Power-law Viscosity Research Articles

Finite Element Modelling of Rheological Property of Curing PMMA Bone Cement - Part 2 Effect of Bone Cement Amount

The only grouting material used for anchoring cemented arthroplasties to contiguous bones is PMMA (Polymethyl methacrylate) bone cement. In this study the flow of bone cement through porous cancellous bone is modelled to determine the degree of penetration in total hip replacement using FIDAP simulation software. Power law viscosity model is used with constant consistency index and power law index less than 1 for pseudoplastic behaviour of Simplex P® and Zimmer bone cement. The effect of bone cement amount has been investigated under four different prosthesis insertion velocity 5, 10, 15 and 20 mm/s. The result shows that the depth of penetration increases with decreasing bone cement amount. In the case of Zimmer bone cement more penetration through cancellous bone was observed than Simplex P® bone cement.

Effect of dune sand on the properties of flowing sand-concrete (FSC)

Abstract Sand-concrete is being researched for potential usage in construction in Saharan regions of Algeria, because of shortage in coarse aggregate resources. This research work deals with the effect of dune sand, available in huge quantities in these regions, on the properties of flowing sand-concrete (FSC) prepared with different proportions of dune and river sands. Mini-cone slump test, v-funnel flow-time test and viscosity measurements were used to characterize the behaviour of FSC in fresh state. The 28-day compressive strength was also determined. Test results show that an optimal content of dune sand, which makes satisfied fresh and hardened properties of FSC, is obtained. Moreover, the obtained flow index (constant b) calculated by the help of power-law viscosity model is successfully correlated to the experimental results of v-funnel flow time.

Models of nanoparticles movement, collision, and friction in chemical mechanical polishing (CMP)

Nanoparticles have been widely used in polishing slurry such as chemical mechanical polishing (CMP) process. The movement of nanoparticles in polishing slurry and the interaction between nanoparticles and solid surface are very important to obtain an atomic smooth surface in CMP process. Polishing slurry contains abrasive nanoparticles (with the size range of about 10–100 nm) and chemical reagents. Abrasive nanoparticles and hydrodynamic pressure are considered to cause the polishing effect. Nanoparticles behavior in the slurry with power-law viscosity shows great effect on the wafer surface in polishing process. CMP is now a standard process of integrated circuit manufacturing at nanoscale. Various models can dynamically predict the evolution of surface topography for any time point during CMP. To research, using a combination of individual nanoscale friction measurements for CMP of SiO2, in an analytical model, to sum these effects, and the results scale CMP experiments, can guide the research and validate the model. CMP endpoint measurements, such as those from motor current traces, enable verification of model predictions, relating to friction and wear in CMP and surface topography evolution for different types of CMP processes and patterned chips. In this article, we explore models of the microscopic frictional force based on the surface topography and present both experimental and theoretical studies on the movement of nanoparticles in polishing slurry and collision between nanoparticles, as well as between the particles and solid surfaces in time of process CMP. Experimental results have proved that the nanoparticle size and slurry properties have great effects on the polishing results. The effects of the nanoparticle size and the slurry film thickness are also discussed.

Laminar and turbulent power law fluid flow passing a square cylinder

In this work, a two-dimensional laminar and turbulent Power law fluid flow passing a square cylinder is numerically investigated. In the investigation, a finite volume code based on the SIMPLEC algorithm and non-staggered grid was used. In the discretization of the convective and diffusive terms, the third-order QUICK and the second-order central difference scheme, respectively were used. The turbulent flow was simulated using the model. Extensive numerical results of the drag coefficient, root mean square of the lift coefficient, Strouhal number, stream functions, pressure coefficient, time-averaged velocities and power law viscosity are presented to determine the influence of the Power law index and Reynolds number. Laminar flows discussed in the present work are within the ranges: and covering shear thinning, Newtonian and shear thickening fluids. Turbulent flows within the ranges of Re=13000 and 22000 and were also evaluated numerically and discussed. Key words: Single square cylinder, turbulence modeling, power law fluid, lift and drag coefficients, Strouhal number.

Computational Fluid Dynamics Analysis of Pulsatile Blood Flow Behavior in Modelled Stenosed Vessels with Different Severities

This study focuses on the behavior of blood flow in the stenosed vessels. Blood is modelled as an incompressible non‐Newtonian fluid which is based on the power law viscosity model. A numerical technique based on the finite difference method is developed to simulate the blood flow taking into account the transient periodic behaviour of the blood flow in cardiac cycles. Also, pulsatile blood flow in the stenosed vessel is based on the Womersley model, and fluid flow in the lumen region is governed by the continuity equation and the Navier‐Stokes equations. In this study, the stenosis shape is cosine by using Tu and Devil model. Comparing the results obtained from three stenosed vessels with 30%, 50%, and 75% area severity, we find that higher percent‐area severity of stenosis leads to higher extrapressure jumps and higher blood speeds around the stenosis site. Also, we observe that the size of the stenosis in stenosed vessels does influence the blood flow. A little change on the cross‐sectional value makes vast change on the blood flow rate. This simulation helps the people working in the field of physiological fluid dynamics as well as the medical practitioners.

