Showing papers on "Lubrication theory published in 2020"

Microvascular blood flow with heat transfer in a wavy channel having electroosmotic effects.

Abstract: The present paper addresses microvascular blood flow with heat and mass transfer in complex wavy microchannel modulated by electroosmosis. Investigation is carried out with joule heating and chemical reaction effects. Further, viscous dissipation is also considered. Using Debye-Huckel, lubrication theory, and long wavelength approximations, analytical solutions of dimensionless boundary value problems are obtained. The impacts of different parameters are examined for temperature and concentration profile. Furthermore, nature of pressure rise is also investigated to analyze the pumping characteristics. Important results of flow phenomena are explored by means of graphs.

Direct Measurement of the Elastohydrodynamic Lift Force at the Nanoscale

Abstract: We present the first direct measurement of the elastohydrodynamic lift force acting on a sphere moving within a viscous liquid, near and along a soft substrate under nanometric confinement. Using atomic force microscopy, the lift force is probed as a function of the gap size, for various driving velocities, viscosities, and stiffnesses. The force increases as the gap is reduced and shows a saturation at small gap. The results are in excellent agreement with scaling arguments and a quantitative model developed from the soft lubrication theory, in linear elasticity, and for small compliances. For larger compliances, or equivalently for smaller confinement length scales, an empirical scaling law for the observed saturation of the lift force is given and discussed.

Start-up flow in shallow deformable microchannels

Abstract: Microfluidic systems are usually fabricated with soft materials that deform due to the fluid stresses. Recent experimental and theoretical studies on the steady flow in shallow deformable microchannels have shown that the flow rate is a nonlinear function of the pressure drop due to the deformation of the upper soft wall. Here, we extend the steady theory of Christov et al. (J. Fluid Mech., vol. 841, 2018, pp. 267–286) by considering the start-up flow from rest, both in pressure-controlled and in flow-rate-controlled configurations. The characteristic scales and relevant parameters governing the transient flow are first identified, followed by the development of an unsteady lubrication theory assuming that the inertia of the fluid is negligible, and that the upper wall can be modelled as an elastic plate under pure bending satisfying the Kirchhoff–Love equation. The model is governed by two non-geometrical dimensionless numbers: a compliance parameter , which compares the characteristic displacement of the upper wall with the undeformed channel height, and a parameter that compares the inertia of the solid with its flexural rigidity. In the limit of negligible solid inertia, , a quasi-steady model is developed, whereby the fluid pressure satisfies a nonlinear diffusion equation, with as the only parameter, which admits a self-similar solution under pressure-controlled conditions. This simplified lubrication description is validated with coupled three-dimensional numerical simulations of the Navier equations for the elastic solid and the Navier–Stokes equations for the fluid. The agreement is very good when the hypotheses behind the model are satisfied. Unexpectedly, we find fair agreement even in cases where the solid and liquid inertia cannot be neglected.

Electrokinetic membrane pumping flow model in a microchannel

Abstract: A microfluidic pumping flow model driven by electro-osmosis mechanisms is developed to analyze the flow characteristics of aqueous electrolytes. The pumping model is designed based on a single propagative rhythmic membrane contraction applied on the upper wall of a microchannel. The flow lubrication theory coupled with a nonlinear Poisson–Boltzmann equation is used to model the microchannel unsteady creeping flow and to describe the distribution of the electric potential across the electric double layer. A generic solution is obtained for the Poisson–Boltzmann equation without the Debye–Huckel linearization. The effects of zeta potential, Debye length, and electric field on the potential distribution, pressure distribution, velocity profiles, shear stress, and net flow rate are computed and interpreted in detail. The results have shown that this electrokinetic membrane pumping model can be used to understand microlevel transport phenomena in various physiological systems. The proposed model can also be integrated with other microfluidic devices for moving microvolume of liquids in artificial capillaries used in modern biomedical applications.

