Incompressible Newtonian Fluid Research Articles

Folding of a growing hyperelastic sheet in a viscous fluid

Understanding the growth-induced deformation of soft materials in viscous environments is important for a variety of problems in nature and engineering. Here, we focus on the fluid–structure interaction of a hyperelastic sheet growing in an incompressible Newtonian fluid in the Stokes flow regime. We develop a computational framework for simulating this problem, where the isogeometric boundary integral method is used with the Kirchhoff–Love shell formulation and elastic–plastic decomposition of the deformation gradient tensor. We quantify the relative effects of the growth rate, the sheet bending rigidity, and the fluid viscosity on the fold formation and development of the growing sheet. Our results suggest that the viscous resistance to in-plane deformation promotes fold formation, whereas the viscous resistance to out-of-plane deformation suppresses fold development. We also investigate the effects of the thickness and aspect ratio of the rectangular sheet. Finally, we compare the growth- and prestrain-induced deformations to find a common behavior of sheets under viscous environments.

Numerical investigation of LDL nanoparticle collision in coronary artery grafts with porous wall and different implantation angles and two state of inlet velocity.

This study aimed to reduce the risk of graft occlusion by evaluating the two-phase flow of blood and LDL nanoparticles in coronary artery grafts. The study considered blood as an incompressible Newtonian fluid, with the addition of LDL nanoparticles, and the artery wall as a porous medium. Two scenarios were compared, with constant inlet velocity (CIV) and other with pulsatile inlet velocity (PIV), with LDL nanoparticles experiencing drag, wall-induced lift, and induced Saffman lift forces, or drag force only. The study also evaluated the concentration polarization of LDLs (CP of LDLs) near the walls, by considering the artery wall with and without permeation. To model LDL nanoparticles, the study randomly injected 100, 500, and 1000 nanoparticles in three release states at each time step, using different geometries. Numerical simulations were performed using COMSOL software, and the results were presented as relative collision of nanoparticles to the walls in tables, diagrams, and shear stress contours. The study found that a graft implantation angle of 15° had the most desirable conditions compared to larger angles, in terms of nanoparticle collision with surfaces and occlusion. The nanoparticle release modes behaved similarly in terms of collision with the surfaces. A difference was observed between CIV and PIV. Saffman lift and wall-induced lift forces having no effect, possibly due to the assumption of a porous artery wall and perpendicular outlet flow. In case of permeable artery walls, relative collision of particles with the graft wall was larger, suggesting the effect of CP of LDLs.

Effects of porous-wall acceleration on laminar flows in semi-porous channels with a rectangular cross section

This paper aims to examine the effects of wall acceleration on the steady laminar flow of an incompressible Newtonian fluid along a semi-porous channel with a rectangular cross section. The lower wall of the channel is impermeable and at rest, while the upper wall is porous, and experiences longitudinal acceleration so that the flow is steady despite the accelerated movement of the wall. The fluid is injected or suctioned through the porous wall at uniform and constant velocity, orthogonally to the wall. The positive acceleration ratio defined as the ratio of longitudinal and transverse velocities, and the Reynolds number constructed by adding these velocities are the governing parameters. The similarity-solutions method, which is applied for the vorticity stream-function equation, gives numerical solutions using the shooting technique. Results indicate that the flow under study exists in the case of injection if the acceleration ratio does not exceed the value of 1, but in the case of suction, the flow remains unchanged if the acceleration ratio varies above the value of 9.5. For increasing acceleration ratios, the absolute value of transverse velocity decreases, the transverse pressure gradient remains unchanged at a specific fluid layer, the absolute value of longitudinal velocity increases near the porous wall and decreases near the impermeable wall, and in the case of injection, the algebraic wall shear stress decreases for the impermeable wall and increases for the porous wall. In the case of suction, there is a specific fluid layer at which the longitudinal velocity cancels by changing sign.

On fluid-saturated poro-hyperelastic rotating cylinder: A centrifugal filtration

One of the applications of porous materials is centrifugal filtration. This study develops the Lagrangian equations that govern a steady-state, fluid-saturated, poro-hyperelastic, axisymmetric rotating cylinder. The formulation assumes incompressible solid and Newtonian fluid constituents to address the filtration process. The differential scheme takes into account the impact of porosity on the reduction of the drained shear and bulk moduli of the solid skeleton. Additionally, the normalized Kozeny-Carman formula considers the effect of porosity changes due to deformation on permeability. The Standard Galerkin Finite Element Method solves the derived equations using FlexPDE. ANSYS is unable to solve the current problem due to the lack of centrifugal and Coriolis accelerations in Darcy's law and its inability to account for changes in initial permeability and porosity resulting from the deformation of the solid skeleton. Therefore, the validation of the governing equations and the applied solution is investigated in three limited cases.It is shown that a rise in the angular velocity causes the expansion in the Von-Mises stress of solid constituent, radial displacement, negative pore pressure, and radial filtration velocity because of the increase in the centrifugal force. Also, the permeability and radial displacement grow with the initial porosity rise. The radial filtration velocity rises with the increased permeability resulting from the deformation. Moreover, drained shear and bulk moduli of the solid skeleton fall with increased porosity, resulting in a rise in the radial displacement. Besides, the radial displacement and filtration velocity expand with the increase of solid and fluid densities.

