Fluid Stress Tensor Research Articles

Optimization of entropy and heat transfer in a magnetohydrodynamic marangoni convection flow of biviscosity bingham hybrid nanofluid through convergent channel

This study examines the entropy generation and heat transfer performance in a Jeffrey-Hamel flow of biviscosity Bingham fluid with the addition of Al2O3 and Cu nanomaterials in the presence of a thermal Marangoni convective process. An emerging Jeffrey-Hamel problem is extended with the implementation of the Bingham fluid stress tensor in a Naiver Stokes equation. The governing equations with Marangoni boundary conditions due to surface tension are solved computationally utilizing the Keller-Box methodology. The findings demonstrate the complex interplay of entropy production processes, fluid-solid interfaces, and thermal Marangoni convection. Findings demonstrated that increasing Marangoni, Bingham parameters, and thermal radiation enhances the rate of heat transmission. The influence of the Marangoni and Bingham parameters on skin friction is conflicting in a narrow channel. System entropy and flow field uplift with a higher Marangoni convection parameter. Increasing the Reynolds number significantly increases the drag force, whereas the effect of the magnetic variable is the reverse. Velocity is an increasing function of the Reynolds and Bingham parameters and deteriorates with the load of nanomaterials. Temperature is a rising function of nanomaterial load, Eckert, and Bingham parameter. The results of this investigation have important ramifications for improving heat transfer, coolant systems, and nozzles design.

Thermocapillary thin film flows on a slippery substrate with odd viscosity effects

This study investigates the behavior of a thin liquid with odd viscosity effects as it flows down a uniformly heated, slippery inclined plane, where the liquid’s time-reversal symmetry is broken. The breaking of symmetry results in interesting effects, as the antisymmetric part of the fluid stress tensor does not vanish. Two models, the Benney-type equation model (BEM) and the weighted residual model (WRM), are constructed to account for the combined effects of slip length, thermocapillarity, and odd viscosity. A detailed stability analysis determines both models’ critical Reynolds numbers Rec. For small slip lengths, the first-order WRM is better at capturing the instability threshold than the first-order BEM. While both models account for the effects of odd viscosity and thermocapillarity, only the Rec of WRM incorporates the wall slip effects. Another significant finding is that the BEM effectively avoids the issue of finite-time blow-up by incorporating odd viscosity. Additionally, employing a weakly nonlinear stability analysis with multiple scales uncovers four flow regions in BEM: supercritical stable, subcritical unstable, unconditional stable, and explosive zones. Two separate bifurcation scenarios emerge for various wave numbers: supercritical within a specific range and subcritical for larger wave numbers. The presence of odd viscosity alleviates the reduction of the unconditional stable zone and the increase in the explosive zone, which are caused by the combined influence of slip and thermal effects. Numerical investigation of traveling wave solutions of WRM shows that wave height is promoted by slip and thermal effects but reduced with increasing odd viscosity coefficient. Further numerical simulations of WRM on a larger domain demonstrate the stabilizing effects of odd viscosity and its interaction with destabilizing slip and thermocapillary effects.

Multiphase flow development in gravitational and magnetic fields

Multiphase flows of non-Newtonian fluid with heat transfer through an inclined channel are presented in this article. Eyring-Powell fluid is considered the main continuous phase. Two separate types of bi-phase suspensions are formulated with the help of gold and silver metallic particles under the effects of applied magnetic fields. Mathematical expressions for multiphase flow dynamics are developed employing Eyring-Powell fluid's stress tensor. Thermal transport is governed by Fourier's law of conduction. A semi-analytic solution is obtained for the nonlinear and coupled differential equations. The present results are compared with the Newtonian multiphase flows for the limiting case. The study reveals that gold particles offer less drag as compared to silver particles in the multiphase suspensions. Moreover, Eyring-Powell fluid is more suitable for viscous suspensions.