Chemomechanical simulation of soap film flow on spherical bubbles

Abstract: Soap bubbles are widely appreciated for their fragile nature and their colorful appearance. The natural sciences and, in extension, computer graphics, have comprehensively studied the mechanical behavior of films and foams, as well as the optical properties of thin liquid layers. In this paper, we focus on the dynamics of material flow within the soap film, which results in fascinating, extremely detailed patterns. This flow is characterized by a complex coupling between surfactant concentration and Marangoni surface tension. We propose a novel chemomechanical simulation framework rooted in lubrication theory, which makes use of a custom semi-Lagrangian advection solver to enable the simulation of soap film dynamics on spherical bubbles both in free flow as well as under body forces such as gravity or external air flow. By comparing our simulated outcomes to videos of real-world soap bubbles recorded in a studio environment, we show that our framework, for the first time, closely recreates a wide range of dynamic effects that are also observed in experiment.

Forces and torques on a sphere moving near a dihedral corner in creeping flow

Abstract: The low-Reynolds-number flow past a sphere moving near a right dihedral corner made by a stationary and a tangentially sliding wall is considered. Using the superposition principle, the arbitrary motion of the sphere is decomposed into simple elementary motions. Fully-resolved spectral-element simulations are carried out in the frame of reference translating and rotating with the particle such that the velocity on the particle’s surface vanishes. Forces and torques on the sphere are obtained as functions of the particle position near the corner. The data obtained are fitted by closed-form expressions which take into account symmetries of the problem, exact solutions, and asymptotic solutions from lubrication theory. The correlations obtained can easily be implemented in larger-scale one-way-coupled particulate-flow simulations to correct the particle motion near dihedral corners where mere point-particle models break down.

Cox-Voinov theory with slip

Abstract: Most of our understanding of moving contact lines relies on the limit of small capillary number. This means the contact line speed is small compared to the capillary speed, where is the surface tension and the viscosity, so that the interface is only weakly curved. The majority of recent analytical work has assumed in addition that the angle between the free surface and the substrate is also small, so that lubrication theory can be used. Here, we calculate the shape of the interface near a slip surface for arbitrary angles, and for two phases of arbitrary viscosities, thereby removing a key restriction in being able to apply small capillary number theory. Comparing with full numerical simulations of the viscous flow equation, we show that the resulting theory provides an accurate description up to in the dip coating geometry, and a major improvement over theories proposed previously.

Viscous flow under an elastic sheet

Abstract: We study the spreading of viscous fluid injected under an elastic sheet, which is driven by gravity and by elastic bending and tension forces and resisted by viscous forces. The injected fluid forms a large blister and spreads outwards analogously to a viscous gravity current or a capillary droplet. The relative strengths of the three driving forces are determined by how the horizontal length scales of the system compare with three key transition length scales. Bending is dominant on small length scales, tension is dominant on intermediate length scales and gravity is dominant on large length scales. We show how to use the method of matched asymptotic expansions to predict the spreading rate and thickness profile of the blister of fluid in the seven possible asymptotic regimes, for both two-dimensional and axisymmetric geometries. Consideration of different physical effects at the fluid front increases the number of regimes yet further.

A thin-film model for droplet spreading on soft solid substrates.

Abstract: The spreading of droplets on soft solid substrates is relevant to applications such as tumor biophysics and controlled droplet condensation and evaporation. In this paper, we apply lubrication theory to advance fundamental understanding of the important limiting case of spreading of a planar droplet on a linear viscoelastic solid. The contact-line region is described by a disjoining-pressure/precursor-film approach, and nonlinear evolution equations describing how the liquid-air and liquid-solid interfaces evolve in space and time are derived and solved numerically. Parametric studies are conducted to investigate the effects of solid thickness, viscosity, shear modulus, and wettability on droplet spreading. Softer substrates are found to speed up spreading for perfectly wetting droplets but slow down spreading for partially wetting droplets. For perfectly wetting droplets, faster spreading is a result of more liquid being pumped toward the contact line due to a larger liquid-film thickness there arising from the repulsive component of the disjoining pressure. In contrast, slower spreading of partially wetting droplets is a result of less liquid being pumped toward the contact line due to a smaller liquid-film thickness there arising from the attractive component of the disjoining pressure. The model predictions for partially wetting droplets are qualitatively consistent with experimental observations, and allow us to disentangle the effects of substrate deformability and wettability on droplet spreading. Due to its systematic formulation, our model can readily be extended to more complex situations involving multiple droplets, substrate inclination, and droplet phase changes.

