Experimental and modeling study of Newtonian and non-Newtonian fluid flow in pore network micromodels

The in situ rheology of polymeric solutions has been studied experimentally in etched silicon micromodels which are idealizations of porous media. The rectangular channels in these etched networks have dimensions typical of pore sizes in sandstone rocks. Pressure drop/flow rate relations have been measured for water and non-Newtonian hydrolyzed-polyacrylamide (HPAM) solutions in both individual straight rectangular capillaries and in networks of such capillaries. Results from these experiments have been analyzed using pore-scale network modeling incorporating the non-Newtonian fluid mechanics of a Carreau fluid. Quantitative agreement is seen between the experiments and the network calculations in the Newtonian and shear-thinning flow regions demonstrating that the 'shift factor,'alpha, can be calculated a priori. Shear-thickening behavior was observed at higher flow rates in the micromodel experiments as a result of elastic effects becoming important and this remains to be incorporated in the network model.     

Numerical analysis of thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions

Thermophoresis of colloidal particles in aqueous media is more frequently applied in biomedical analysis with processed fluids as biofluids. In this work, a numerical analysis of the thermophoresis of charged colloidal particles in non-Newtonian concentrated electrolyte solutions is presented. In a particle-fixed reference frame, the flow field of non-Newtonian fluids has been governed by the Cauchy momentum equation and the continuity equation, with the dynamic viscosity following the power-law fluid model. The numerical simulations reveal that the shear-thinning effect of pseudoplastic fluids is advantageous to the thermophoresis, and the shear-thickening effect of dilatant fluids slows down the thermophoresis. Both the shear-thinning and shear-thickening effects of non-Newtonian fluids on a thermodiffusion coefficient are pronounced for the case when the thickness of electric double layer (EDL) surrounding a particle is moderate or thin. Finally, the reciprocal of the dynamic velocity at the particle surface is calculated to approximately estimate the thermophoretic behavior of a charged particle with moderate or thin EDL thickness.     

Evaluation of the use of capillary numbers for quantifying the removal of DNAPL trapped in a porous medium by surfactant and surfactant foam floods

The capillary number is used to quantify the mobilization potential of organic phases trapped within porous media. The capillary number has been defined in three different forms, according to types of flow velocity and viscosity used in its definition. This study evaluated the suitability of the capillary number definitions representing surfactant and surfactant foam floods by constructing capillary number-TCE saturation relationships. The results implied that the capillary number should be correctly employed, according to scale and fluid flow behavior. This study suggests that the pore-scale capillary number should be used only for investigating the organic-phase mobilization at the pore scale because it is defined by the pore velocity and the dynamic viscosity. The Newtonian-fluid capillary number using the Darcy velocity and the dynamic viscosity may be suitable for quantifying flood systems representing Newtonian fluid behavior. For viscous-force modified flood systems such as surfactant-foam floods, the apparent capillary number definition employing macroscopic properties (permeability and potential gradient) may be used to appropriately represent the desaturation of organic phases from porous media.     

Modeling and Scaling of Food Dispersions

Scaling laws, determined by dimensional analysis, have been used to make experimental predictions of constitutive shear-flow rheology. This study aimed to scale and model the flow curves of various suspensions consisting of xanthan gum (0.5, 1 wt%) and WPI (2, 4 wt%), and to determine the best-scaling law and rheological model. The scaling methods were relative viscosity, Péclet number, and Reynolds number. When the apparent viscosity is reduced relative to the viscosity of the medium at zero-shear rate, a distinct reduced flow curve is obtained, regardless of xanthan and WPI concentrations. This study tough to develop a technique of simplifying complex non-Newtonian flow curves and, therefore, predicting the rheological flow curves and fluid mechanics when different modifiers are added to food suspensions. The flow behavior of all samples was successfully modeled with the power law, Ellis, and Cross models; the power law model best described the flow behavior of dispersions. Results showed that both G′ and G″ increased with xanthan and WPI. However, viscoelastic behavior was mainly governed by the xanthan gum content.     