On aerodynamic force computation in fluid–structure interaction problems — Comparison of different approaches

This paper is interested in the numerical approximation of a two-dimensional fluid–structure interaction problem. A special attention is paid to the numerical realization of aerodynamic force (AF) calculations. Three different AF computations within finite element method framework are described and compared. First, the extrapolation of fluid stress tensor components from the interior of the fluid domain is the most straightforward method; however, this approach is of lower theoretical accuracy due to the explicit computation of velocity gradient. Second, the local reconstruction method applied on the velocity gradient is based idea of the least square fit of the gradients evaluated at finite element centroids from local patch. Third, the weak reformulation technique using the weak formulation of the fluid flow problem leads to the expression of AF in an integral form. As it avoids direct velocity gradient computation it is of higher accuracy compared to previous methods.The experimental convergence of all mentioned methods for the drag and lift coefficients is tested on the benchmark of a static cylinder in a cross-flow and further extended to the case with prescribed motion of the cylinder. Further, two FSI simulations compare the transferred energy from the fluid to the structure for the case of structure vibrations submerged in the viscous fluid and also for the flow-induced structural vibrations. The critical inlet velocity of flutter instability is determined and it is shown that for a given numerical setting the choice of AF computation can lead to the different FSI behavior.

A Mathematical Proof to the HKLam Theory by Linear/Tensor Algebra and Analysis

In the previous papers, I have mentioned several times of HKLam Theory and their everyday usage but without the abstract mathematical proof. In order to remediate the flaws, I am now trying to proof the theory through both Tensor Algebra and Analysis as well as the statistical inference in this present paper. Indeed, people always say that mathematicians are linear animals or participate much in the subject of linear algebra while the British Scientist Newton observed a falling apple and discovered the gravity together with the development of calculus. In a similar case, my proof in the part of tensor algebra will be an analogy to the linear mapping, transformation etc while there are the corresponding corollary real physical life cases – 2 to 3 dimensional vectors calculus or even higher dimension of tensor analysis. Indeed, my proof will be based on the order two tensor but the HKLam theory may be extended up to nth order tensor but NOT applicable to the topic of the planned politics or even economics etc.The main aim is to show the proof of HKLam Theory by linear/Tensor algebra together with some applications in fluid dynamic and stress tensor field etc.

Influence of surface properties on the dynamics of fluid flow

In this paper, we study how the fluid flow near the surface of a monocrystalline body is affected by the surface properties due to atom-surface scattering. We propose a toy model for this system by parameterizing the surface with a periodic function of the tangential position. This allows us to derive the velocity probability density function in the Knudsen layer and determine statistical averages of fluid velocity and stress tensor components in the region of interest. The results of this analysis provide a potentially more fundamental and accurate explanation for empirically observed phenomena such as the no-slip boundary condition, boundary layer formation, and the onset of hydrodynamic instability.

Shear-Thinning in Oligomer Melts-Molecular Origins and Applications.

We investigate the molecular origin of shear-thinning in melts of flexible, semiflexible and rigid oligomers with coarse-grained simulations of a sheared melt. Entanglements, alignment, stretching and tumbling modes or suppression of the latter all contribute to understanding how macroscopic flow properties emerge from the molecular level. In particular, we identify the rise and decline of entanglements with increasing chain stiffness as the major cause for the non-monotonic behaviour of the viscosity in equilibrium and at low shear rates, even for rather small oligomeric systems. At higher shear rates, chains align and disentangle, contributing to shear-thinning. By performing simulations of single chains in shear flow, we identify which of these phenomena are of collective nature and arise through interchain interactions and which are already present in dilute systems. Building upon these microscopic simulations, we identify by means of the Irving–Kirkwood formula the corresponding macroscopic stress tensor for a non-Newtonian polymer fluid. Shear-thinning effects in oligomer melts are also demonstrated by macroscopic simulations of channel flows. The latter have been obtained by the discontinuous Galerkin method approximating macroscopic polymer flows. Our study confirms the influence of microscopic details in the molecular structure of short polymers such as chain flexibility on macroscopic polymer flows.