Modeling the Effect of Channel Tapering on the Pressure Drop and Flow Distribution Characteristics of Interdigitated Flow Fields in Redox Flow Batteries

Abstract: Optimization of flow fields in redox flow batteries can increase performance and efficiency, while reducing cost. Therefore, there is a need to establish a fundamental understanding on the connection between flow fields, electrolyte flow management and electrode properties. In this work, the flow distribution and pressure drop characteristics of interdigitated flow fields with constant and tapered cross-sections are examined numerically and experimentally. Two simplified 2D along-the-channel models are used: (1) a CFD model, which includes the channels and the porous electrode, with Darcy’s viscous resistance as a momentum sink term in the latter; and (2) a semi-analytical model, which uses Darcy’s law to describe the 2D flow in the electrode and lubrication theory to describe the 1D Poiseuille flow in the channels, with the 2D and 1D sub-models coupled at the channel/electrode interfaces. The predictions of the models are compared between them and with experimental data. The results show that the most influential parameter is γ , defined as the ratio between the pressure drop along the channel due to viscous stresses and the pressure drop across the electrode due to Darcy’s viscous resistance. The effect of R e in the channel depends on the order of magnitude of γ , being negligible in conventional cells with slender channels that use electrodes with permeabilities in the order of 10 − 12 m 2 and that are operated with moderate flow rates. Under these conditions, tapered channels can enhance mass transport and facilitate the removal of bubbles (from secondary reactions) because of the higher velocities achieved in the channel, while being pumping losses similar to those of constant cross-section flow fields. This agrees with experimental data measured in a single cell operated with aqueous vanadium-based electrolytes.

The Singular Hydrodynamic Interactions Between Two Spheres In Stokes Flow

Abstract: We study exact solutions for the slow viscous flow of an infinite liquid caused by two rigid spheres approaching each either along or parallel to their line of centers, valid at all separations. This goes beyond the applicable range of existing solutions for singular hydrodynamic interactions (HIs), which, for practical applications, are limited to the near-contact or far field region of the flow. For the normal component of the HI, by the use of a bipolar coordinate system, we derive the stream function for the flow as the Reynolds number (Re) tends to zero and a formula for the singular (squeeze) force between the spheres as an infinite series. We also obtain the asymptotic behavior of the forces as the nondimensional separation between the spheres goes to zero and infinity, rigorously confirming and improving upon the known results relevant to a widely accepted lubrication theory. Additionally, we recover the force on a sphere moving perpendicularly to a plane as a special case. For the tangential component, again by using a bipolar coordinate system, we obtain the corresponding infinite series expression of the (shear) singular force between the spheres. All results hold for retreating spheres, consistent with the reversibility of Stokes flow. We demonstrate substantial differences in numerical simulations of colloidal fluids when using the present theory compared with the existing multipole methods. Furthermore, we show that the present theory preserves positive definiteness of the resistance matrix R in a number of situations in which positivity is destroyed for multipole/perturbative methods.

Modelling film flows down a fibre influenced by nozzle geometry

Abstract: We study the effects of nozzle geometry on the dynamics of thin fluid films flowing down a vertical cylindrical fibre. Recent experiments show that varying the nozzle diameter can lead to different flow regimes and droplet characteristics in the film. Using a weighted residual modelling approach, we develop a system of coupled equations that account for inertia, surface tension effects, gravity and a film stabilization mechanism to describe both near-nozzle fluid structures and downstream bead dynamics. We report good agreement between the predicted droplet properties and the experimental data.

Mathematical analysis of a non-Newtonian polymer in the forward roll coating process

Abstract: Abstract This article describes the development of a mathematical model of forward roll coating of a thin film of a non-Newtonian material when it passes through a small gap between the two counter-rotating rolls. The conservation equations of mass, momentum, and energy in the light of LAT (lubrication approximation theory) are non-dimensionalized and solutions for the velocity profile, flow rate, pressure distribution, pressure, forces, stresses, power input to the roller, and temperature distribution are calculated analytically. It is found that by changing (increasing/decreasing) the value of material parameters, one can really control the engineering parameters like, stress and the most important the coating thickness and is a quick reference for the engineer working in coating industries. Some results are shown graphically. From the present study, it has been established that the material parameter is a device to control flow rate, coating thickness, separation points, and pressure distribution.

The effect of wall slip on the dewetting of ultrathin films on solid substrates: Linear instability and second-order lubrication theory

Abstract: The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely, the weak, intermediate, and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurately predict the linear dynamics of the film for arbitrary slip lengths.

