Dependence Of Effective Viscosity Research Articles

Impacts of entropy generation in radiative peristaltic flow of variable viscosity nanomaterial

Current analysis highlights the aspects of different nanoparticles in peristalsis with entropy generation. Mathematical equations of considered problem are modelled via conservation laws for mass, momentum and energy. Such equations contain variable viscosity, nonlinear thermal radiation, viscous dissipation, heat generation/absorption and mixed convection aspects. Boundary conditions comprise the second order velocity and first order thermal slip effects. Entropy expression is obtained by utilization thermodynamics. Simplified and dimensionless forms of the considered conservative laws are obtained through lubrication technique. Resulting system of equations subject to the considered boundary conditions is solved numerically via built-in shooting procedure in Mathematica. Such numerical procedure is very suitable to obtain numerical results directly and fastly in the form of graphs. Further all the considered flow quantities are discussed graphically for the significant parameters of interest in detail. Both velocity and temperature are decreasing against large volume fraction parameter. Increasing temperature dependent viscosity effects decrease the entropy and enhance the Bejan number.

Computational Analysis of the Dynamics of Generalized-Viscoelastic-Fluid-Based Nanofluids Subject to Exothermic-Reaction in Shear-Flow

A novel problem that describes laminar simple shear-flow of generalized-viscoelastic-fluid-based nanofluids (GVFBN) containing spherical shaped nano-particles under non-isothermal conditions but with isothermal walltemperature boundary-conditions is investigated. The GVFBN model is an extension of the VFBN to include shear-rate dependent viscosity effects. The Generalized non-isothermal Giesekus constitutive model (which is reducible to generalized Oldroyd-B model) with essential modifications for thermodynamics is used to account for the viscoelastic effects. Spherical shaped nano-particles are homogeneously mixed to the viscoelastic base fluid. To characterize the shear-thinning-viscosity, a viscosity-constitutive-model of the Carreau-type is employed. A temperature-dependent thermal conductivity is also considered. Additionally, empirical models are employed to account for to the nano-particle effects on the thermal conductivity. We use an efficient, semi-implicit, numerical scheme, based on finite difference methods (FDM), to obtain the numerical solutions of the model equations. The numerical scheme is computationally implemented in MATLAB. Results are graphically presented in both a qualitative and quantitative sense with regards to the various embedded parameters. Specifically, the thermodynamic and fluid-dynamical impacts of variations in the volume fraction of nano-particles are explored. In summary, we notice enhanced thermal conductivity and hence also increased temperature with increasing nano-particle volume fraction. The GVFBN model accounts for all four nanofluid types, Generalized-Newtonian-fluid-based nanofluids (GNFBN), Newtonian-fluid-based nanofluids (NFBN), Generalized-viscoelastic-fluid-based nanofluids (GNFBN), and viscoelastic-fluid-based nanofluids (VFBN). The comparative thermal runaway susceptibility of the four nanofluid types is presented and we demonstrate that the order of susceptibility from the most to the least susceptible is GNFBN, NFBN, GVFBN, VFBN.

Nonlinear thermal radiation and temperature dependent viscosity effects on MHD heat and mass transfer in a thin liquid film over a stretching surface

This paper describes nonlinear thermal radiation effects on MHD heat and mass transfer in a thin liquid film over a permeable unsteady stretching surface taking temperature-dependent fluid viscosity with convective boundary condition. For the non-linearity of the momentum, energy and mass diffusion equations, the problem is solved numerically. At first, Similarity transformations is used to the governing equations to reduce the equations into a set of ordinary differential equations. Then the resulting nonlinear ordinary differential equations are solved using Runge-Kutta-Felberg method with shooting technique. Different physical parameters effects on heat and mass transfer in a thin liquid film are presented graphically. It is found that increase in the unsteadiness parameter leads to increase in the velocity distribution, temperature and concentration gradient. Further, increase in the value of magnetic parameter results in a decrease in the velocity profile and increase in the temperature and concentration gradient. For enhancement of thermal radiation decreases the temperature gradient of the thin film flow. Also, for increase in viscosity variation parameter is to decrease velocity distribution but reverse effects shown in case of temperature and concentration gradient.