Variational formulation of compressible hydrodynamics in curved spacetime and symmetry of stress tensor

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation becomes asymmetric for the exchange of the indices, different from the standard Euclidean one. Its incompressible limit suggests that the viscous term should be represented with the Bochner Laplacian. Moreover the modified Navier–Stokes–Fourier equation proposed by Brenner can be considered even in the curved spacetime. To confirm the compatibility with the symmetry principle, SVM is applied to the gauge-invariant Lagrangian of a charged compressible fluid and then the Lorentz force is reproduced as the interaction between the Abelian gauge fields and the viscous charged fluid.

Research on the magnetic fluid levitation force received by a permanent magnet suspended in magnetic fluid: Consideration a surface instability

This paper focus on the magnetic fluid levitation force received by a permanent magnet immersed in magnetic fluid under the magnetic field created by the magnet itself. A more understandable equation for calculating the magnetic fluid levitation force is derived using magnetic fluid stress tensor, and the equation concentrates on the boundary interface between magnetic fluid and surroundings. The magnetic fluid spikes appearing over the interface between magnetic fluid and air caused by the surface instability of magnetic fluid is taken into consideration, and the dependence between magnetic fluid levitation force and magnetic fluid spikes is studied. Two groups of experiments are designed, both theoretical analysis and experiments show that the magnetic fluid levitation force relies on the magnetic fluid spikes which indicates that the magnetic fluid spikes can be used to evaluate the magnetic fluid levitation force for the self-levitation of a permanent magnet. The equation presented in this paper are clear in physical meaning and easy to understand.

Deformation of human red blood cells in extensional flow through a hyperbolic contraction.

Flow-induced damage to red blood cells has been an issue of considerable importance since the introduction of the first cardiovascular devices. Early blood damage prediction models were based on measurements of damage by shear stress only. Subsequently, these models were extrapolated to include other components of the fluid stress tensor. However, the expanded models were not validated by measurements of damage in response to the added types of stress. Recent investigations have proposed that extensional stress might be more damaging to red cells than shear stress. In this study, experiments were conducted to compare human red cell deformation under laminar extensional stress versus laminar shear stress. It was found that the deformation caused by shear stress is matched by that produced by an extensional stress that is approximately 34 times smaller. Assuming that blood damage scales directly with cell deformation, this result indicates that mechanistic blood damage prediction models should weigh extensional stress more than shear stress.

Characterization of erythrocyte membrane tension for hemolysis prediction in complex flows.

Hemolysis is a persistent issue with blood-contacting devices. Many experimental and theoretical contributions over the last few decades have increased insight into the mechanisms of hemolysis in both laminar and turbulent flows, with the ultimate goal of developing a comprehensive, mechanistic hemolysis model. Many models assume that hemolysis scales with a resultant, scalar stress representing all components of the fluid stress tensor. This study critically evaluates this scalar stress hypothesis by calculating the response of the red blood cell membrane to different types of fluid stress (laminar shear and extension, and three turbulent shear and extension cases), each with the same scalar stress. It was found that even though the scalar stress is the same for all cases, membrane tension varied by up to three orders of magnitude. In addition, extensional flow causes constant tension, while tank-treading in shear flow causes periodic tension, with tank-treading frequency varying by three orders of magnitude among the cases. For turbulent flow, tension also depends on eddy size. It is concluded, therefore, that scalar stress alone is inadequate for scaling hemolysis. Fundamental investigations are needed to establish a new index of the fluid stress tensor that provides reliable hemolysis prediction across the wide range of complex flows that occur in cardiovascular devices.

Microscopic derivation of the hydrodynamics of active-Brownian-particle suspensions.

We derive the hydrodynamic equations of motion for a fluid of active particles described by underdamped Langevin equations that reduce to the active-Brownian-particle model, in the overdamped limit. The contraction into the hydrodynamic description is performed by locally averaging the particle dynamics with the nonequilibrium many-particle probability density, whose formal expression is found in the physically relevant limit of high friction through a multiple-time-scale analysis. This approach permits us to identify the conditions under which self-propulsion can be subsumed into the fluid stress tensor and thus to define systematically and unambiguously the local pressure of the active fluid.