Comprehensive model of electromigrative transport in microfluidic paper based analytical devices

A complete mathematical model for electromigration in paper-based analytical devices is derived, based on differential equations describing the motion of fluids by pressure sources and EOF, the transport of charged chemical species, and the electric potential distribution. The porous medium created by the cellulose fibers is considered like a network of tortuous capillaries and represented by macroscopic parameters following an effective medium approach. The equations are obtained starting from their open-channel counterparts, applying scaling laws and, where necessary, including additional terms. With this approach, effective parameters are derived, describing diffusion, mobility, and conductivity for porous media. While the foundations of these phenomena can be found in previous reports, here, all the contributions are analyzed systematically and provided in a comprehensive way. Moreover, a novel electrophoretically driven dispersive transport mechanism in porous materials is proposed. Results of the numerical implementation of the mathematical model are compared with experimental data, showing good agreement and supporting the validity of the proposed model. Finally, the model succeeds in simulating a challenging case of free-flow electrophoresis in paper, involving capillary flow and electrophoretic transport developed in a 2D geometry.     

Does macroscopic flow geometry influence wetting dynamic?

The macroscopic flow geometry has long been assumed to have little impact on dynamic wetting behavior of liquids on solid surfaces. This study experimentally studied both spontaneous spreading and forced wetting of several kinds of Newtonian and non-Newtonian fluids to study the effect of the macroscopic flow geometry on dynamic wetting. The relationship between the dynamic contact angle, θ(D), and the velocity of the moving contact line, U, indicates that the macroscopic flow geometry does not influence the advancing dynamic wetting behavior of Newtonian fluids, but does influence the advancing dynamic wetting behavior of non-Newtonian fluids, which had not been discovered before.     

Dynamic wetting of Boger fluids

The impact of fluid elasticity on the dynamic wetting of polymer solutions is important because many polymer solutions in technological use exhibit non-Newtonian behaviors in the high shear environment of the wedge-like flow near a moving contact line. Our former study [G.K. Seevaratnam, Y. Suo, E. Ramé, L.M. Walker, Phys. Fluids 19 (2007) Art. No. 012103] showed that shear thinning induced by a semi-flexible high molecular weight polymer reduces the viscous bending near a moving contact line as compared to a Newtonian fluid having the same zero-shear viscosity. This results in a dramatic reduction of the dependence of the effective dynamic contact angle on contact line speed. In this paper, we discuss dynamic wetting of Boger fluids which exhibit elasticity-dominated rheology with minimal shear thinning. These fluids are prepared by dissolving a dilute concentration of high molecular weight polymer in a "solvent" of the oligomer of the polymer. We demonstrate that elasticity in these fluids increases curvature near the contact line but that the enhancement arises mostly from the weakly non-Newtonian behavior already present in the oligomeric solvent. We present evidence of instabilities on the liquid/vapor interface near the moving contact line.     

Anisotropy in nonlinear polymer rheology

A theory describing the behavior of liquids with anisotropic relaxation times in terms of the extended (locally nonequilibrium) thermodynamics of irreversible processes has been formulated. The theory forms the basis for a general approach to the investigation of anisotropy of the rheological properties of orientable polymer liquids. Uniaxial shear and elongation flows of a viscoelastic fluid in one preferred direction have been considered. The pattern of the obtained viscometric functions indicates the important role of macroscopic orientation effects in the rheology of polymeric media.     

Structural rationale of a non-Newtonian flow

The complex rheological behavior of structured systems, namely, suspensions, emulsions, polymer melts and solutions, micellar fluids, and liquid crystalline systems is analyzed. The behavior of such systems is characterized by the coexistence of different flow regimes in a wide range of shear rates. It is shown that the generalized flow equation (GFE) effectively describes plastic and pseudoplastic flow systems. The Newtonian and non-Newtonian behavior of structured flowable systems is explained within the structural microrheological model.     

Active colloids in complex fluids

We review recent work on active colloids or swimmers, such as self-propelled microorganisms, phoretic colloidal particles, and artificial micro-robotic systems, moving in fluid-like environments. These environments can be water-like and Newtonian but can frequently contain macromolecules, flexible polymers, soft cells, or hard particles, which impart complex, nonlinear rheological features to the fluid. While significant progress has been made on understanding how active colloids move and interact in Newtonian fluids, little is known on how active colloids behave in complex and non-Newtonian fluids. An emerging literature is starting to show how fluid rheology can dramatically change the gaits and speeds of individual swimmers. Simultaneously, a moving swimmer induces time dependent, three dimensional fluid flows that can modify the medium (fluid) rheological properties. This two-way, non-linear coupling at microscopic scales has profound implications at meso- and macro-scales: steady state suspension properties, emergent collective behavior, and transport of passive tracer particles. Recent exciting theoretical results and current debate on quantifying these complex active fluids highlight the need for conceptually simple experiments to guide our understanding.     