Nonlinear thermal radiation and temperature dependent viscosity effects on MHD heat and mass transfer in a thin liquid film over a stretching surface

Nonlinear thermal radiation and temperature dependent viscosity effects on MHD heat and mass transfer in a thin liquid film over a stretching surface

Turbulence modulation by finite-size spherical particles in Newtonian and viscoelastic fluids

We experimentally investigate the influence of finite-size spherical particles in turbulent flows of a Newtonian and a drag reducing viscoelastic fluid at varying particle volume fractions and fixed Reynolds number. Experiments are performed in a square duct at a Reynolds number Re2H of nearly 1.1 × 104, Weissenberg number Wi for single phase flow is between 1 and 2 and results in a drag-reduction of 43% compared to a Newtonian flow (at the same Re2H). Particles are almost neutrally-buoyant hydrogel spheres having a density ratio of 1.0035 ± 0.0003 and a duct height 2H to particle diameter dp ratio of around 10. We measure flow statistics for four different volume fractions ϕ namely 5, 10, 15 and 20% by using refractive-index-matched Particle Image Velocimetry (PIV). For both Newtonian Fluid (NF) and Visceolastic Fluid (VEF), the drag monotonically increases with ϕ. For NF, the magnitude of drag increase due to particle addition can be reasonably estimated using a concentration dependent effective viscosity for volume fractions below 10%. The drag increase is, however, underestimated at higher ϕ. For VEF, the absolute value of drag is lower than NF but, its rate of increase with ϕ is higher. Similar to particles in a NF, particles in VEF tend to migrate towards the center of the duct and form a layer of high concentration at the wall. Interestingly, relatively higher migration towards the center and lower migration towards the walls is observed for VEF. The primary Reynolds shear stress reduces with increasing ϕ throughout the duct height for both types of fluid.

Properties of Film Materials Based on Composite Nanofibers from Aliphatic Copolyamide and Carbon Nanotubes for Tissue Engineering

The investigation of the dependence of effective viscosity on shear rate for a water-alcohol solution of an aliphatic copolyamide and its mixtures with single-wall carbon nanotubes reveals that additives of the nanoparticles in the amount of 0.5 wt % lead to a substantial reduction in the effective viscosity as the shear rate rises. The measurement of the surface tension and electrical conductivity of the solutions bearing 0.1–2.0 wt % of the nanotubes allows one to choose an optimal mode for electrospinning of the composite nanofibers based on the aliphatic copolyamide. The introduction of carbon nanofibers reduces the specific resistance of the material to 8.9 × 109 Ω m, but increases the elastic modulus. The lack of cytotoxicity of the resulting materials and the high proliferative activity of human dermal fibroblasts on their surface allow one to use the film materials based on the composite nanofibers in cell technologies and as matrices for tissue engineering.

Strong temperature dependent viscosity effects on bio-magnetic fluid flow under the action of localized magnetic field and viscous dissipation

In this study consideration has been given to the two-dimensional, unsteady, laminar flow of an electrically conducting bio-fluid (blood) in a rectangular channel. In this model both magnetization and electrical conductivity of blood are taken into account. The viscosity of the fluid is also assumed to be a strong function of temperature. The coupled, nonlinear system of equations are transformed into the stream function-vorticity-temperature formulation. These equations along with the suitable boundary conditions are solved iteratively by using the upwind scheme along with successive over relaxation method. The numerical results obtained here are illustrated in terms of streamlines, vorticity function, velocity component and temperature function contours. The results show that the flow is effected to a great extent owing to the presence of the magnetic source. It is observed that the temperature values increases due to an increase in magnetic intensity for all the contours plotted in this study. It is also noticed that variable viscosity greatly influenced the flow field and generates a lot of vortices within the vicinity of the walls.

