Flow Of Such Fluids Research Articles

Flow of oil nanoclusters in a porous medium capillary

In the article, we consider movement of hydrophilic and hydrophobic liquids in a capillary. It is known that structure of flow of such fluids depends on set of conditions. The issue of correct choice of control parameters is of great importance for controlling the transition of the flow into different modes. The most important issue in the filtration problem is morphological stability of displacement front during filtration. It is generally assumed that it is sufficient to control the capillary number to change the flow regimes. The article shows that another parameter can be singled out, which is the disjoining pressure. If mechanisms of influence on wedging pressure can be found, then it is possible to control effectively flow by changing thickness of jet and to control the process of clustering (splitting of jet into droplets). In the article, it is shown that such mechanism can be interaction of hydrocarbon molecules with nanoparticles.

Symmetrical form of the two-component fluid flow’s stability curve as a part of analysis devices

The devices for analysis have different channels for mixing and separating flows. The media in most cases is multicomponent and predicts special properties. The constitutive equation FENE-P is chosen as a rheological model to describe a non-Newtonian fluid that has particles that can change their conformation. This model predicts properties such as viscosity anomaly, finite stress relaxation time, and dependence of the longitudinal viscosity on the longitudinal strain rate. For the non-Newtonian fluid the effect of the shape’s symmetry loss and manifestation of asymmetry are possible. The Weissenberg number (We) and the degree of stretching of the flexible particle (L2) are the determining parameters of the flows of such fluids. In this work the values of these modeling parameters, at which the flow behaviour changes so that the initial symmetrical flow form becomes unstable and turns into asymmetrical form even in laminar creeping flow (Re<<1) have been established. A number of numerical experiments have been carried out and the dependence of the manifestation of instability of the symmetrical flow form on the set of values of We and L2 has been obtained. The simulation results with the Newtonian fluid. The solution is obtained using the finite volume method (FVM) in the OpenFOAM software environment.

Modeling cross model non-Newtonian fluid flow in porous media

Fluids exhibiting non-Newtonian rheologies are used in a range of applications, including hydraulic fracturing, enhanced oil recovery, remediation, and industrial processes. Hydraulic fracturing in particular has received attention from environmental scientists, policy-makers, and the general public due in part to concerns about the possibility of contamination of groundwater resources by the complex and potentially harmful fluids used in the process. The non-Newtonian nature of many hydraulic fracturing fluids complicates the prediction of their movement, and precludes use of most traditional flow and transport models. To improve understanding of the flow of such fluids in porous media, a series of column experiments was conducted and a pore-scale lattice Boltzmann model (LBM) was developed, verified, and used to simulate analogous systems. Flow experiments were conducted with guar gum solutions of varying concentration and three porous media systems. The LBM was developed for transient, three-dimensional porous medium systems and included a shear rate-dependent dynamic viscosity based on the Cross rheological model. The LBM was verified using a semi-analytical solution for Cross model fluid flow, OpenFOAM simulations, and grid resolution inter-comparisons between two different solution approaches. Simulations were performed on synthetic porous medium systems produced with a sphere packing algorithm to approximate the properties of the experimental systems. The simulations were in good agreement with the experimental results, particularly for systems that exhibited the greatest non-Newtonian character. The modeling approach developed in this work provides a valuable tool for investigating relationships between pore-scale fluid flow and macroscale variables of interest for simulating movement of non-Newtonian fluids at larger scales.