Nonlinear glassy rheology

Dense colloidal suspensions and related glass-forming fluids show pronounced nonlinear (non-Newtonian) flow effects, since slow internal relaxation competes with the imposed external driving. The microscopic processes governing the macroscopic material behavior are nonlocal both in time and space, encoding the divergence of viscosity in the fluid, and the rigidity of the amorphous solid that forms at the glass transition. Current theoretical approaches starting from either extreme, the homogeneous fluid flow and the spatially heterogeneous amorphous solid, are reviewed.     

Elastic instabilities in the electroosmotic flow of non-Newtonian fluids through T-shaped microchannels

Electroosmotic flow (EOF) has been widely used to transport fluids and samples in micro- and nanofluidic channels for lab-on-a-chip applications. This essentially surface-driven plug-like flow is, however, sensitive to both the fluid and wall properties, of which any inhomogeneity may draw disturbances to the flow and even instabilities. Existing studies on EOF instabilities have been focused primarily upon Newtonian fluids though many of the chemical and biological solutions are actually non-Newtonian. We carry out a systematic experimental investigation of the fluid rheological effects on the elastic instability in the EOF of phosphate buffer-based polymer solutions through T-shaped microchannels. We find that electro-elastic instabilities can be induced in shear thinning polyacrylamide (PAA) and xanthan gum (XG) solutions if the applied direct current voltage is above a threshold value. However, no instabilities are observed in Newtonian or weakly shear thinning viscoelastic fluids including polyethylene oxide (PEO), polyvinylpyrrolidone (PVP), and hyaluronic acid (HA) solutions. We also perform a quantitative analysis of the wave parameters for the observed elasto-elastic instabilities.     

Strain-Dependent Rheological Model and Pressure Wave Prediction for Shut in and Restart of Waxy Oil Pipelines

Waxy oil gelation and rheology is investigated and modeled using strain-dependent viscosity correlations. Rotational rheometry shows a sharp viscosity increase upon gel formation. High creeping flow viscosities are observed at small deformation conditions prior to yielding. A new strain-dependent rheological model, following analogous formulation to the Carreau–Yasuda shear rate-dependent model, captures viscosity reduction associated with yielding. In addition, shear viscosity and extensional viscosity are investigated using a capillary rheometry method. Distinct shear-thinning behavior is observed in the shear mode of deformation, while distinct tension-thinning behavior is observed in the extensional mode of deformation for the model fluid systems. High Trouton ratios are obtained for the gelled model fluid systems, confirming strongly non-Newtonian fluid rheology. Finally, axial pressure wave profiles are computed at real pipeline dimensions for idealized moderate yield stress fluids using a computationally efficient 1D pipeline simulator. The Rønningsen time-dependent gel degradation model is used to emulate the fluid rheology in the simulator. Axial stress localization phenomena are shown to depend on the overall magnitude of gel degradation as established by the reduction in yield value. A high degree of gel degradation serves to afford flow commencement in a timely manner.     

Sol–gel transition and rheological properties of silica nanoparticle dispersions

Possible variants of the rheological behavior of silica model dispersions have been analyzed. Different types of interaction between the particles and a dispersion medium make it possible to obtain different systems from low-viscosity sols to gels. Proton-donor (water) and aprotic (dimethyl sulfoxide) media have been used for comparison. Dispersions in the aprotic medium behave as non-Newtonian viscous fluids exhibiting shear thinning or shear thickening depending on deformation rate. Aqueous dispersions are viscoelastic and viscoplastic objects that exhibit the shear thickening at stresses higher than the yield stress. The introduction of small amounts of poly(ethylene oxide) into the organic dispersion medium initiates gelation. An increase in the polymer content in the dispersion medium above the concentration corresponding to the formation of a macromolecular network promotes an increase in stiffness and strength of the gels. The rheological behavior of gels is influenced by the polymer molecular mass and its affinity for a solvent.     

Molecular dynamic simulations of systems undergoing shear

Non-equilibrium molecular dynamics have been used to simulate, at a molecular level, fluids undergoing planar Couette flow. The results give a microscopic picture of the processes involved in viscoelasticity, shear dilatancy, shear birefringence, normal stress effects and shear thinning behavior. The calculations prove that shear dilatant fluids are not necessarily shear thickening. The results also suggest that the constitutive relations governing non-Newtonian behavior are non-analytic functions of strain rate.The calculations have led directly to the development of non-linear irreversible thermodynamics. This generalization of thermodynamics provides a macroscopic understanding of such processes as shear induced phase changes and the relation of shear dilatancy to shear induced energy changes.     