New asymptotic heat transfer model in thin liquid films

In this article, we present a model of heat transfer occurring through a li\-quid film flowing down a vertical wall. This new model is formally derived using the method of asymptotic expansions by introducing appropriately chosen dimensionless variables. In our study the small parameter, known as the film parameter, is chosen as the ratio of the flow depth to the characteristic wavelength. A new Nusselt solution should be explained, taking into account the hydrodynamic free surface variations and the contributions of the higher order terms coming from temperature variation effects. Comparisons are made with numerical solutions of the full Fourier equations in a steady state frame. The flow and heat transfer are coupled through Marangoni and temperature dependent viscosity effects. Even if these effects have been considered separately before, here a fully coupled model is proposed. Another novelty consists in the asymptotic approach in contrast to the weighted residual approach which have been formerly applied to these problems.

On the Linear Stability of Thermal Convection with Three Different Imposed Shear Flows

The problem of convection in a fluid with temperature dependent viscosity and imposed shear flow, driven by pressure gradients and by a top moving wall, is studied for the case of poorly thermal conducting horizontal walls. Analytical expressions accounting for temperature dependent viscosity effects were obtained for the critical Rayleigh number and frequency of oscillation under a shallow water approximation for Poiseuille, Couette and returning primary flows. The results of this investi- gation contirbute and extend previous findings showing that the onset of convection can be achieved at smaller critical Rayleigh and wavenumbers. The results include approximations of weak and strong shear flows along with conditions for rigid-rigid and rigid-free boundaries. It was found that the imposed shear flow does not influence the critical wavenumber but it does increases the critical Rayleigh number. In this case convection sets in as oscillatory.

Thickness dependent effective viscosity of a polymer solution near an interface probed by a quartz crystal microbalance with dissipation method.

The solution viscosity near an interface, which affects the solution behavior and the molecular dynamics in the solution, differs from the bulk. This paper measured the effective viscosity of a dilute poly (ethylene glycol) (PEG) solution adjacent to a Au electrode using the quartz crystal microbalance with dissipation (QCM-D) technique. We evidenced that the effect of an adsorbed PEG layer can be ignored, and calculated the zero shear rate effective viscosity to remove attenuation of high shear frequency oscillations. By increasing the overtone n from 3 to 13, the thickness of the sensed polymer solution decreased from ~70 to 30 nm. The zero shear rate effective viscosity of the polymer solution and longest relaxation time of PEG chains within it decrease with increasing solution thickness. The change trends are independent of the relation between the apparent viscosity and shear frequency and the values of the involved parameter, suggesting that the polymer solution and polymer chains closer to a solid substrate have a greater effective viscosity and slower relaxation mode, respectively. This method can study the effect of an interface presence on behavior and phenomena relating to the effective viscosity of polymer solutions, including the dynamics of discrete polymer chains.

Viscosity scaling in concentrated dispersions and its impact on colloidal aggregation.

Gaining fundamental knowledge about diffusion in crowded environments is of great relevance in a variety of research fields, including reaction engineering, biology, pharmacy and colloid science. In this work, we determine the effective viscosity experienced by a spherical tracer particle immersed in a concentrated colloidal dispersion by means of Brownian dynamics simulations. We characterize how the effective viscosity increases from the solvent viscosity for small tracer particles to the macroscopic viscosity of the dispersion when large tracer particles are employed. Our results show that the crossover between these two regimes occurs at a tracer particle size comparable to the host particle size. In addition, it is found that data points obtained in various host dispersions collapse on one master curve when the normalized effective viscosity is plotted as a function of the ratio between the tracer particle size and the mean host particle size. In particular, this master curve was obtained by varying the volume fraction, the average size and the polydispersity of the host particle distribution. Finally, we extend these results to determine the size dependent effective viscosity experienced by a fractal cluster in a concentrated colloidal system undergoing aggregation. We include this scaling of the effective viscosity in classical aggregation kernels, and we quantify its impact on the kinetics of aggregate growth as well as on the shape of the aggregate distribution by means of population balance equation calculations.

