constriction monotonically decreases with $De$, similar to the contraction. However, at high $De$, in contrast to a linear decrease for the contraction, the pressure drop across the constriction reaches a plateau due to the vanishing contribution of elastic normal stresses, leaving elastic shear stresses as the sole driver of the reduction. Furthermore, we elucidate the spatial relaxation of elastic stresses and pressure gradient in the exit channel following both constriction and contraction geometries, showing that the relaxation length is significantly shorter in the case of a constriction.

physics.flu-dyn↗

arXiv2025

Diffusioosmotic flow in a soft microfluidic configuration induces fluid-structure instability

Diffusioosmotic flow arises in microfluidic configurations due to solute concentration gradients. In soft microfluidic channels, internal pressure gradients generated by diffusioosmotic flow to conserve mass result in elastic deformation of the channel walls, triggering fluid-structure interaction. In this work, we analyze the fluid-structure interaction between diffusioosmotic flow of an electrolyte solution and a deformable microfluidic channel. We provide insight into the physical behavior of the system by developing a reduced-order model, in which a viscous film is confined between a rigid bottom surface and an elastic top substrate, represented as a rigid plate connected to a linear spring. Considering a slender configuration and applying the lubrication approximation, we derive a set of two-way coupled governing equations describing the evolution of the fluidic film thickness and the solute concentration. Our theoretical predictions show that above a certain concentration gradient threshold, negative pressures induced by diffusioosmotic flow give rise to fluid-structure instability, causing the elastic top substrate to collapse onto the bottom surface. We employ theoretical analysis to elucidate the underlying physical mechanisms for the onset of fluid-structure instability by performing a linear stability analysis of the system and identifying three distinct dynamic regimes. We validate our theoretical results with finite-element simulations and find excellent agreement. The understanding of this instability is of fundamental importance for improving the control and design of microfluidic systems driven by diffusioosmotic flow and containing soft elements.

physics.flu-dyn↗

arXiv2025

Transient rod-climbing in an Oldroyd-B fluid

The Weissenberg effect, or rod-climbing phenomenon, occurs in non-Newtonian fluids where the fluid interface ascends along a rotating rod. Despite its prominence, theoretical insights into this phenomenon remain limited. In earlier work, Joseph \& Fosdick (\emph{Arch. Rat. Mech. Anal.}, vol. 49, 1973, pp. 321--380) employed domain perturbation methods for second-order fluids to determine the equilibrium interface height by expanding solutions based on the rotation speed. In this work, we investigate the time-dependent interface height through asymptotic analysis with dimensionless variables and equations using the Oldroyd-B model. We begin by neglecting surface tension and inertia to focus on the interaction between gravity and viscoelasticity. In the small-deformation scenario, the governing equations indicate the presence of a boundary layer in time, where the interface rises rapidly over a short time scale before gradually approaching a steady state. By employing a stretched time variable, we derive the transient velocity field and corresponding interface profile on this short time scale and recover the steady-state profile on a longer time scale. Subsequently, we reintroduce small but finite inertial effects to investigate their interplay with viscoelasticity and propose a criterion for determining the conditions under which rod-climbing occurs.

physics.flu-dyn↗

arXiv2024

Viscoelastic fluid flow in a slowly varying planar contraction: the role of finite extensibility on the pressure drop

We analyze the steady viscoelastic fluid flow in slowly varying contracting channels of arbitrary shape and present a theory based on the lubrication approximation for calculating the flow rate-pressure drop relation at low and high Deborah ($De$) numbers. Unlike most prior theoretical studies leveraging the Oldroyd-B model, we describe the fluid viscoelasticity using a FENE-CR model and examine how the polymer chains' finite extensibility impacts the pressure drop. We employ the low-Deborah-number lubrication analysis to provide analytical expressions for the pressure drop up to $O(De^4)$. We further consider the ultra-dilute limit and exploit a one-way coupling between the parabolic velocity and elastic stresses to calculate the pressure drop of the FENE-CR fluid for arbitrary values of the Deborah number. Such an approach allows us to elucidate elastic stress contributions governing the pressure drop variations and the effect of finite extensibility for all $De$. We validate our theoretical predictions with two-dimensional numerical simulations and find excellent agreement. We show that, at low Deborah numbers, the pressure drop of the FENE-CR fluid monotonically decreases with $De$, similar to the previous results for the Oldroyd-B and FENE-P fluids. However, at high Deborah numbers, in contrast to a linear decrease for the Oldroyd-B fluid, the pressure drop of the FENE-CR fluid exhibits a non-monotonic variation due to finite extensibility, first decreasing and then increasing with $De$. Nevertheless, even at sufficiently high Deborah numbers, the pressure drop of the FENE-CR fluid in the ultra-dilute and lubrication limits is lower than the corresponding Newtonian pressure drop.

