Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

A Generalized Model for the Field Assessment of Drilling Fluid Viscoelasticity

Recent studies highlight the significant role of drilling fluid elasticity in particle suspension and hole cleaning during drilling operations. Traditional methods to quantify fluid elasticity require the use of advanced rheometers not suitable for field application. The main objectives of the study were to develop a generalized model for determining viscoelasticity of a drilling fluid using standard field-testing equipment, investigate the factors influencing drilling fluid viscoelasticity in the field, and provide an understanding of the viscoelasticity concept. Over 80 fluid formulations used in this study included field samples of oil-based drilling fluids as well as laboratory samples formulated with bentonite and other polymers such as partially-hydrolyzed polyacrylamide, synthesized xanthan gum, and polyacrylic acid. Detailed rheological characterizations of these fluids used a funnel viscometer and a rotational viscometer. Elastic properties of the drilling fluids (quantified in terms of the energy required to cause an irreversible deformation in the fluid's structure) were obtained from oscillatory tests conducted using a cone-and-plate type rheometer. Using an empirical approach, a non-iterative model for quantifying elasticity correlated test results from a funnel viscometer and a rotational viscometer. The generalized model was able to predict the elasticity of drilling fluids with a mean absolute error of 5.75%. In addition, the model offers practical versatility by requiring only standard drilling fluid testing equipment to predict viscoelasticity. Experimental results showed that non-aqueous fluid (NAF) viscoelasticity is inversely proportional to the oil-water ratio and the presence of clay greatly debilitates the elasticity of the samples while enhancing their viscosity. The work efforts present a model for estimating drilling fluid elasticity using standard drilling fluid field-testing equipment. Furthermore, a revised approach helps to describe the viscoelastic property of a fluid that involves quantifying the amount of energy required to irreversibly deform a unit volume of viscoelastic fluid. The methodology, combined with the explanation of the viscoelasticity concept, provides a practical tool for optimizing drilling operations based on the viscoelasticity of drilling fluids.

Flow of Non-Newtonian Fluids in a Single-Cavity Microchannel

Having a basic understanding of non-Newtonian fluid flow through porous media, which usually consist of series of expansions and contractions, is of importance for enhanced oil recovery, groundwater remediation, microfluidic particle manipulation, etc. The flow in contraction and/or expansion microchannel is unbounded in the primary direction and has been widely studied before. In contrast, there has been very little work on the understanding of such flow in an expansion–contraction microchannel with a confined cavity. We investigate the flow of five types of non-Newtonian fluids with distinct rheological properties and water through a planar single-cavity microchannel. All fluids are tested in a similarly wide range of flow rates, from which the observed flow regimes and vortex development are summarized in the same dimensionless parameter spaces for a unified understanding of the effects of fluid inertia, shear thinning, and elasticity as well as confinement. Our results indicate that fluid inertia is responsible for developing vortices in the expansion flow, which is trivially affected by the confinement. Fluid shear thinning causes flow separations on the contraction walls, and the interplay between the effects of shear thinning and inertia is dictated by the confinement. Fluid elasticity introduces instability and asymmetry to the contraction flow of polymers with long chains while suppressing the fluid inertia-induced expansion flow vortices. However, the formation and fluctuation of such elasto-inertial fluid vortices exhibit strong digressions from the unconfined flow pattern in a contraction–expansion microchannel of similar dimensions.

Low Reynolds Number Pulsatile Flow of a Viscoelastic Fluid Through a Channel: Effects of Fluid Rheology and Pulsation Parameters

As the first endeavour, we have analyzed the pulsatile flow of Oldroyd-B viscoelastic fluid where the combined effects of fluid elasticity and pulsation parameters on the flow characteristics are numerically studied at a low Reynolds number. Computations are performed using a finite-volume based open-source solver OpenFOAM\textsuperscript{\textregistered} by appending the log-conformation tensor approach to stabilize the numerical solution at high Deborah number. Significant flow velocity enhancement is achieved by increasing the viscoelastic behaviour of the fluid. High-velocity gradient zones and high polymeric stress regions are observed near the channel wall. The magnitude of axial velocity attenuates with increasing pulsation amplitude or pulsation frequency, and the extent of this attenuation is highly dependent on the Deborah number or the retardation ratio. This work finds application in the transport of polymeric solutions, extrusion, and injection moulding of polymer melts in several process industries.

Viscoelastic microfluidics: progress and challanges

The manipulation of cells and particles suspended in viscoelastic fluids in microchannels has drawn increasing attention, in part due to the ability for single-stream three-dimensional focusing in simple channel geometries. Improvement in the understanding of non-Newtonian effects on particle dynamics has led to expanding exploration of focusing and sorting particles and cells using viscoelastic microfluidics. Multiple factors, such as the driving forces arising from fluid elasticity and inertia, the effect of fluid rheology, the physical properties of particles and cells, and channel geometry, actively interact and compete together to govern the intricate migration behavior of particles and cells in microchannels. Here, we review the viscoelastic fluid physics and the hydrodynamic forces in such flows and identify three pairs of competing forces/effects that collectively govern viscoelastic migration. We discuss migration dynamics, focusing positions, numerical simulations, and recent progress in viscoelastic microfluidic applications as well as the remaining challenges. Finally, we hope that an improved understanding of viscoelastic flows in microfluidics can lead to increased sophistication of microfluidic platforms in clinical diagnostics and biomedical research.