Membrane paradigm for Einstein-Gauss-Bonnet gravity

We construct the membrane paradigm for black objects in Einstein-Gauss-Bonnet gravity in spacetime dimensions $\ensuremath{\ge}5$. As in the case of general relativity, the horizon can be modeled as a membrane endowed with fluidlike properties. We derive the stress tensor for this membrane fluid and study the perturbation around static backgrounds with constant curvature horizon cross section, for which the stress tensor can be regularized with the usual redshift factor, and expressed in the form of a Newtonian viscous fluid with pressure, shear viscosity and bulk viscosity. We evaluate the transport coefficients for black holes with constant curvature horizons and negative or zero cosmological constant. For the black brane geometry our result for the ratio of shear viscosity to entropy density agrees with that obtained previously in different frameworks.

Combined interface boundary condition method for fluid–structure interaction: Some improvements and extensions

The combined interface boundary condition (CIBC) method devises the increments to correct traditional interface conditions for partitioned computation of fluid–structure interaction. However, the restricted use of the CIBC method has been realized recently. In this paper we present some improvements and extensions of the CIBC method as follows: (1) the method is reformulated in the general situation by using the complete fluid stress tensor; (2) the structural traction rate, which results in the inconsistency in the interfacial traction and may cause the loss of numerical accuracy, is totally removed from the CIBC formulation via a simple revision; (3) we analyze the instability source due to the CIBC compensation and propose an approach to recover the two-sided corrections for Dirichlet and Neumann interface conditions; (4) the CIBC method is extended to the generalized planar rigid-body motion. A novel CBS-based partitioned semi-implicit coupling approach is adopted to couple different fields within the nondimensional ALE finite element framework. The interaction between incompressible flows and a rigid/flexible body is numerically simulated to demonstrate the validity of the developed method. The reasonable agreement is disclosed between the present and available data.

Constitutive equations for thixotropic fluids

To distinguish it clearly from nonlinear viscoelasticity, we define “ideal thixotropy” as “a time-dependent viscous response to the history of the strain rate, with fading memory of that history,” endowing such fluids with memory but no elasticity. An “ideal thixotropic fluid” has instantaneous stress relaxation upon cessation of flow and no elastic recoil on removal of stress. We describe “nonideal thixotropic” fluids as those whose viscoelastic time scales governing stress relaxation are much shorter than those governing the thixotropic response. This ensures that a clear distinction can be maintained between “thixotropy” and “nonlinear viscoelasticity.” The stress tensor for an ideal thixotropic fluid can in general be expressed as a contraction product of a fourth rank viscosity tensor with the velocity gradient tensor, in which the viscosity tensor depends on the history of the flow. We show examples of constitutive equations that meet the definitions of ideal thixotropy or nonideal thixotropy. We also show examples of constitutive equations that have been designated as “thixotropic” by virtue of containing an equation for evolution of a “structure parameter,” but whose behavior is indistinguishable from that of ordinary nonlinear viscoelasticity, and so should not be considered thixotropic.

Linearized fluid/gravity correspondence: from shear viscosity to all order hydrodynamics

In ref. \cite{1406.7222}, we reported a construction of all order linearized fluid dynamics with strongly coupled $\mathcal{N}=4$ super-Yang-Mills theory as underlying microscopic description. The linearized fluid/gravity correspondence makes it possible to resum all order derivative terms in the fluid stress tensor. Dissipative effects are fully encoded by the shear term and a new one, emerging starting from third order in hydrodynamic derivative expansion. In this work, we provide all computational details omitted in \cite{1406.7222} and present additional results. We derive closed-form linear holographic RG flow-type equations for momenta-dependent transport coefficient functions. Generalized Navier-Stokes equations are shown to emerge from the constraint components of the bulk Einstein equations. We perturbatively solve the RG equations for the viscosity functions, up to third order in derivative expansion, and up to this order compute spectrum of small fluctuations. Finally, we solve the RG equations numerically, thus accounting for all order derivative terms in the boundary stress tensor.