physics.flu-dyn↗

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

A note about convected time derivatives for flows of complex fluids

We present a direct derivation of the typical time derivatives used in a continuum description of complex fluid flows, harnessing the principles of the kinematics of line elements. The evolution of the microstructural conformation tensor in a flow and the physical interpretation of different derivatives then follow naturally.

physics.flu-dyn↗

arXiv2023

Non-Newtonian fluid-structure interaction: Flow of a viscoelastic Oldroyd-B fluid in a deformable channel

We analyze the steady non-Newtonian fluid-structure interaction between the flow of an Oldroyd-B fluid and a deformable channel. Specifically, we provide a theoretical framework for calculating the leading-order effect of the fluid's viscoelasticity on the flow rate-pressure drop relation and on the deformation of the channel's elastic wall. We first identify the characteristic scales and dimensionless parameters governing the fluid-structure interaction in slender and shallow channels. Applying the lubrication approximation for the flow and employing a perturbation expansion in powers of the Deborah number $De$, we derive a closed-form expression for the pressure as a function of the non-uniform shape of the channel in the weakly viscoelastic limit up to $\mathrm{O}(De)$. Coupling the hydrodynamic pressure to the elastic deformation, we provide the leading-order effect of the interplay between the viscoelasticity of the fluid and the compliance of the channel on the pressure and deformation fields, as well as on the flow rate-pressure drop relation. For the flow-rate-controlled regime and in the weakly viscoelastic limit, we show analytically that both the compliance of the deforming top wall and the viscoelasticity of the fluid decrease the pressure drop. Furthermore, we reveal a trade-off between the influence of compliance of the channel and the fluid's viscoelasticity on the deformation. While the channel's compliance increases the deformation, the fluid's viscoelasticity decreases it.

physics.flu-dyn↗

arXiv2022

Flow rate-pressure drop relation for deformable channels via fluidic and elastic reciprocal theorems

Viscous flows through configurations manufactured from soft materials apply both pressure and shear stress at the solid-liquid interface, leading to deformation of the cross-section, which affects the flow rate-pressure drop relation. Conventionally, calculating this flow rate-pressure drop relation requires solving the complete elastohydrodynamic problem, which couples the fluid flow and elastic deformation. In this work, we use the reciprocal theorems for Stokes flow and linear elasticity to derive a closed-form expression for the flow rate-pressure drop relation in deformable channels, bypassing the detailed calculation of the solution to the fluid-structure-interaction problem. For small deformations (under a domain perturbation scheme), our theory provides the leading-order effect, of the interplay between the fluid stresses and the compliance of the channel, on the flow rate-pressure drop relation. Our approach uses solely the fluid flow solution and the elastic deformation due to the fluid stress distribution in an undeformed channel, eliminating the need to solve the coupled elastohydrodynamic problem. Unlike previous theoretical studies that neglected the presence of lateral sidewalls and considered shallow geometries of effectively infinite width, our approach allows to determine the influence of confining sidewalls on the flow rate-pressure drop relation. For the flow-rate-controlled situation and the plate-bending theory for the elastic deformation, we show a trade-off between the effect of compliance of the deforming top wall and the drag due to sidewalls on the pressure drop. While increased compliance decreases the pressure drop, the effect of the sidewalls increases it. Our theoretical framework may provide insight into existing experimental data and pave the way for the design of novel optimized soft microfluidic configurations of different cross-sectional shapes.