A Channel Model for Bi-viscous Fluid Flow in Fractures

In the last decade, the interest towards fluids characterized by a complex rheology has increased in the scientific community. Physicochemical, rheological and fluid mechanical approaches are adopted to characterize the peculiarities of non-Newtonian fluids. These fluids show remarkable properties that can be exploited to improve remediation techniques or optimize industrial operations. While the existence of actual yield stress is still debated, the presence of a plug or pseudo-plug zone is frequent in emulsions, soft glassy materials, jammed non-colloidal suspensions or colloidal gels. Even if simple yield stress models are often faulted because of their acknowledged deficiencies, they allow to study important phenomena without introducing excessive complexity. In this study, the randomness describing the aperture field of a natural rock fracture is coupled with a bi-viscous fluid rheology of parameter $$\epsilon$$ , representing the viscosity ratio; the cases $$\epsilon =0$$ and $$\epsilon \rightarrow {1}$$ represent the Bingham and Newtonian behaviour, respectively. The conceptual model proposed describes the flow of such fluids through a fracture with aperture variable along a single direction, the aperture being constant along the other. The aperture variation is modelled via a generic probability distribution function of assigned mean and variance. Two limit flow cases are considered: (1) parallel arrangement (PA), representing the case of maximum conductance, with the fluid flowing in the direction of channels of constant aperture; and (2) series arrangement (SA), the case of minimum conductance, with flow directed orthogonally to the constant aperture side of the fracture. Results are illustrated for log normal and gamma aperture distributions. The influence of aperture variability and applied pressure gradient on flow rate is investigated for both arrangements. The pressure gradient affects in a nonlinear fashion the flow rate, with a marked increase around a threshold value for both PA and SA. The channel flow rate exhibits a direct dependency upon aperture variability for PA, an inverse one for SA. The shape of the distribution has an impact on model responses: for the PA, the influence is significant but limited to an intermediate threshold range of pressure gradients, while results for the SA are affected in the whole range of pressure gradient. An example application in dimensional form is included.

Flow of shear-thinning fluids through porous media

Pseudo-plastic fluids exhibit a non-linear stress-strain relationship which can provoke large, localized viscosity gradients. For the flow of such fluids in porous media the consequence is a strong variability of the effective permeability with porosity, angle of the macroscopic pressure gradient, and rheological parameters of the fluid. Such a variability is investigated on the basis of adjoint homogenization theory for a Carreau fluid in an idealized porous medium geometry, highlighting differences with respect to the Newtonian case. It is shown in particular that the more we depart from Newtonian conditions, the more the (often used) hypothesis of an effective viscosity in Darcy’s law is a poor approximation, for the effective permeability tensor becomes strongly anisotropic.

EXACT SOLUTIONS FOR OSCILLATING MOTIONS OF SOME FLUIDS WITH POWER-LAW DEPENDENCE OF VISCOSITY ON THE PRESSURE

Analytical expressions for the steady-state components of the dimensionless starting solutions corresponding to some oscillatory motions through a horizontal rectangular channel of two classes of incompressible Newtonian fluids with power-law dependence of viscosity on the pressure are established in the simplest forms. The fluid motion is generated by the lower plate that oscillates in its plane. For validation, three limiting cases are considered and interesting graphical representations are provided. It is worth pointing out the fact that such solutions are important in practice for those who want to eliminate the transients from their experiments. In addition, the dimensionless steady shear stresses corresponding to the simple Couette flow of such fluids are constants on the whole flow domain although the adequate velocity fields are functions of y

On the Classification of Incompressible Fluids and a Mathematical Analysis of the Equations That Govern Their Motion

In the first part of the paper we provide a new classification of incompressible fluids characterized by a continuous monotone relation between the velocity gradient and the Cauchy stress. The considered class includes Euler fluids, Navier-Stokes fluids, classical power-law fluids as well as stress power-law fluids, and their various generalizations including the fluids that we refer to as activated fluids, namely fluids that behave as an Euler fluid prior activation and behave as a viscous fluid once activation takes place. We also present a classification concerning boundary conditions that are viewed as the constitutive relations on the boundary. In the second part of the paper, we develop a robust mathematical theory for activated Euler fluids associated with different types of the boundary conditions ranging from no-slip to freeslip and include Navier's slip as well as stick-slip. Both steady and unsteady flows of such fluids in three-dimensional domains are analyzed.

