Values Of Viscosity Ratio Research Articles

Oscillatory one-roll and two-roll solutions in laminar viscoelastic Rayleigh-Bénard convection in a square cavity

Rayleigh-Bénard convection in square closed cavities filled with Oldroyd-B fluid was studied using OpenFOAM-based RheoTool. For the RBC in Newtonian fluids, the transition always occurs from conduction to steady state convection with increasing Rayleigh number (Ra). On the other hand, the viscoelastic fluids may also show the transition from conduction to oscillatory convection. Further increase in Ra may result in a steady state convective solutions. It is further noted that the behavior is similar to Newtonian fluids for larger values of viscosity ratio (B). Considering the abovementioned different flow behavior at different values of the parameters, it is noted that there are five different types of solutions possible for the viscoelastic fluids viz. pure conduction (PC), one roll periodic oscillations (ORPO), one roll steady state (ORSS) convection, two roll periodic oscillations (TRPO), simultaneous one and two roll steady state convection. Therefore, a bifurcation diagram in the parametric space of Ra and B is presented, depicting these five regions corresponding to each type of solution. The boundaries of these regions have been identified by numerical simulation. Note that all these regions exist in the laminar flow regime, and the transition to turbulence is not considered here. Interestingly, at low values of B, as one increases Ra, it is seen that the ORSS region is sandwiched between ORPO and TRPO. The likely reason for this interesting behavior is explained. Moreover, representative solutions in each region in terms of isotherms, streamlines, and vector plots have been included to demonstrate the dynamics of each delineated region.

Axisymmetric Stokes flow of a spherical droplet or slip particle in the presence of a circular disk

This article deals with the axisymmetric flow of a Newtonian fluid droplet moving along the axis of a thin circular disk under the conditions of a low Reynolds number in the quasi-steady limit. The system is immersed in a second Newtonian fluid. With the same geometry, the motion of a slip spherical particle is treated also. Basic solutions are constructed in cylindrical and spherical coordinates according to the appropriate flow region. A combined analytic-numerical solution procedure in conjunction with a dual integral equation is used. Numerical results show that the normalized drag force coefficient acting on the droplet/ slip particle is obtained with good convergence for various values of viscosity ratio, slip parameter, and clearance parameter. The findings demonstrate that the results of the drag coefficient are in good agreement with the limiting cases available in the literature.

Effects of viscosification, ultra-low interfacial tension, and emulsification on heavy oil recovery by combination flooding

Heavy oil recovery mechanisms by combination flooding have well recognized as viscosification, ultra-low interface tension (IFT) and emulsification, however, the role or relative contribution of each mechanism to oil recovery is still not clear (especially under different water-oil viscosity ratios). To address this, two emulsified and one ultra-low IFT mixtures were collected and systematically compared in their IFT, emulsion stability and oil recovery performances. The results show that, as excepted, the used formulas have different IFT and emulsion stability properties: for the ultra-low IFT one, IFT indeed reaches an ultra-low level, but the stability of its emulsion is very poor. The emulsified formulas (with non-ultra-low, ultra-low IFT) are more powerful in stabilizing heavy oil emulsion than the former. Significant discrepancy in combination flooding under different viscosity ratios in homogeneous and heterogeneous models reveals that: when the viscosity ratio is lower than 0.2, the mobility control by the combination mixture is insufficient, and the contribution of emulsification is relatively high (6.4–24.0 %), the dominant oil recovery mechanism is the synergy of those three mechanisms. As the viscosity ratio gets higher than 0.2, the mobility control is strong, resultingly, the contribution of emulsification is reduced, making it less important. In addition, although the presence of heterogeneity does not change the critical value of viscosity ratio, it has a significant impact on the detailed contribution of the dominant mechanisms.