physics.flu-dyn↗

arXiv2021

Pressure-driven flow of the viscoelastic Oldroyd-B fluid in narrow non-uniform geometries: analytical results and comparison with simulations

We analyze the pressure-driven flow of a viscoelastic fluid in arbitrarily shaped, narrow channels and present a theoretical framework for calculating the relationship between the flow rate $q$ and pressure drop $Δp$. We utilize the Oldroyd-B model and first identify the characteristic scales and dimensionless parameters governing the flow in the lubrication limit. Employing a perturbation expansion in powers of the Deborah number ($De$), we provide analytical expressions for the velocity, stress, and the $q-Δp$ relation in the weakly viscoelastic limit up to $O(De^2)$. Furthermore, we exploit the reciprocal theorem derived by Boyko $\&$ Stone (Phys. Rev. Fluids, vol. 6, 2021, pp. L081301) to obtain the $q-Δp$ relation at the next order, $O(De^3)$, using only the velocity and stress fields at the previous orders. We validate our analytical results with two-dimensional numerical simulations of the Oldroyd-B fluid in a hyperbolic, symmetric contracting channel and find excellent agreement. For the flow-rate-controlled situation, both our theory and simulations reveal weak dependence of the velocity field on the Deborah number, so that the velocity can be approximated as Newtonian. In contrast to the velocity, the pressure drop strongly depends on the viscoelastic effects and decreases with $De$. Elucidating the relative importance of different terms in the momentum equation contributing to the pressure drop, we identify that a pressure drop reduction for narrow contracting geometries is primarily due to gradients in the viscoelastic shear stresses, while viscoelastic axial stresses have a minor effect on the pressure drop along the symmetry line.

physics.flu-dyn↗

arXiv2021

Shaping liquid films by dielectrophoresis

We present a theoretical model and experimental demonstration of thin liquid film deformations due to a dielectric force distribution established by surface electrodes. We model the spatial electric field produced by a pair of parallel electrodes and use it to evaluate the stress on the interface through Maxwell stresses. By coupling this force with the Young-Laplace equation, we obtain the deformation of the interface. To validate our theory, we design an experimental setup which uses microfabricated electrodes to achieve spatial dielectrophoretic actuation of a thin liquid film, while providing measurements of microscale deformations through digital holographic microscopy. We characterize the deformation as a function of the electrode-pair geometry and film thickness, showing very good agreement with the model. Based on the insights from the characterization of the system, we pattern conductive lines of electrode pairs on the surface of a microfluidic chamber and demonstrate the ability to produce complex two-dimensional deformations. The films can remain in liquid form and be dynamically modulated between different configurations or polymerized to create solid structures with high surface quality.

cond-mat.soft↗

arXiv2019

Non-uniform electro-osmotic flow drives fluid-structure instability

We demonstrate the existence of a fluid-structure instability arising from the interaction of electro-osmotic flow with an elastic substrate. Considering the case of flow within a soft fluidic chamber, we show that above a certain electric field threshold, negative gauge pressure induced by electro-osmotic flow causes the collapse of its elastic walls. We combine experiments and theoretical analysis to elucidate the underlying mechanism for instability and identify several distinct dynamic regimes. The understanding of this instability is important for the design of electrokinetic systems containing soft elements.

physics.flu-dyn↗

arXiv2019

Electroosmotic flow dipole: experimental observation and flow field patterning

We experimentally demonstrate the phenomenon of electroosmotic dipole flow that occurs around a localized surface charge region under the application of an external electric field in a Hele-Shaw cell. We use localized deposition of polyelectrolytes to create well-controlled surface charge variations, and show that for a disk-shaped spot, the internal pressure distribution that arises, results in uniform flow within the spot and dipole flow around it. We further demonstrate the superposition of surface charge spots to create complex flow patterns, without the use of physical walls.

cond-mat.soft↗

arXiv2018

Elastohydrodynamics of a pre-stretched finite elastic sheet lubricated by a thin viscous film with application to microfluidic soft actuators