Length-scale dependent relaxation shear modulus and viscoelastic hydrodynamic interactions in polymer liquids

A quantitative theory of hydrodynamic interactions in unentangled polymer melts and concentrated solutions is presented. The study is focussed on the pre-Rouse transient time regimes (t < τ(R), the Rouse relaxation time) where the hydrodynamic response is governed mainly by the viscoelastic effects. It is shown that transient viscoelastic hydrodynamic interactions are not suppressed (screened) at large distances and are virtually independent of polymer molecular mass. A number of transient regimes of unusual and qualitatively different behavior of isotropic and anisotropic hydrodynamic response functions are elucidated. The regimes are characterized in terms of two main length-scale dependent characteristic times: momentum spreading time τ(i) ∝ r(4∕3) and viscoelastic time τ(∗) ∝ r(4). It is shown that for t > τ(i) the viscoelastic hydrodynamic interactions can be described in terms of the time or length scale dependent effective viscosity which, for t < τ(R) and/or for r < R(coil), turns out to be much lower than the macroscopic "polymer" viscosity η(m). The theory also involves a quantitative analysis of the length-scale dependent stress relaxation in polymer melts. The general predictions for hydrodynamic interactions in thermostated systems with Langevin friction are obtained as well.

Solitary-waves in geophysical two-phase viscous media: A semi-analytical solution

To better understand the process of geofluid (melt, water) migration in the earth’s mantle, we have investigated the mathematical formulation of the two-phase theory for compaction, which implicitly accounts for a porosity dependent effective (bulk) viscosity of the two-phase mixture. Following previous studies, we have searched for solitary waves solution of permanent shape. Our results confirm analytically the existence of such solitary waves. To highlight their characteristics, a comparison of the properties of these waves with the waves produced in a two-phase mixture with constant effective (bulk) viscosity is presented. In particular, the solitary waves that are observed in porosity dependent effective viscosity simulations are steeper and their speed decreases as a function of one over the background porosity. These characteristics may have important implications for the interpretation of the geochemistry and morphology of melt-related processes. Additionally, our analytical solutions can be used for numerical benchmarking of two-phase codes.

Entrance and Temperature Dependent Viscosity Effects on Laminar Forced Convection in Straight Ducts With Uniform Wall Heat Flux

Abstract In this paper a parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously, i.e., hydro-dynamically and thermally, developing laminar flows of liquids in straight ducts of constant cross sections. Uniform heat flux boundary conditions are imposed on the heated walls of the ducts. Different cross-sectional geometries are considered, corresponding to both axisymmetric (circular and concentric annular) and three-dimensional (rectangular and trapezoidal) ducts. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor are presented for different values of the Pearson and Prandtl numbers. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions. Correlations are also provided for the local Nusselt number and the apparent Fanning friction factor in simultaneously developing flows in ducts of different cross sections.

Direct numerical simulation of modulation of isotropic turbulence by poly‐dispersed particles

SUMMARYA direct numerical simulation technique based on two‐way coupling is presented to study a particle‐laden, decaying isotropic turbulent flow. Physical characteristics of turbulence modulation because of the mono‐dispersed (i.e., particles with single Stokes number) and poly‐dispersed particles (i.e., particles with more than one Stokes number) were investigated. A scale dependent effective viscosity that summarizes the aspects of the interaction between the velocity field and particles is defined in the study. Particles of Stokes number (St) 3.2,6.4 and 12.8 were used in performing the simulations. Poly‐dispersed particles were acquired by mixing particles of two different Stokes numbers at a time. As a whole, decay of turbulence because of the poly‐dispersed particles is observed to be larger than that of the decay of turbulence because of the mono‐dispersed particles. Simulations of poly‐dispersed particle indicate nonlinear characteristics in the modification of the temporal evolution of turbulence energy and dissipation. The scale dependent effective viscosity, which correlates with the energy spectrum plot, indicates that the decay of turbulence is mostly observed at the intermediate scales of turbulence. The effective viscosity for the simulations of the poly‐dispersed particles was calculated to be higher than that of the simulations of the mono‐dispersed particles. Copyright © 2011 John Wiley &amp; Sons, Ltd.

On the nonlinear rheology of magnetic fluids

The influence of chain aggregates on the rheological properties of magnetic fluids is studied theoretically. The dependence of effective viscosity on the shear rate of stationary flow is investigated. The character and the relaxation time of the viscosity of fluids after the jumpwise changes in the shear rate are determined.