Effect of Polymer Fluid Viscoelastic Properties on the Initiation of Transition From Laminar to Turbulent Flow Regime and the Drag Reduction in the Flow Through Horizontal Pipe

This study investigated the flow of viscoelastic fluids through horizontal pipeline mainly focusing on the effect of fluid elasticity on drag reduction and onset of transition to turbulent flow regime. In order to be able to see the sole effect of fluid elasticity (independent from shear viscosity), three non-Newtonian fluids having the same shear viscosity but different viscoelastic properties were tested in the horizontal flow loop. Those fluids were the dilute solutions of partially hydrolysed polyacrylamide (HPAM) and they were prepared by using three polymer grades of HPAM (i.e. 5 × 105, 8 × 106, 20 × 106 g/gmol) in different compositions. Experiments have shown that increasing fluid elasticity resulted in higher drag reduction in pipe flow. Moreover, fluid elasticity affected the onset of turbulent flow and an earlier transition to turbulent flow regime (as compared to water flow) was only observed for the flow of fluid having the highest elastic properties. So, understanding effects of fluid elasticity on flow dynamics might improve the performance of fluids engineered for hole cleaning/cuttings transport in oil and gas well drilling or proppant transport in hydraulic fracturing operations. Also, field efforts to find solutions to problems caused by excessive dynamic pressure losses encountered in drilling horizontal or extended reach wells or in transporting hydrocarbons through pipeline might benefit from the findings of this or further extended research on this subject.

Development of Elastic Drag Coefficient Model and Explicit Terminal Settling Velocity Equation for Particles in Viscoelastic Fluids

Summary Viscoelastic fluids are frequently used as drilling or fracturing fluids to enhance cuttings or proppant transport efficiency. The solid transport performance of these fluids largely depends on the settling behaviors of suspended particles. Different from viscoinelastic fluids, the elastic and viscous characteristics of viscoelastic fluids both affect particle settling behaviors. In this study, to separately quantify the contribution degrees of the shear viscosity and fluid elasticity on the terminal settling velocity, we decompose the total drag force into a viscous drag force and an elastic drag force. Based on the experimental data from the available literature, it is concluded that the elastic drag force is a function of the fluid elasticity, particle diameter, particle terminal settling velocity, and density difference between the fluid and particle. The formula for the elastic drag force is determined on the basis of the force analysis, and a relationship between the elastic drag coefficient and particle Reynolds number (Re) is developed. An explicit equation that directly predicts the terminal settling velocity in viscoelastic fluids is determined by correlating the dimensionless particle diameter and Re. To validate the proposed model, a total of 108 settling experiments in viscoelastic fluids are conducted. The absolute percentage error (APE) between the predicted and measured terminal settling velocities is 15.26%, which indicates that the proposed explicit terminal settling velocity equation can provide satisfactory prediction accuracy of the terminal settling velocity for particles in viscoelastic fluids. Furthermore, an illustrative example is provided to show that the proposed model can be used to calculate the required fluid elasticity to obtain the desired terminal settling velocity when the fluid shear viscosity is fixed. The proposed models are valid with a consistency index range of approximately 0.16 to 1.2 Pa⋅sn, flow behavior index range of approximately 0.282 to 0.579, an Re range of approximately 0.005 to 30, and a fluid relaxation time range of approximately 0.183 to 110 seconds. This study can help operators choose proper drilling/fracturing fluids to enhance the cuttings/proppant transport and maximize drilling/fracturing performance.

Period-Bubbling Transition to Chaos in Thermo-Viscoelastic Fluid Systems

We report a 6D nonlinear dynamical system for thermo-viscoelastic fluid by selecting higher modes of infinite Fourier series of flow quantities. This nonlinear system demonstrates overstable convective motion and some organized structures such as period-bubbling and Arnold tongue-like structures. Studies reveal that the stability of the conduction state does not alter for the new 6D system in comparison with the lowest order 4D system of Khayat [1995] . However, the stabilities of the convective state have some differences. The onset of unsteady convection in the 6D system is delayed for weak elasticity of the fluid. There exists a critical range of fluid elasticity where the 4D system exhibits subcritical Hopf bifurcation while the 6D system shows supercritical Hopf bifurcation, which ensures the increase of the domain of stability. In this range, catastrophic route to chaos occurs in the 4D system, whereas the 6D system exhibits intermittent onset of chaos. Comparing the two-parameter dependent dynamics for the two systems, the chaotic zones enclosed by periodic regions are suppressed in the 6D system, so the flow behaviors become more predictable. Owing to interacting thermal buoyancy and fluid elasticity, both the models exhibit period-bubbling transition to chaos, but the period-bubbling cascade in the 6D model occurs at lower Rayleigh number than the 4D model. The convergence rate of the period-bubbling process slows down compared to usual period-doubling and approaches the square root of the Feigenbaum constant asymptotically.