The interaction of a thin viscous film with an elastic sheet results in coupling of pressure and deformation, which can be utilized as an actuation mechanism for surface deformations in a wide range of applications, including microfluidics, optics, and soft robotics. Implementation of such configurations inherently takes place over finite domains and often requires some pre-stretching of the sheet. Under the assumptions of strong pre-stretching and small deformations of the lubricated elastic sheet, we use the linearized Reynolds and Foppl-von Karman equations to derive closed-form analytical solutions describing the deformation in a finite domain due to external forces, accounting for both bending and tension effects. We provide a closed-form solution for the case of a square-shaped actuation region and present the effect of pre-stretching on the dynamics of the deformation. We further present the dependence of the deformation magnitude and timescale on the spatial wavenumber, as well as the transition between stretching- and bending-dominant regimes. We also demonstrate the effect of spatial discretization of the forcing (representing practical actuation elements) on the achievable resolution of the deformation. Extending the problem to an axisymmetric domain, we investigate the effects arising from nonlinearity of the Reynolds and Foppl-von Karman equations and present the deformation behavior as it becomes comparable to the initial film thickness and dependent on the induced tension. These results set the theoretical foundation for implementation of microfluidic soft actuators based on elastohydrodynanmics.

physics.flu-dyn↗

arXiv2018

Viscous-elastic dynamics of power-law fluids within an elastic cylinder

In a wide range of applications, microfluidic channels are implemented in soft substrates. In such configurations, where fluidic inertia and compressibility are negligible, the propagation of fluids in channels is governed by a balance between fluid viscosity and elasticity of the surrounding solid. The viscous-elastic interactions between elastic substrates and non-Newtonian fluids are particularly of interest due to the dependence of viscosity on the state of the system. In this work, we study the fluid-structure interaction dynamics between an incompressible non-Newtonian fluid and a slender linearly elastic cylinder under the creeping flow regime. Considering power-law fluids and applying the thin shell approximation for the elastic cylinder, we obtain a non-homogeneous p-Laplacian equation governing the viscous-elastic dynamics. We present exact solutions for the pressure and deformation fields for various initial and boundary conditions for both shear-thinning and shear-thickening fluids. We show that in contrast to Stokes' problem where a compactly supported front is obtained for shear-thickening fluids, here the role of viscosity is inversed and such fronts are obtained for shear-thinning fluids. Furthermore, we demonstrate that for the case of a step in inlet pressure, the propagation rate of the front has a $t^{\frac{n}{n+1}}$ dependence on time ($t$), suggesting the ability to indirectly measure the power-law index ($n$) of shear-thinning liquids through measurements of elastic deformation.

physics.flu-dyn↗

arXiv2016

Flow of Power-Law Liquids in a Hele-Shaw Cell Driven by Non-Uniform Electroosmotic Slip in the Case of Strong Depletion

We analyze flow of non-Newtonian fluids in a Hele-Shaw cell, subjected to spatially non-uniform electroosmotic slip. Motivated by their potential use for increasing the characteristic pressure fields, we specifically focus on power-law fluids with wall depletion properties. We derive a p-Poisson equation governing the pressure field, as well as a set of linearized equations representing its asymptotic approximation for weakly non-Newtonian behavior. To investigate the effect of non-Newtonian properties on the resulting fluidic pressure and velocity, we consider several configurations in one- and two-dimensions, and calculate both exact and approximate solutions. We show that the asymptotic approximation is in good agreement with exact solutions even for fluids with significant non-Newtonian behavior, allowing its use in the analysis and design of microfluidic systems involving electro-kinetic transport of such fluids.

physics.flu-dyn↗

arXiv2015

Electroosmotic flow in Hele-Shaw configurations with non-uniform surface charge

We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations which relate the pressure and the stream function, respectively, to gradients in the zeta potential distribution parallel and perpendicular to the applied electric field. We solve the governing equations for the fundamental case of a disk with uniform zeta potential and show that the flow-field in the outer region takes the form of a pure dipole. We illustrate the ability to generate complex flow-fields around smooth convex regions by superposition of such disks with uniform zeta potential and a uniform pressure driven flow. This method may be useful for future on-chip devices, allowing flow control without the need for mechanical components.

physics.flu-dyn↗