Proposing an Adaptive Neuro-Fuzzy System-Based Swarm Concept Method for Predicting the Physical Properties of Nanofluids

This paper employs dispersed nanoparticles (NPs) to build an adaptive neuro-fuzzy system (ANFIS) for predicting their thermal conductivity (TC) and viscosity according to the most important input data including concentration, size, the thickness of the interfacial layer, and intensive properties of NPs. In this regard, we gather an extensive and comprehensive data set from different sources. Here, the ANFIS model factors are optimized by using the particle swarm optimization (PSO) technique. Afterward, the obtained results are compared with previously published models which did a better job in predicting target values. In the following, to investigate the validity of our proposed model, statistical and graphical techniques are employed and it was proved that this model is efficient to evaluate the output values. Amounts of results obtained from the PSO-ANFIS model evaluation are 0.988 and 0.985 for the R2 and 0.0156 and 0.0876 for root mean squared error (RMSE) of TC ratio and viscosity ratio values, respectively, letting out a valid forecast of targets. Finally, by performing various statistical analyzes, it can be said that this model shows a high ability to predict target values and can be considered a good alternative to previous models.

Mathematical Modeling of Oil Reservoir Waterflooding Using Fixed Streamtube at Various Values of Viscosity Ratio

Mathematical Modeling of Oil Reservoir Waterflooding Using Fixed Streamtube at Various Values of Viscosity Ratio

Effects of coolant and wall temperature variations on impingement jet array thermal performance

Provided are numerically predicted flow structural data for a flow passage with an impingement jet array, as well as numerically predicted surface Nusselt number data for the target surface of the passage, which are obtained using a SST turbulence closure model. The closure model and numerical prediction approach are validated by oil film flow visualization experimental results. Spatially averaged Nusselt number data are well represented by the impingement cooling temperature ratio correlation equation of Goodro et al., which indicates that associated Nusselt number ratios decrease as the Tw/To,in temperature ratio increases to values as high as 2.0. Local, spatially resolved Nusselt numbers and spanwise-averaged surface Nusselt number distributions for TR = 1.1 are consistently higher than TR = 2.0 values, when compared at particular surface locations. Cross flow influences are evidenced by spanwise-averaged, periodically varying Nusselt number values which generally increase with streamwise development. When surface oil flow visualization results are considered with numerically predicted turbulent viscosity ratio results, flow features include locally increased viscosity ratio values near impingement jet stagnation regions, horseshoe vortex signatures, and more focused and more narrow viscosity ratio distributions with streamwise development.

Generation of Newtonian and non-Newtonian droplets in silicone oil flow by means of a micro cross-junction

In this paper the generation of non-Newtonian and Newtonian droplets in a continuous silicone oil flow through a micro cross-junction has been studied experimentally by focusing the attention on the behavior of the device at values of continuous Capillary number (Cac) larger than 0.01. Different liquids have been used as dispersed phase: (i) pure water; (ii) water with Tween 20; (iii) Xanthan gum aqueous solutions. A wide range of volumetric flow rates of the continuous and dispersed phase have been imposed at the inlets of the micro cross-junction with the aim to correlate the main droplet regimes (squeezing, dripping and jetting) to the continuous and dispersed Capillary number (Cac, Cad) and to the volumetric flow rate ratio (α). The role of the viscosity ratio of the immiscible liquids (λ) on the droplet regime is discussed. The experimental results confirm that the transition between squeezing and dripping depends mainly on the Capillary number associated to the continuous phase and not on the viscosity ratio. On the contrary, larger viscosity ratio values tend to reduce the Capillary number in correspondence of which the transition between dripping and jetting is observed. In addition, it has been observed that an increase in the viscosity of the dispersed phase tends to reduce the range of the operative conditions in correspondence of which monodispersed emulsions can be generated.

Effect of homogeneous and heterogeneous reactions on the solute dispersion in composite porous medium

The Taylor dispersion of a solute for composite porous medium between two parallel plates with first-order chemical reaction is studied analytically. The fluids in both the regions are incompressible and the transport properties are assumed to be constant. The results are shown graphically for various values of viscosity ratio, pressure gradient and porous parameter on the effective dispersion coefficient and volumetric flow rate. It is found that for both homogeneous and heterogeneous chemical reactions, the effective dispersion coefficient decreases as porous parameter increases. The validity of the results obtained for composite porous media is verified by comparison with the available porous medium results for one fluid model and good agreement is found. Also two fluid model in the absence of porous matrix is compared with the available one fluid model results and the values tally very well.Keywords: Taylor dispersion, immiscible fluids, horizontal channel, porous medium, chemical reaction.