Endothermic and exothermic chemical reactions’ influences on a nanofluid flow across a permeable microchannel with a porous medium

The compact dimensions and large surface area-to-volume ratio characteristic of microchannel geometries can efficiently utilise endothermic and exothermic chemical reactions to enhance heat transfer, control temperature, adjust reactivity, intensify processes and develop innovative thermal management techniques. Becasue of this, the exothermic and endothermic chemical reaction mechanism is explored by considering the titanium oxide (TiO2) nanoparticles with water (H2O) as the base fluid. An incompressible Newtonian fluid flows through the porous microchannel. The pressure gradient factor assumes the flow in the microchannel. Energy and solutal transportation analyses are made with Robin’s boundary conditions and activated energy phenomena. Similar variables are introduced to convert the model into non-dimensional. A numerical scheme, namely the Runge–Kutta-Fehlberg 45th (RKF-45) scheme, is implemented to execute solutions. The results explore that thermal distribution decreases for elevated activation energy values and Biot number values in the exothermic case while enhanced in the endothermic case. The rate of thermal distribution declines with the addition of solid fractions and chemical reaction parameters in the endothermic case; the opposite trend is observed in the exothermic case.

Start-Up Rotation of a Porous Colloidal Sphere in a Cavity

The starting rotation of a porous sphere induced by the sudden application of a continuous torque about its diameter at the center of a spherical cavity filled with an incompressible Newtonian fluid at low Reynolds numbers is analyzed. The unsteady Stokes and Brinkman equations governing the fluid velocities outside and inside the porous particle, respectively, are solved via the Laplace transform, and an explicit formula of its dynamic angular velocity as a function of the pertinent parameters is obtained. The behavior of the start-up rotation of an isolated porous particle and the cavity wall effect on the particle rotation are interesting. The angular velocity of the particle grows incessantly over time from an initial zero to its final value, while the angular acceleration declines with time continuously. In general, the transient angular velocity is an increasing function of the porosity of the particle. A porous sphere with higher fluid permeability rotates at higher angular velocity and acceleration relative to the reference particle at any elapsed time but lags behind the reference particle in the percentage growth of angular velocity towards the respective terminal values. The transient angular velocity decreases with increasing particle-to-cavity radius ratio, but it is not a sensitive function of the radius ratio when the resistance to fluid flow inside the porous particle or the radius ratio itself is small.

Turbulence calculation based on the extended Navier–Stokes equations

In this study, phenomenological observations and the Kreuer interpretation of the origin of viscosity were used to develop a computational method for solving the turbulence problem of incompressible viscous Newtonian fluids based on extended Navier–Stokes (N–S) equations. The shear process in fluid flow was hypothesized to be accompanied by eddy formation, and the effects of eddies on the convection and diffusion were considered. The classical N–S equations were improved to obtain extended N–S equations. The extended equations are closed, and the sources of the velocity fluctuations are explicitly considered to be additional convection and diffusion. The extended equations are compatible with the classical N–S equations; thus, they can describe laminar and turbulent flows in a unified manner. In fluid flow simulations, the equations describing the mean flow quantities could be directly obtained from the extended N–S equations without any additional turbulence models. A numerical investigation was carried out to verify the extended equations by exploring the flow over a cube placed in a channel. The simulation results were compared with both the large eddy simulation and experimental results.