Heat transfer and Helmholtz-Smoluchowski velocity in Bingham fluid flow

Abstract: A mathematical study is developed for the electro-osmotic flow of a non-Newtonian fluid in a wavy microchannel in which a Bingham viscoplastic fluid model is considered. For electric potential distributions, a Poisson-Boltzmann equation is employed in the presence of an electrical double layer (EDL). The analytical solutions of dimensionless boundary value problems are obtained with the Debye-Huckel theory, the lubrication theory, and the long wavelength approximations. The effects of the Debyelength parameter, the plug flow width, the Helmholtz-Smoluchowski velocity, and the Joule heating on the normalized temperature, the velocity, the pressure gradient, the volumetric flow rate, and the Nusselt number for heat transfer are evaluated in detail using graphs. The analysis provides important findings regarding heat transfer in electroosmotic flows through a wavy microchannel.

A criterion for the pinning and depinning of an advancing contact line on a cold substrate

Abstract: The influence of solidification on the spreading of liquids is addressed in the situation of an advancing liquid wedge on a cold sub-strate at Tp < T f , of infinite thermal conductivity, where T f is the melting temperature. We propose a model derived from lubrication theory of contact-line dynamics, where an equilibrium between capillary pressure and viscous stress is at play, adapted here for the geometry of a quadruple line where the vapour, liquid, solidified liquid and basal substrate meet. The Stefan thermal problem is solved in an intermediate region between molecular and mesoscopic scales, allowing to predict the shape of the solidified liquid surface. The apparent contact angle versus advancing velocity U exhibits a minimal value, which is set as the transition from continuous advancing to pinning. We postulate that this transition corresponds to the experimentally observed critical velocity , dependent on undercooling temperature T f − Tp, below which the liquid is pinned and advances with stick-slip dynamics. The analytical solution of the model shows a qualitatively fair agreement with experimental data. We discuss on the way to get better quantitative agreement, which in particular can be obtained when the mesoscopic cutoff length is made temperature-dependent.

Taylor drop in a closed vertical pipe

Abstract: In this work, we study the ascent dynamics of a liquid Taylor drop formed from a lock-exchange configuration in a closed vertical pipe. We focus on the buoyancy-driven motion of an elongated drop surrounded by a denser fluid when viscous forces dominate over inertial and surface tension effects. While gaseous Taylor bubbles have been studied extensively, a liquid Taylor drop moving in a closed pipe is less well understood. We formulate an analytical model for estimating the ascent speed and drop thickness from first principles. First, we use a lubrication approximation to solve for the velocity profiles in the two fluids. Then, we analyse the mechanical energy balance of the whole system, including the effect of viscous dissipation, to understand how the ascent speed and drop thickness scale with the viscosity ratio. We show that a drop with density ratio in the dissipative regime. Through a comparison with existing experimental data, we demonstrate that our model correctly predicts the ascent speed of a Taylor drop if the material properties of the fluids and the geometry of the conduit are known. Our theoretical framework can be generalized to an isolated Taylor drop rising in a vertical pipe.

A model for the fluid dynamic behavior of a film coating suspension during tablet coating

Abstract: This work models the behavior of a liquid-particle suspension on the surface of a tablet during the pharmaceutical film-coating process. The model uses the “mixture modeling” approach and the lubrication approximation method to simulate how the suspension moves and dries on the surface of a tablet, considering how important physical properties of the suspension, such as the density and viscosity, change when the carrier fluid evaporates. The model also accounts for the absorption of the coating suspension inside the core of the porous tablet, yielding the tablet water content, a key quantity characterizing the coating process. The numerical results, obtained with the gPROMS Modelbuilder platform, agree with experimental data taken from the literature and Volume-Of-Fluid CFD simulations.

The effect of wall slip on the dewetting of ultrathin films on solid substrates: Linear instability and second-order lubrication theory

Abstract: The influence of wall slip on the instability of a non-wetting liquid film placed on a solid substrate is analyzed in the limit of negligible inertia. In particular, we focus on the stability properties of the film, comparing the performance of the three lubrication models available in the literature, namely the weak, intermediate and strong slip models, with the Stokes equations. Since none of the aforementioned leading-order lubrication models is shown to be able to predict the growth rate of perturbations for the whole range of slipping lengths, we develop a parabolic model able to accurately predict the linear dynamics of the film for arbitrary slip lengths.