An experimental study on rheological behavior of ethylene glycol based nanofluid: Proposing a new correlation as a function of silica concentration and temperature

In this study, SiO2/EG nanofluids viscosity dependence on temperature and concentration was examined. The experiments were performed in the silica volume fraction range of 0.1–3.0% under the temperatures ranging from 30°C to 50°C. The experimental findings revealed that all nanofluid samples were Newtonian at all temperatures considered. The measurements also showed that the dynamic viscosity rises with growing the nanoparticles concentration and diminishes with rising temperature. The values of viscosity ratio indicated that with increasing the solid volume fraction from 0.1 to 3%, the dynamic viscosity increases up to 116%. Finally, using experimental data, in order to predict the dynamic viscosity of silica/ethylene glycol nanofluids, a new correlation has been suggested.

On the effect of mucus rheology on the muco-ciliary transport

A two dimensional numerical model is used to study the muco-ciliary transport process in human respiratory tract. Here, hybrid finite difference-lattice Boltzmann method is used to model the flow physics of the transport of mucus and periciliary liquid (PCL) layer in the airway surface liquid. The immersed boundary method is also used to implement the propulsive effect of the cilia and also the effects of the interface between the mucus and PCL layers. The main contribution of this study is on elucidating the role of the viscoelastic behavior of mucus on the muco-ciliary transport and for this purpose an Oldroyd-B model is used as the constitutive equation of mucus for the first time. Results show that the viscosity and viscosity ratio of mucus have an enormous effect on the muco-ciliary transport process. It is also seen that the mucus velocity is affected by mucus relaxation time when its value is less than 0.002 s. Results also indicate that the variation of these properties on the mucus velocity at lower values of viscosity ratio is more significant.

Analytical and Level Set Method-Based Numerical Study for Two-Phase Stratified Flow in a Pipe

A nondimensional analytical study for fully developed and three-dimensional numerical study of developing viscosity stratified flow is presented, at various values of viscosity ratio η, inlet area fraction of the less viscous fluid α 1,in , and Reynolds number. With increasing α 1,in , a change in the trend of axial variation in interface–from inlet to the fully developed region–is found at α 1,in = α 1,in,c . With increasing η, development length is found to asymptotically decrease for α 1,in = 0.2 and increase for α 1,in = 0.5 and 0.8. A physical model for flow development is also presented for single- and two-fluid flow. A favorable operating condition to reduce the cost of transportation of more viscous fluids by pipe is proposed.

Drop deformation in two-roll mills considering wall effects

Experimental, theoretical and numerical results of dynamics of drop deformation in strong flows generated by a co-rotating two-roll mill and considering the influence of near rigid walls are presented. The drop dynamics is altered, with respect to a drop free of wall effects, by the proximity of the rigid boundaries as well as caused by a non-linear and non-uniform flow due to gradients of flow-type parameter and shear rate. Simulations were carried out using the Boundary Element Method (BEM). Since the inclusion of the whole boundaries (drop and rollers surfaces) is not an easy and trivial task, bi-dimensional numerical simulations was performed as a first approach. The experimental and numerical results were obtained for a flow type of α = 0.03 and two values of viscosity ratio λ = 0.012 and 16. In general, numerical results for the stationary deformation parameters, up to intermediate confinements, are in agreement with the experiments, with and without wall effects. Since the case of drops with a high viscosity ratio did not match existing theoretical models, the wall-effect theory of Shapira and Haber was modified, considering Cox's second-order theory as the converging theory without wall effects. From low to intermediate confinements, the new Cox-Shapira-Haber model fitted the observed experimental deformations.

Role of Viscosity Ratio in Liquid-Liquid Jets under Radial Electric Field

The effect of viscosity ratio (λ, defined as viscosity of surrounding medium/viscosity of fluid jet) on st ability of axisymmetric (m=0) and asymmetric (m=1) modes of perturbation on a liquid-liquid jet in presence of radial electr ic field (E 0 ), is studied using linear stability analysis. The viscos ity ratio is shown to have a damping effect on both the modes of perturba tion. However the effect was found more pronounced for the m=1 mode as compared to m=1 mode. Investigating the effect of b oth E 0 and λ simultaneously, an operating diagram is generated, which clearly shows the regions of dominance of the two modes for a range of electric field and viscosity ratio values.