MODELING AND OPTIMIZATION OF PERISTALTIC FLUID TRANSPORT IN AXISYMMETRIC, POROUS STRUCTURES

Peristaltic transport, a fundamental physiological and engineering process, involves the movement of fluid through a distensible tube via sequential compression and relaxation. This study investigates the peristaltic transport of an incompressible Newtonian fluid in an axisymmetric, porous, corrugated tube, emphasizing the interplay between fluid dynamics and the tube's structural characteristics. Utilizing lubrication theory and perturbation analysis within a wave frame of reference, we explore the effects of hydraulic resistivity, geometric parameters of the corrugation, and porous layer thickness on the phenomena of trapping and circulation. Our findings reveal that hydraulic resistivity significantly influences the development of circulation regions within the fluid core, which has implications for the efficiency of mixing and nutrient absorption in biological and industrial applications. Additionally, the geometric configuration of the wavy porous layer—specifically its amplitude and thickness—critically impacts the formation of trapping and circulation regions, thereby affecting fluid transport efficiency. This work not only advances our understanding of peristaltic pumping mechanisms but also highlights the potential for optimizing fluid transport processes in both biological systems and industrial applications. The insights gained from this study contribute to the design of more efficient peristaltic pumps and offer a valuable framework for future research aimed at enhancing substance delivery and mixing through peristaltic transport.

Rising and settling 2-D cylinders with centre-of-mass offset

Rotational effects are commonly neglected when considering the dynamics of freely rising or settling isotropic particles. Here, we demonstrate that particle rotations play an important role for rising as well as for settling cylinders in situations when mass eccentricity, and thereby a new pendulum time scale, is introduced to the system. We employ two-dimensional simulations to study the motion of a single cylinder in a quiescent unbounded incompressible Newtonian fluid. This allows us to vary the Galileo number, density ratio, relative moment of inertia (MOI) and centre-of-mass (COM) offset systematically and beyond what is feasible experimentally. For certain buoyant density ratios, the particle dynamics exhibits a resonance mode, during which the coupling via the Magnus lift force causes a positive feedback between translational and rotational motions. This mode results in vastly different trajectories with significantly larger rotational and translational amplitudes and an increase of the drag coefficient easily exceeding a factor two. We propose a simple model that captures how the occurrence of the COM offset induced resonance regime varies, depending on the other input parameters, specifically the density ratio, the Galileo number and the relative MOI. Remarkably, depending on the input parameters, resonance can be observed for COM offsets as small as a few per cent of the particle diameter, showing that the particle dynamics can be highly sensitive to this parameter.

Transient slow motion of a porous sphere

The start-up creeping motion of a porous spherical particle, which models a permeable polymer coil or floc of nanoparticles, in an incompressible Newtonian fluid generated by the sudden application of a body force is investigated for the first time. The transient Stokes and Brinkman equations governing the fluid velocities outside and inside the porous sphere, respectively, are solved by using the Laplace transform. An analytical formula for the transient velocity of the particle as a function of relevant parameters is obtained. As expected, the particle velocity increases over time, and a particle with greater mass density lags behind a corresponding less dense particle in the growth of the particle velocity. In general, the transient velocity is an increasing function of the porosity of the particle. On the other hand, a porous particle with a higher fluid permeability will have a greater transient velocity than the same particle with a lower permeability, but may trail behind the less permeable particle in the percentage growth of the velocity. The acceleration of the porous particle is a monotonic decreasing function of the elapsed time and a monotonic increasing function of its fluid permeability. In particular, the transient behavior of creeping motions of porous particles may be much more important than that of impermeable particles.

A stabilized finite element method for modeling dispersed multiphase flows using orthogonal subgrid scales

We propose a finite-element formulation for simulating multi-component flows occupying the same domain with spatially varying concentrations. Each constituent is assumed to behave as an incompressible Newtonian fluid, and solutions are sought for the velocities and volume fractions of each phase, as well as the common pressure. Stabilization terms are derived within the framework of the variational multiscale method based on an approximation of the finite-element residual to achieve control of the pressure and volume fractions. We utilize the concept of term-by-term stabilization in conjunction with orthogonal subgrid scales, thus incorporating only those terms of the residual essential to obtain stability and projecting them on a space orthogonal to the finite element space. The resulting system of equations is solved in a monolithic manner, requiring a small number of nonlinear iterations. Several benchmark tests have been performed to confirm the stability and optimal asymptotic convergence rates for linear and higher-order elements using the proposed formulation.

Effective double-poroelasticity derived via homogenization of two non-interacting solid phases percolated by a viscous fluid

This work carries out the derivation of the governing equations for a composite material that has the following microstructure. Our microstructure possesses an elastic matrix that has an incompressible Newtonian fluid flowing in the pores and then the latter is additionally reinforced by an elastic network that is fully surrounded by the fluid. We exploit the length scale separation that exists in the system between the microscale and the overall size of the material to apply the asymptotic homogenization technique. The resulting model comprises additional terms and equations to account for the discontinuity between the elastic phases, and reduces to more standard poroelastic formulations only when the two elastic phases are in contact. The coefficients of the novel model are to be computed by solving appropriate periodic cell differential problems. The coefficients encode the details of the geometry and stiffness of the microstructure. The model is applicable to a variety of scenarios, such as artificial constructs and biomaterials.