Measurement of Drilling Fluid Rheology and Modeling of Thixotropic Behavior

AbstractDrilling fluids perform a number of important functions during a drilling operation, including that of lifting drilled cuttings to the surface and balancing formation pressures. Drilling fluids are usually designed to be structured fluids exhibiting shear thinning and yield stress behavior, and most drilling fluids also exhibit thixotropy. Accurate modeling of drilling fluid rheology is necessary for predicting friction pressure losses in the wellbore while circulating, the pump pressure needed to resume circulation after a static period, and how the fluid rheology evolves with time while in static or near-static conditions. Although modeling the flow of thixotropic fluids in realistic geometries is still a formidable future challenge to be solved, considerable insights can still be gained by studying the viscometric flows of such fluids. We report a detailed rheological characterization of a water-based drilling fluid and an invert emulsion oilbased drilling fluid. The micro structure responsible for thixotropy is different in these fluids which results in different thixotropic responses. Measurements are primarily focused at transient responses to step changes in shear rate, but cover also steady state flow curves and stress overshoots during start-up of flow. We analyze the shear rate step change measurements using a structural kinetics thixotropy model.

Numerical scheme for simulation of transient flows of non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient and the Cauchy stress tensor

We propose a numerical scheme for simulation of transient flows of incompressible non-Newtonian fluids characterised by a non-monotone relation between the symmetric part of the velocity gradient (shear rate) and the Cauchy stress tensor (shear stress). The main difficulty in dealing with the governing equations for flows of such fluids is that the non-monotone constitutive relation allows several values of the stress to be associated with the same value of the symmetric part of the velocity gradient. This issue is handled via a reformulation of the governing equations. The equations are reformulated as a system for the triple pressure-velocity-apparent viscosity, where the apparent viscosity is given by a scalar implicit equation. We prove that the proposed numerical scheme has---on the discrete level---a solution, and using the proposed scheme we numerically solve several flow problems.

Fully discrete finite element approximation of unsteady flows of implicitly constituted incompressible fluids

Abstract Implicit constitutive theory provides a very general framework for fluid flow models, including both Newtonian and generalized Newtonian fluids, where the Cauchy stress tensor and the rate of strain tensor are assumed to be related by an implicit relation associated with a maximal monotone graph. For incompressible unsteady flows of such fluids, subject to a homogeneous Dirichlet boundary condition on a Lipschitz polytopal domain $\varOmega \subset \mathbb{R}^d$, $d \in \{2,3\}$, we investigate a fully discrete approximation scheme, using a spatial mixed finite element approximation on general shape-regular simplicial meshes combined with backward Euler time-stepping. We consider the case when the velocity field belongs to the space of solenoidal functions contained in $\textrm{L}^\infty (0,T;\textrm{L}^2(\varOmega )^d)\cap \textrm{L}^q(0,T;\textrm{W}^{1,q}_0(\varOmega )^d)$ with $q\in \left (2d/(d+2), \infty \right )$, which is the maximal range of $q$ with respect to existence of weak solutions. In order to facilitate passage to the limit with the discretization parameters for the sub-range $q \in \left (2d/(d+2), (3d+2)/(d+2) \right )$, we introduce a regularization of the momentum equation by means of a penalty term, and first show convergence of a subsequence of approximate solutions to a weak solution of the regularized problem; we then pass to the limit with the regularization parameter. This is achieved by the use of a solenoidal parabolic Lipschitz truncation method, a local Minty-type monotonicity result, and various weak compactness techniques. For $q \geq (3d+2)/(d+2)$ convergence of a subsequence of approximate solutions to a weak solution can be shown directly, without the regularization term.

Holographic turbulence in a large number of dimensions

We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large number of dimensions satisfy the aforementioned restrictions and their dynamics are captured by hydrodynamics with a naturally truncated derivative expansion. Using analytic and numerical techniques we analyze two and three-dimensional turbulent flow of such fluids in various regimes and its relation to geometric data.