The modified constrained volume model predictions in shearing flow at nonunity viscosity ratio values

In this paper, the modified constrained volume model, which describes the evolution of anisotropy of immiscible polymer blends, composed of Newtonian components, was examined during shearing motion (steady and oscillatory) at various viscosity ratio values. We found that the linear correction to the rate of deformation tensor causes the droplet to change its volume at viscosity ratio values lower than unity, and to cause premature tumbling at viscosity ratio values larger than unity, in a case where retraction, breakup, and coalescence modules of the model were turned off. The use of Eshelby tensor, together with a closure to relate anisotropy to the Eshelby concentration tensor, mostly solved the problem. The model’s predictions are then shown at various capillary number values and at various viscosity ratio values. Comparison of model predictions to single droplet data at nonunity viscosity ratio value showed good agreement. Finally, model predictions of first normal stress difference during startup of steady shear are compared to experimental rheological results for immiscible polymer blends that are available in literature. Good predictions can be achieved by the introduction of a new switch function that controls the retraction and breakup modules. The model’s predictions at large amplitude oscillatory shear were examined. It was found that linear corrections to the velocity gradient tensor can be used for strains up to 100 %. For larger strain values, the Eshelby concentration tensor must be used.

Effects of Homogeneous and Heterogeneous Reactions on the Dispersion of a Solute for Immiscible Viscous Fluids between Two Plates

The paper presents an analytical solution for the dispersion of a solute of two immiscible viscous fluids in the presence of an irreversible first-order chemical reaction. The effects of both homogeneous and heterogeneous reactions on the dispersion are studied. The results are presented graphically and in tabular form for various values of viscosity ratio and pressure gradients on the volumetric flow rate and effective Taylor dispersion coefficient. It is found that for homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as reaction rate parameter increases. The validity of the results obtained from an analytical method for two fluid models is verified by comparison with the available one fluid model results, and good agreement is found.

Motion of a power-law long drop in a capillary tube filled by a Newtonian fluid

The inertialess motion of two immiscible liquids in a capillary tube is theoretically and numerically analyzed for the case where a non-Newtonian power-law long drop flows into a pressure-driven capillary tube filled by a Newtonian fluid. We use an elliptic mesh generation technique, coupled with the Galerkin Finite Element Method, to compute the velocity field and determine the position and shape of the interface. The main focus of the present work is to investigate the fraction of mass attached to the wall and the flow regimes the problem exhibits as functions of the capillary number (Ca), the viscosity ratio of the two fluids (Nη) and the power-law index (n). The numerical results have shown that for a fixed viscosity ratio and capillary number the fraction of mass remaining in the tube is an increasing function of n. Within the range of dimensionless numbers investigated, we have found that the shape of the interface is strongly influenced by n when Ca is large, but does not change significantly for low values of the capillary number. We have constructed maps of streamlines in the Cartesian space defined by n and Ca for some fixed viscosity ratios in order to capture bypass and recirculating flow regimes, as sketched by Taylor (1961). These regimes can be associated to instabilities of the flow. Displacing fluids with lower power-law index tend to induce bypass flow regimes, especially for high Ca. We found that, not only the Newtonian–Newtonian displacement case, but also the viscosity-thinning–Newtonian displacement has a critical value of viscosity ratio below which it is impossible to have a bypass flow regime. The same does not happen in the case of viscosity-thickening–Newtonian displacement, where every level of viscosity ratio admits bypass and recirculating flow regimes.