Dissipation in nonequilibrium thermodynamics and its connection to the Rayleighian functional

We examine quantitatively the role of dissipation in nonequilibrium thermodynamics and its connection to variational principles and the Rayleighian functional. The extremum of the Rayleighian is sometimes used to describe the inertialess (dissipation-dominated) dynamics of continuum systems, and it has been applied recently for the modeling of soft matter dynamics. We discuss how dissipation is considered within one of the modern complete descriptions of nonequilibrium thermodynamics, namely the single generator bracket formalism. Within this formalism, dissipation is introduced through the use of the dissipation bracket, describing irreversible dynamics, which is added to a Poisson bracket that describes the reversible dynamics of the system. A possible connection with the Rayleighian functional is then demonstrated that in all cases considered herein, the Rayleighian is equal to minus one half of the effective dissipation rate of the Lagrangian functional. The effective dissipation rate is obtained starting with an inertial (i.e., flux-based or velocity-based) system description, involving the Poisson bracket and the primitive part (i.e., without the entropy correction term) of the dissipative bracket. Several examples are discussed in detail, ranging from an algebraic model (damped oscillator) to continuum ones: modeling of fluid flow in porous particle media, viscous Newtonian compressible and incompressible fluid flows, and more interestingly, flow of a nematic liquid-crystalline material.

Stokes’ Second Flow Problem Revisited for Particle–Fluid Suspensions

Abstract An alternative analytical model is proposed for hydrodynamics of incompressible Newtonian fluids with suspended solid particles. Unlike existing single-phase models that do not distinguish the velocity field of suspended particles from the velocity field of host fluid, the present model accounts for the relative shift between the two velocity fields and assumes that its effect can be largely captured by substituting the inertia term of Navier–Stokes equations with the acceleration field of the mass center of the representative unit cell. The proposed model enjoys a relatively concise mathematical formulation. The oscillating flow of a particle–fluid suspension between two flat plates is studied with the present model, and detailed results are presented for Stokes’ second flow problem on the oscillating flow of a suspension half-space induced by an oscillating plate with specific examples of dusty gases and nanofluids. Remarkably, leading-order asymptotic expressions derived by the present model, for the effect of suspended particles on the decay index and wavenumber of the velocity field, are shown to be identical to known results derived based on the widely adopted Saffman model for dusty gases. It is hoped that the present work could offer a relatively simplified and yet reasonably accurate model for hydrodynamic problems of particle–fluid suspensions.

Diode-like response of conical-shaped nanochannels to external stimuli: The importance of slip length

The present study reports the effect of slip length on the ionic current rectification and ion selectivity in conical-shaped electrolyte-loaded nanochannels with and without a coated polyelectrolyte layer (PEL). The electrolyte was considered a salted incompressible Newtonian fluid. The polyelectrolyte layer was also modeled as a rigid and charged porous solid saturated with a salted Newtonian fluid. The electrolyte-polyelectrolyte layer interface was modeled as a surface, considering ion partitioning with distinct physical properties across the interface. The results demonstrated that the relationship between the slip length and the rectification factor depended on the surface charge density, the concentration of the electrolyte solution, and the type of nanochannel. Moreover, the effect of slip length on the ion selectivity factor is remarkably higher in the solid-state nanochannel compared to the PEL-coated nanochannel. Furthermore, the slip length considerably enhances the ion selectivity factor in the solid-state nanochannel. Considering a bulk concentration of 100 mM, a charge density of 60 mol m−3, and a surface charge density of −20 mC m−2, the ionic rectification factor was degraded by 49% and enhanced by 43%, respectively, for the solid-state and PEL-coated nanochannels when the slip length is taken into account.

Evolution of solitary hydroelastic strain waves in two coaxial cylindrical shells with the Schamel physical nonlinearity