Invariant Forms of Conservation Equations and Some Examples of Their Exact Solutions

A scale-invariant model of statistical mechanics is described leading to invariant Boltzmann equation and the corresponding invariant Enskog equation of change. A modified form of Cauchy stress tensor for fluid is presented such that in the limit of vanishing intermolecular spacing, all tangential forces vanish in accordance with perceptions of Cauchy and Poisson. The invariant forms of mass, thermal energy, linear momentum, and angular momentum conservation equations derived from invariant Enskog equation of change are described. Also, some exact solutions of the conservation equations for the problems of normal shock, laminar, and turbulent flow over a flat plate, and flow within a single or multiple concentric spherical liquid droplets made of immiscible fluids located at the stagnation point of opposed cylindrically symmetric gaseous finite jets are presented.

Stress Measures Affecting Deformation of Granular Materials

For the saturated case with only one pore fluid, either water or air, the roles of both the intergranular stress tensor and the pore fluid stress can be distinguished easily. In the unsaturated case, the capillary water is recognized to induce capillary suction in the pores and capillary‐suction‐induced interparticle forces. At the macroscale, volume averaging of these forces would lead to the capillary‐suction‐induced intergranular stress tensor. In its approximate formulation, the concept of the fabric stress tensor is applied, enabling the effect of the spatial distribution of the intergranular fabric on the capillary water bridges as occurring in the drier pendular saturation phase to be accounted for. Subsequently, the combined intergranular stress tensor and the combined pore fluid stress tensor can be derived directly. The constitutive relation of a granular skeleton, composed of elastic particles with mainly frictional interaction, like quartz sands and silts, is considered to remain independent of the degree of saturation. Under such restrictive conditions, only the additional physical parameters of the capillary‐suction‐induced intergranular stress tensor need to be determined, which can be achieved by means of inverse modeling, taking advantage of all macroscale experimental data and physical modeling for the whole unsaturated range. For clays and peats, with potential physicochemical and biochemical actions and double porosity and/or fibrous microstructures, the constitutive models can be expected to be physically more complicated, thus involving more physically relevant parameters. Hence, clays and peats must be considered to fall outside the scope of the proposed model framework.

A two-scale non-local model of swelling porous media incorporating ion size correlation effects

A new two-scale model is proposed for derivation of the macroscopic modified effective stress principle for swelling porous media saturated by an electrolyte solution containing finite size ions. A non-local pore-scale model is developed within the framework of Statistical Mechanics in conjunction with the thermodynamic approach based on Density Functional Theory leading to a nonlinear integral Fredholm equation of second kind for the ion/nanopore correlation function coupled with Poisson problem for the electric double layer potential. When combined with the fluid equilibrium condition such non-local electrochemical problem gives rise to a constitutive law for the fluid stress tensor in terms of the disjoining pressure which is decomposed into several components of different nature. The homogenization procedure based on formal asymptotic expansions is applied to up-scale the model to the macroscale leading to a two-scale constitutive law for the swelling pressure appearing in the modified effective stress principle with improved accuracy incorporating the deviations from the Gouy–Chapman Poisson–Boltzmann-based theory due to the finite size short-range ion–ion correlation effects. The integro-differential problem posed in a periodic cell is discretized by collocation schemes. Numerical results are obtained for a stratified arrangement of parallel macromolecules showing that the effects of ion–ion correlation forces give rise to anomalous attraction patterns between the particles for divalent ions.

A general formulation of the reversible stress tensor for a nonlocal fluid

The nonlocal stress tensor is an indispensable constitutive equation required to close the thermodynamic system of nonlocal fluid dynamics. A nonlocal functional variational principle is employed to derive a general expression for the thermodynamically reversible stress tensor for a two-phase, single component, nonlocal fluid. The Euler–Lagrange equation and Noether’s current are used to obtain the general form of the stress tensor, which is then used to derive a wide range of functional forms found in the literature. We also clarify some existing ambiguities. The general form of the nonlocal stress tensor is able to represent micro scale intermolecular interactions, and provides an efficient mesoscale numerical tool for multi-scale analysis using Lattice Boltzmann simulation.