Steady transonic dense gas flow past two‐dimensional compression/expansion ramps

AbstractThe dynamic behaviour of compressible fluids depends crucially on the curvature of isentropes in the pressure/specific volume diagram. Most conveniently this curvature is expressed in form of a non‐dimensional quantity Γ now commonly referred to as the fundamental derivative of gasdynamics, Thompson [5]. Bethe‐Zel'dovich‐Thompson (BZT) fluids have the distinguishing property that they exhibit embedded regions in the general neighbourhood of the thermodynamic critical point where Γ is negative in contrast to classical gases of low molecular complexity including perfect gases where Γ is strictly positive.The behaviour of steady transonic flows of such fluids is essentially governed by two non‐dimensional parameters: (Γ) and its derivative with respect to the density at constant entropy (Λ), Cramer and Fry [2], Kluwick [4]. The resulting response to external forcing is surprisingly rich in nonclassical phenomena such as rarefaction shocks, sonic shocks, split shocks, etc. and is studied in detail for the canonical problem of two‐dimensional flow past compression/expansion ramps. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Shear-banding predicted by a constitutive model with a structural parameter in cylindrical Couette flows

Dense suspensions of non-Brownian particles may partially behave as thixotropic yield stress fluids. We study the flow of such fluids between two concentric cylinders using a phenomenological structural kinetics model. The structural kinetics approach balances the simplicity of phenomenological continuum approaches with a simplified model for structure against the complexity a more fundamental model based on particle micromechanics. A modified version of Houska’s model, which includes a diffusive term for the structural parameter, is considered. Depending on the breakdown rate of the structural parameter, shear-banding may be observed. For shear-banding in steady flows, the stress selection depends on the diffusion of the structural parameter. If there is no structural diffusion, the displacement of the interface between the flowing and the static regions fixes the stress at the interface during the transient flow. In the cases of very small diffusive coefficients, the stress at the fluid / solid interface converges to a limit value which is different from the yield stress of the structured material as expected without any diffusion. Nevertheless, the inner torque and the flow profile are quite similar in both cases and the differences are localized near the fluid / solid interface. For shear-banding, the gradients of the structural parameter and the strain rate are very abrupt but the continuity is preserved by the diffusion.

On laminar-turbulent transition in nanofluid flows

The paper presents experimental data on the laminar-turbulent transition in the nanofluid flow in the pipe. The transition in the flows of such fluids is shown to have lower Reynolds numbers than in the base fluid. The degree of the flow destabilization increases with an increase in concentration of nanoparticles and a decrease in their size. On the other hand, in the turbulent flow regime, the presence of particles in the flow leads to the suppression of smallscale turbulent fluctuations. The correlation of the measured viscosity coefficient of considered nanofluids is presented.

Global weak solutions to a class of non‐Newtonian compressible fluids

We consider a class of compressible fluids with nonlinear constitutive equations that guarantee that the divergence of the velocity field remains bounded. We study mathematical properties of unsteady three‐dimensional flows of such fluids in bounded domains. In particular, we show the long‐time and large‐data existence result of weak solutions with strictly positive density. Copyright © 2015 John Wiley &amp; Sons, Ltd.

Non-dissipative hydrodynamics: effective actions versus entropy current

While conventional hydrodynamics incorporating dissipative effects is hard to derive from an action principle, it is nevertheless possible to construct classical actions when the dissipative terms are switched off. In this note we undertake a systematic exploration of such constructions from an effective field theory approach and argue for the existence of non-trivial second order non-dissipative hydrodynamics involving pure energy-momentum transport. We find these fluids to be characterized by five second-order transport coefficients based on the effective action (a three parameter family is Weyl invariant). On the other hand since all flows of such fluids are non-dissipative, they entail zero entropy production; one can therefore understand them using the entropy current formalism which has provided much insight into hydrodynamic transport. An analysis of the most general stress tensor with zero entropy production however turns out to give a seven parameter family of non-dissipative hydrodynamics (a four parameter sub-family being Weyl invariant). The non-dissipative fluids derived from the effective action approach are a special case of the fluid dynamics constrained by conservation of the entropy current. We speculate on the reasons for the mismatch and potential limitations of the effective action approach.