The paper considers the formulation and solution of the hydroelasticity problem for studying wave processes in the system of two coaxial shells containing fluids in the annular gap between them and in the inner shell. We investigate the axisymmetric case for Kirchhoff–Lave type shells whose material obeys a physical law with a fractional exponent of the nonlinear term (Schamel nonlinearity). The dynamics of fluids in the shells is considered within the framework of the incompressible viscous Newtonian fluid model. The derivation of the Schamel nonlinear equations of shell dynamics makes it possible to develop a mathematical formulation of the problem, which includes the obtained equations, the dynamics equations of two shells, the fluid dynamics equations and the boundary conditions at the shell-fluid interfaces and at the flow symmetry axis. The asymptotic analysis of the problem is performed using perturbation techniques, and the system of two generalized Schamel equations is obtained. This system describes the evolution of nonlinear solitary hydroelastic strain waves in the coaxial shells filled with viscous fluids, taking into account the inertia of the fluid motion. In order to determine the fluid stress at the shell-fluid interfaces, we perform linearization of the fluid dynamics equations for fluids in the annular gap and in the inner shell. The linearized equations are solved by the iterative method. The inertial terms are excluded from the equations in the first iteration, while, in the second iteration, these are the values found in the first iteration. A numerical solution of the system of nonlinear evolution equations is obtained by applying a new difference scheme developed using the Gröbner basis technique. Computational experiments are performed to investigate the effect of fluid viscosity and the inertia of fluid motion in the shells on the wave process. In the absence of fluids in the inner shell, the results of calculations demonstrate that the strain waves in the shells during elastic interactions do not change their shape and amplitude, i.e., they are solitons. The presence of viscous fluid in the inner shell leads to attenuation of the wave process.

Regularity for the steady Stokes-type flow of incompressible Newtonian fluids in some generalized function settings

A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving p-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper also provides a relatively complete picture of our main results in two regards: problems with nonlinearity is regular with respect to the gradient variable; and asymptotically regular problems, whose nonlinearity satisfies a particular structure near infinity. For such Stokes-type systems, we derive regularity estimates for both velocity gradient and its associated pressure in two special classes of function spaces: the generalized Lorentz and ψ-generalized Morrey spaces.

A Study on Oscillatory Micropolar Flow Beyond a Contaminated Micropolar Fluid Sphere

In this paper, the hypothesis of the axisymmetric rectilinear oscillatory flow beyond a micropolar tainted fluid sphere particle in an incompressible non-Newtonian fluid and also the axisymmetric rectilinear oscillatory flow over a viscous tainted fluid sphere particle in an incompressible Newtonian fluid with small amplitude oscillations have been investigated. The velocity field is exhibited in terms of stream functions, and a slip condition is considered on the boundary. The fluid velocities and microrotation components were derived through analytical procedure. The drag force acting on the particle was also computed and verified for special cases. The real drag and imaginary drag values are numerically extracted for varying slip parameter i.e., 2≤s≤30, micro polarity i.e., 8≤e≤32 , and viscosity ratio i.e., 5≤μ≤20 at a fixed parameter values k=0.1,ρ=0.6,ω=0.6,t=0.6. Graphs and tables are used to display the numerical results. It was observed that there was an inverse proportion between slip parameter values, real drag and direct proportion between slip parameter and imaginary drag, for different viscosity ratio and micro polarity values.

Development of a contact force model with a fluid damping factor for immersed collision events

Impact behavior in a fluidic environment is an inevitable phenomenon in multibody systems. This investigation studies the motion of a contact body in an unbounded and incompressible Newtonian viscous fluid. In allusion to the physical impact in immersed fluid, a dissipated coefficient is introduced to describe the dissipated energy caused by the hydrodynamic forces, including the drag force, added mass force, and history force. To attain the fluid damping factor during impact, the kinetic energy corresponding to the physical impact has four discrepant destinations at the end of the compression phase. According to this principle, a new fluid damping factor is derived based on the energy conservation during impact for simultaneously depicting the coupling between liquid and solid and the coupling between solid and solid. More importantly, to determine the coefficient of restitution (CoR) corresponding to the actual physical impact, a new CoR is proposed according to the definitions of dry and wet CoRs. Subsequently, since both compression and recovery phases happen in the presence of hydrodynamic forces, fluid damping force should be imposed on the Hertz contact model. Consequently, a new contact force model with a fluid damping factor tailored for immersed collision events is proposed. Although the viscosity of the fluid is not explicitly exhibited in the hysteresis damping loop from the new contact force model, the effect of fluid on the immersed collision cannot be neglected, especially for the initial distance of contact bodies. Finally, the rationality and correctness of the proposed model are validated by the reference solution obtained from the solitary wave propagation of a horizontal one-dimension granular chain.

Lid driven cavity flow with two porous square obstacles

The flow of Newtonian incompressible fluid inside a two-dimensional lid-driven cavity with two non-adherent porous square blocks was numerically studied. The non-linear governing equations, Darcy-Forchheimer-Brinkman for the porous medium and Navier-Stokes for the free fluid region, were solved using the finite element method. The streamlines and velocity profile of the fluid inside the cavity, as well as the maximum value of the stream function and the coordinates of the main vortex created, are investigated to determine the effect of the Reynolds number, the different combinations of Darcy number and the different placements of the porous squares, on the behaviour of the fluid flow.