Mathematical modeling of micropolar fluid in blade coating using lubrication theory

Abstract: The blade coating process of a micropolar fluid using the plane and exponential coater has been studied. Equations are simplified utilizing lubrication approximation theory. The analytical expressions for flow rate, pressure gradient, and velocity are obtained, while load and coating thickness are computed numerically with the help of the shooting method. We show how the microrotation parameters $$\epsilon$$ and the coupling number $$N$$ influence the flow characteristics, such as pressure distribution, velocity, pressure gradient and related engineering quantities such as load and thickness in the blade coating process, and they are shown graphically as well as in tabular form. We find that, for coupling number $$N$$ and microrotation parameter $$\epsilon$$ , the pressure increases when compared to the Newtonian fluid. Moreover, the coating thickness decreases for the Newtonian case when $$N$$ increases.

Axisymmetric mixed convective propulsion of a non-Newtonian fluid through a ciliated tubule

Abstract: Thousands of chemical reactions occur in the human body when certain biological fluids, such as blood, semen, mucus, and synovial joint materials, move in various organs. These reactions play a vital role in regulating the life sustaining metabolic processes in the body. Analysis of thermal effects on these chemical reactions is relatively a new area in modern clinical medications. The present study investigates a simulation of the combined response due to heat and mass transport mechanisms taking place in the human body during the flow of physiological fluids. In particular, we focus our attention on the human male reproductive system, wherein the semen transports through the ductus efferentes due to metachronal waves of cilia. The constitutive relations of the robust Jeffrey viscoelastic fluid are used to model the human semen. The mathematical model of the present problem constitutes the axisymmetric flow of a Jeffrey fluid inside a vertical tubule under the influence of mixed convective heat and mass transfers. The inner side of the tubule is covered with ciliated structures. The influence of thermal behaviors of various metabolic processes in the human body due to an external heat source or sink is also taken into account. The mathematical formulation consists of using the approach of lubrication theory approximation; the nonlinear momentum, energy, and concentration equations are simplified to get analytical solutions. Explicit expressions for temperature, concentration, velocity, pressure gradient, and volume flow rate of the proposed bodily fluid (i.e., human semen) are formulated. The expression for the volume flow rate is used to estimate the volume flux of the semen under the influence of various parameters. A comparison between the theoretical and experimentally obtained values of the flow rate of the human semen is also made. It is noted that our calculated values are very close to the estimated values. Industrial applications of the present results are obvious in the fabrication of artificial cilia pumping systems for microfluidic flow systems.

Impact of Curvature-Dependent Channel Walls on Peristaltic Flow of Newtonian Fluid Through a Curved Channel with Heat Transfer

Abstract: The basic idea of the present article is to model and study the aspects of curvature-dependent channel walls on peristalsis of laminar viscous material flow through a curved geometry. Mathematical modeling for such flow configuration is being presented for the first time. Lubrication theory assumptions are used for mathematical modeling of the problem. Moreover, the numerical method is used to solve the resulting system of equation. The impacts of different flow quantities on the heat transfer rate, velocity and temperature profiles are discussed via graphs. Results indicate that the curvature parameter considerably influences the mechanical and thermal aspects of the flow and hence must be included in the modeling of flows through curved a channel.

Deformation characteristics of adaptive hydrostatic thrust bearing under extreme working conditions

Abstract: Investigation of the deformation characteristics of adaptive hydrostatic thrust bearings has been performed under extreme conditions, considering the relationship between viscosity and temperature of lubricating oil. A 3D model is generated, including the oil pad, the oil film and friction pairs. The oil film temperature field and the oil cavity pressure field have been calculated based on CFD. According to the lubrication theory and tribology principle, the force deformation, the thermal deformation, the force and thermal coupling deformation have been studied by using workbench simulation software, and the best working condition of adaptive hydrostatic thrust bearing is obtained. The results show that the load causes the table and the base to undergo inward elastic deformation, and the temperature causes them to undergo outward thermal deformation. The two deformations have opposite directions, and the deformations compensate each other. When the load is between 28 and 32t, the possibility of dry friction generated by the friction pair is low. The research results provide a theoretical basis for the stability of adaptive hydrostatic thrust bearings under extreme working conditions.