Flow of fluids with pressure- and shear-dependent viscosity down an inclined plane

AbstractIn this paper we consider a fluid whose viscosity depends on both the mean normal stress and the shear rate flowing down an inclined plane. Such flows have relevance to geophysical flows. In order to make the problem amenable to analysis, we consider a generalization of the lubrication approximation for the flows of such fluids based on the development of the generalization of the Reynolds equation for such flows. This allows us to obtain analytical solutions to the problem of propagation of waves in a fluid flowing down an inclined plane. We find that the dependence of the viscosity on the pressure can increase the breaking time by an order of magnitude or more than that for the classical Newtonian fluid. In the viscous regime, we find both upslope and downslope travelling wave solutions, and these solutions are quantitatively and qualitatively different from the classical Newtonian solutions.

On the Modeling of the Synovial Fluid

Synovial fluid is a polymeric liquid which generally behaves as a viscoelastic fluid due to the presence of hyaluronan molecules. We restrict ourselves to the regime in which the fluid responds as a viscous fluid. A novel generalized power-law fluid model is developed wherein the power-law exponent depends on the concentration of the hyaluronan. Such a model will be adequate to describe the flows of such fluids as long as they are not subjected to instantaneous stimuli. Assuming two different structures for the form of the power law exponent, both in keeping with physical expectations, we numerically solve for the flow of the synovial fluid (described by the constraint of incompressibility, the balance of linear momentum, and a convection-diffusion equation for the concentration of hyaluronan) in a rectangular cavity. The solutions obtained with our models are compared with the predictions of those based on a model that has been used in the past to describe synovial fluids. While all the three models seem to agree well with available experimental results, one of the models proposed by us seems to fit the data the best; it would, however, be hasty to pass judgment based on this one particular experimental correlation.

Venting of a runaway organic peroxide decomposition in viscous solvents on pilot scale

AbstractRunaway reactions continue to occur in polymerization reactors, which are widely used in the chemical industry. Those of greatest concern include highly viscous multiphase mixtures. Considerable uncertainties exist in the design of emergency pressure‐relief systems for such reactors because there are only limited experimental data available on the flow of such fluids in relief systems.Venting experiments are reported here that have been carried out in a 350 L pilot‐scale reactor for the runaway decomposition of an organic peroxide in xylene solvent, with batch volumes of 150 and 200 L and with a range of concentrations of polystyrene dissolved in the xylene to modify the viscosity. Measurements were made of pressures in the reactor, vent line, and catch tank; temperatures at different levels in the reactor and in the vent line and catch tank; viscosity in the reactor; mass in the catch tank; and two‐phase density in the vent line.Analysis of the results shows that the venting behavior of a high‐viscosity reaction system is complex. There is no simple relationship between maximum pressure and viscosity. The results indicate that the flow regime in the reactor is influenced by the fluid viscosity and that this is of primary importance in explaining the effects on maximum pressure. © Crown Copyright 2006. Published with the permission of the Controller of HMSO and the Queen's printer for Scotland. Process Saf Prog, 2006

Effect of bottom curvature on mudflow dynamics: Theory and experiments

A one‐dimensional mathematical model of mudflow dynamics is formulated assuming mud to behave rheologically as a Herschel‐Bulkley fluid. Novel features of the present contribution regard the propagation of mudflows over a curvilinear bottom. A set of nonlinear partial differential equations is found to govern the unsteady, nonuniform flow of such fluids. Following the approach of Huang and Garcìa (1998), a depth‐integrated form of the continuity equation and shear‐integrated and plug‐integrated forms of the momentum equations are derived. A perturbation analysis is also carried out under the assumption of “slender” flow. The leading‐order problem takes the form of a kinematic wave equation. One straightforward application of this simplified model is the evaluation of the maximum run‐out extension of a mud which flows over a bed with a variable topography. This solution is obtained by solving the steady state problem. Dynamics information are obtained by numerically solving the hyperbolic conservative equation by means of a free oscillating numerical method. The effects of bottom curvature either on the equilibrium solution or mudflow dynamics are analyzed. Experiments are also performed releasing a given volume of kaoline and water mixture from a reservoir into both a constant slope and an upward concave channel. Comparisons between the numerical solution and the experimental data are generally satisfactory, though suggesting limitations typical of any approach that neglects convective accelerations and assumes gradually varied flow.