Modeling the Transport of Nanoparticle-Filled Binary Fluids through Micropores

Understanding the transport of multicomponent fluids through porous medium is of great importance for a number of technological applications, ranging from ink jet printing and the production of textiles to enhanced oil recovery. The process of capillary filling is relatively well understood for a single-component fluid; much less attention, however, has been devoted to investigating capillary filling processes that involve multiphase fluids, and especially nanoparticle-filled fluids. Here, we examine the behavior of binary fluids containing nanoparticles that are driven by capillary forces to fill well-defined pores or microchannels. To carry out these studies, we use a hybrid computational approach that combines the lattice Boltzmann model for binary fluids with a Brownian dynamics model for the nanoparticles. This hybrid approach allows us to capture the interactions among the fluids, nanoparticles, and pore walls. We show that the nanoparticles can dynamically alter the interfacial tension between the two fluids and the contact angle at the pore walls; this, in turn, strongly affects the dynamics of the capillary filling. We demonstrate that by tailoring the wetting properties of the nanoparticles, one can effectively control the filling velocities. Our findings provide fundamental insights into the dynamics of this complex multicomponent system, as well as potential guidelines for a number of technological processes that involve capillary filling with nanoparticles in porous media.     

Flow of non‐newtonian fluids in porous media

The study of flow of non‐Newtonian fluids in porous media is very important and serves a wide variety of practical applications in processes such as enhanced oil recovery from underground reservoirs, filtration of polymer solutions and soil remediation through the removal of liquid pollutants. These fluids occur in diverse natural and synthetic forms and can be regarded as the rule rather than the exception. They show very complex strain and time dependent behavior and may have initial yield‐stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. Non‐Newtonian fluids are generally classified into three main categories: time‐independent whose strain rate solely depends on the instantaneous stress, time‐dependent whose strain rate is a function of both magnitude and duration of the applied stress and viscoelastic which shows partial elastic recovery on removal of the deforming stress and usually demonstrates both time and strain dependency. In this article, the key aspects of these fluids are reviewed with particular emphasis on single‐phase flow through porous media. The four main approaches for describing the flow in porous media are examined and assessed. These are: continuum models, bundle of tubes models, numerical methods and pore‐scale network modeling. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

A multi-domain spectral method for non-Darcian mixed convection flow in a power-law fluid with viscous dissipation

The purpose of this study is to investigate non-Darcian mixed convection flow, heat and mass transfer in a non-Newtonian power-law fluid over a flat plate embedded in porous medium with suction and viscous dissipation and also is to demonstrate the application and utility of a recently developed multi-domain bivariate spectral quasi-linearisation method (MD-BSQLM) in finding the solutions of highly nonlinear differential equations. The flow is subject to, among other source terms, internal heat generation, thermal radiation and partial velocity slip. The coupled system of nonlinear partial differential equations are solved using a MD-BSQLM to find the fluid properties, the skin friction, as well as the heat and mass coefficients. We have presented selected results that give the significance of some system parameters on the fluid properties. This MD-BSQLM has not been used before in the literature to find the nature of the solutions of power-law fluids. Indeed, validation of this numerical method for general fluid flows, heat and mass transfer problems has not yet been done. This study presents the first opportunity to evaluate the accuracy and robustness of the MD-BSQLM in finding solutions of non-Newtonian fluids.     

Insulator-based dielectrophoretic focusing and trapping of particles in non-Newtonian fluids

Insulator-based dielectrophoretic (iDEP) microdevices have been limited to work with Newtonian fluids. We report an experimental study of the fluid rheological effects on iDEP focusing and trapping of polystyrene particles in polyethylene oxide, xanthan gum, and polyacrylamide solutions through a constricted microchannel. Particle focusing and trapping in the mildly viscoelastic polyethylene oxide solution are slightly weaker than in the Newtonian buffer. They are, however, significantly improved in the strongly viscoelastic and shear thinning polyacrylamide solution. These observed particle focusing behaviors exhibit a similar trend with respect to electric field, consistent with a revised theoretical analysis for iDEP focusing in non-Newtonian fluids. No apparent focusing of particles is achieved in the xanthan gum solution, though the iDEP trapping can take place under a much larger electric field than the other fluids. This is attributed to the strong shear thinning-induced influences on both the electroosmotic flow and electrokinetic/dielectrophoretic motions.