Rheology of the deep upper mantle and its implications for the preservation of the continental roots: A review

The longevity of deep continental roots depends critically on the rheological properties of upper mantle minerals under deep upper mantle conditions. Geodynamic studies suggest that the rheological contrast between the deep continental and oceanic upper mantle is a key factor that controls the longevity of the continental roots. Current understanding of rheological properties of deep upper mantle is reviewed to examine how a large enough rheological contrast between the continental and oceanic upper mantle develops that leads to the longevity of the deep continental roots. Based on the microstructures of naturally deformed deep continental rocks as well as on the observations of seismic anisotropy, it is concluded that power-law dislocation creep dominates in most of the deep upper mantle. Deformation by power-law creep is sensitive to water content and therefore the removal of water by partial melting to form depleted continental roots is a likely mechanism to establish a large rheological contrast. The results of experimental studies on the influence of temperature, pressure and water content on plastic flow by power-law dislocation creep are reviewed. The degree of rheological contrast depends critically on the dependence of effective viscosity on water content under “wet” (water-rich) conditions but it is also sensitive to the effective viscosity under “dry” (water-free) conditions that depends critically on the influence of pressure on deformation. Based on the analysis of thermodynamics of defects and high-temperature creep, it is shown that a robust estimate of the influence of water and pressure can be made only by the combination of low-pressure (< 0.5 GPa) and high-pressure (> 5 GPa) studies. A wide range of flow laws has been reported, leading to nearly 10 orders of magnitude differences in estimated viscosities under the deep upper mantle conditions. However, based on the examination of several criteria, it is concluded that relatively robust experimental data are now available for power-law dislocation creep in olivine both under “dry” (water-free) and “wet” (water-saturated) conditions. These data show that the influence of water is large (a change in viscosity up to ∼ 4 orders of magnitude for a constant stress) at the depth of ∼ 200–400 km. I conclude that the conditions for survival of a deep root for a few billions of years can be satisfied when “dry” olivine rheology with a relatively large activation volume (> (10–15) × 10 − 6 m 3/mol)) is used and the substantial water removal occurs to these depths. High degree of water removal requires a large degree of melting in the deep upper mantle that could have occurred in the Archean where geotherm was likely hotter than the current one by ∼ 200 K presumably with the help of water.

Temperature dependent viscosity effects on laminar forced convection in the entrance region of straight ducts

A parametric investigation is carried out on the effects of temperature dependent viscosity in simultaneously developing laminar flow of a liquid in straight ducts of arbitrary but constant cross-sections. Viscosity is assumed to vary with temperature according to an exponential relation, while the other fluid properties are held constant. Different cross-sectional geometries are considered, corresponding both to three-dimensional (rectangular, trapezoidal and hexagonal) and to axisymmetric (circular and concentric annular) duct geometries. Uniform wall temperature boundary conditions are imposed on the heated/cooled walls of the ducts. A finite element procedure is employed for the solution of the parabolized momentum and energy equations. Computed axial distributions of the local Nusselt number and of the apparent Fanning friction factor for ducts of the considered cross-sections are presented with reference to both fluid heating and fluid cooling. Numerical results confirm that, in the laminar forced convection in the entrance region of straight ducts, the effects of temperature dependent viscosity cannot be neglected in a wide range of operative conditions.

Combined Convection-Radiation Interaction Along a Vertical Flat Plate in a Porous Medium

An analysis is presented for the convection-radiation interaction heat transfer in boundary-layer flows over a semi-infinite flat plate with temperature dependent effective viscosity embedded in a fluid-saturated porous medium in the presence of a magnetic field. The conservation equations that govern the problem were reduced to a dimensionless form. The system was solved numerically by the Keller-box method. Asymptotic solutions for small and large values of the distance from the leading edge of the plate are presented. The influence of the various parameters entering into the problem on the velocity and heat transfer is studied.

Active control of laminar stability by feedback control strategy

A new active way to control laminar stability through feedback control strategy is presented in this paper. By applying the expansion method, the small perturbation parameter, which is related to uniform boundary heat flux, is well separated out from the problem we studied. As a result, the heat flux independent coefficients, which reflect the temperature dependent viscosity effects, can be obtained. It is shown that this feedback laminar flow control strategy can considerably dominate the development of fluctuations provided that the phase of heating or cooling and the control position are properly chosen.