Mass and heat transfer from or to a single sphere in simple extensional creeping flow

AbstractThe first detailed numerical investigation on the mass and heat transfer both outside and inside a solid or liquid sphere immersed in a simple extensional flow for a larger range of Peclet numbers (1–100,000) is presented. By making use of the known Stokes velocity field at small Reynolds numbers, a finite difference method with the control volume formulation is adopted to solve the convection‐diffusion transport equation. Simulation results show that the transport rate, which is represented by Sherwood number, is significantly affected by Peclet number and viscosity ratio. The flow direction, no matter a uniaxial extensional flow or a biaxial extensional flow, has no effect on the total transport rate but affects the concentration distribution a lot. Some comparisons between present simulations and previous studies are made to validate each other and confirm the reliability and applicable scopes of reported correlations. A few new correlations are put forward to predict the transfer rate at finite Peclet numbers for various values of viscosity ratios. © 2011 American Institute of Chemical Engineers AIChE J, 58: 3214–3223, 2012

Dispersion in composite porous medium with homogeneous and heterogeneous chemical reactions

The effect of homogeneous and heterogeneous reactions on the dispersion of a solute in a composite porous medium between two parallel plates is studied. The solution approach suggested by Taylor [2] is generalized for the present model. The Brinkman model is used to define the flow through the porous medium. The fluids in both the regions of the parallel-plate channel are incompressible and transport properties are assumed to be constant. The closed-form solutions are obtained in both the regions of the channel. The results are tabulated for various values of viscosity ratio, pressure gradient, and porous parameter on the volumetric flow rate and the effective Taylor dispersion coefficient. It is found that for a homogeneous chemical reaction, the effective Taylor dispersion coefficient decreases as the reaction rate parameter and porous parameter increase. The validity of the results obtained for a composite porous medium is compared with the available porous medium results for a one-fluid model and the values tallied for the small values of porous parameter. Also a two-fluid model in the absence of a porous matrix is compared with the available one-fluid model and good agreement is found. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res, 40(7), 608–640, 2011; Published online 26 July 2011 in Wiley Online Library (wileyonlinelibrary.com/journal/htj). DOI 10.1002/htj.20364

Negative wake generation of FENE-CR fluids in uniform and Poiseuille flows past a cylinder

The effect of flow conditions on the “negative wake” generation (longitudinal velocity overshoot behind a cylinder in the viscoelastic fluid flow along the centerline) has been investigated. FENE-CR model that predicts constant shear viscosity and controlled extensional viscosity was considered as a constitutive equation. The discrete elastic viscous split stress-G/streamline upwind Petrov–Galerkin (DEVSS-G/SUPG) formulation was employed and the high-resolution solutions were obtained with an efficient iterative solver based on the incomplete LU(0)-type preconditioner and BiCGSTAB. We found that the “negative wake” generation was more obvious in uniform flow conditions than in Poiseuille flow, which suggests that the experimentally unrevealed “negative wake” generation of Boger fluids could be partially attributed to the geometrical effect of Poiseuille flow. The “negative wake” generation was more discernable at low extensibility and high value of viscosity ratio, which agrees well with the previous studies. In addition, we could observe an undershoot phenomenon in Poisseuille flow condition, which has never been reported.

Viscosity behaviour of particles with non-adsorbing polymers

Abstract A series of well characterised cis -poly(isoprene) (PIP) polymers ( M w =1180, 8000, 28 300, 31 500, 86 000, 115 000 and 130 000) have been added to dispersions of poly(12-hydroxystearic acid) (PHS) coated poly(methylmethacrylate) (PMMA) particles in dodecane. The ratio of particle size to adsorbed layer was also varied. For a given added polymer molecular weight, the polymer concentration in the continuous phase covered the dilute, semi-dilute and concentrated regimes as defined by the critical concentrations c ∗ and c ∗∗ . The viscosity behaviour of latex dispersions with added polymer were similar for all latex/polymer combinations except when polymer M w =1180 was added. In the latter case, the effect of adding polymer reduced both the viscosity and shear thinning behaviour. This supports the contention that the lower molecular weight polymer acts more like a diluent than a depletent. The behaviour of the viscosity ratio (the viscosity of the dispersion relative to that of the medium) as a function of polymer concentration increased with an increase in the polymer concentration until some critical concentration ( c max ) for all polymers except for a polymer molecular weight 1180 Daltons. The addition of the polymer M w =8000 gave the highest viscosity ratio values in the polymer concentration range studied. It was found that the viscosity of all latex/polymer combinations decreased with an increase in temperature. The results suggest that the viscosity behaviour cannot be explained on the basis of a simple steric–elastic model and require a modified theoretical treatment.