Effect of Liquid-Solid Lubricant on Mixed Lubrication in Line Contact

This paper presents the performance characteristics of two surfaces in line contact under isothermal mixed lubrication with non-Newtonian liquid–solid lubricant base on Power law viscosity model. The time dependent Reynolds equation, elastic equation and viscosity equation were formulated for compressible fluid. Newton-Raphson method and multigrid technique were implemented to obtain film thickness profiles, friction coefficient and load carrying in the contact region at various roughness amplitudes, applied loads, speeds and the concentration of solid lubricant. The simulation results showed that roughness amplitude has a significant effect on the film pressure, film thickness and surface contact pressure in the contact region. The film thickness decrease but friction coefficient and asperities load rapidly increases when surface roughness amplitude increases or surface speed decreases. When the concentration of solid lubricant increased, friction coefficient and asperities load decrease but traction and film thickness increase.

Phase Behavior and Formulation of Palm Oil Esters o/w Nanoemulsions Stabilized by Hydrocolloid Gums for Cosmeceuticals Application

Palm oil esters (POEs) are wax esters derived from palm oil and cis-9-octadecen-1-ol. The excellent wetting behaviour of the esters without the oily feel make them have great potentials in the manufacture of cosmeceutical and pharmaceutical products. However, little is known about their phase behaviors in ternary systems. The purpose of this investigation was to construct phase diagram of the POEs and mixed surfactants and to consequently select nanoemulsions composition for further studies. The preparation and characterization of oil-in-water nanoemulsions stabilized by hydrocolloid gums were then studied. Two types of nonionic surfactants were selected, namely Tween 80 (T80) and Span 80 (S80). Ternary phase diagram of POEs:Tocotrienol/T80:S80 (80:20)/water system was constructed at 25.0 ± 0.5°C. The emulsification properties of 2 hydrocolloids gum (xanthan gum, carbopol ultrez 20 copolymer) were investigated. Gum dispersions were prepared in water (0.8%) and emulsified with 30% oil using a Polytron homogenizer. The flow curve of the emulsions always exhibited shear thinning behavior and obeys the power law viscosity. The emulsions with carbopol ultrez 20 copolymer was the most stable emulsions which composed of very small oil droplets (50% < 142.43 nm) with a narrow size distribution.

Similarity and Boubaker Polynomials Expansion SchemeBPEScomparative solutions to the heat transfer equation for incompressible non-Newtonian fluids: case of laminar boundary energy equation

In this paper, a new model is proposed for the heat transfer characteristics of power law non- Newtonian fluids. The effects of power law viscosity on temperature field were taken into account by assuming that the temperature field is similar to the velocity field with modified Fourier’s law of heat conduction for power law fluid media. The solutions obtained by using Boubaker Polynomials Expansion Scheme (BPES) technique are compared with those of the recent related similarity method in the literature with good agreement to verify the protocol exactness.

Effect of heat generation/absorption on natural convective boundary-layer flow from a vertical cone embedded in a porous medium filled with a non-Newtonian nanofluid

This work is focused on the study of the natural convection boundary-layer flow over a downward-pointing vertical cone in a porous medium saturated with a non-Newtonian nanofluid in the presence of heat generation or absorption. The transformed boundary layer governing equations are solved numerically. The influences of pertinent parameters such as the heat generation or absorption, the solid volume fraction of nanoparticles and the type of nanofluid on the flow and heat transfer rate in terms of Nusselt number are discussed. Comparisons with previously published work on special cases of the problem are performed and found to be in excellent agreement. The generalized governing equations derived in this work can be applied to different cases of non-Newtonian fluids with different values of the power-law viscosity index. The results of this parametric study are shown graphically and the physical aspects of the problem are highlighted and discussed.

On the Use of Lattice-Boltzmann Model for Simulating Lid-Driven Cavity Flows of Strain-hardening Fluids

The effect of a fluid's strain-hardening behavior is investigated on the flow kinematics inside a two-dimensional square cavity. A special form of the Generalized Newtonian Fluid model (referred to as Pinho model) is used in which the strain-hardening behavior of the fluid is accounted for by incorporating a strain-rate term in the power-law viscosity function. Use will be made of the incompressible Lattice Boltzmann Model (LBM) to numerically solve the governing equations. Converged results could be obtained at Reynolds numbers up to Re = 5000 showing that the strain-hardening behavior has indeed a strong effect on the flow kinematics. The size of the corner vortices is predicted to decrease by an increase in the strain-hardening behavior of the fluid. It is also predicted that the streamline pattern becomes quite symmetric by an increase in the fluid's strain-hardening behavior.

Low-volume-fraction limit for polymer fluids

We study a stationary, purely viscous polymer flow through a porous medium modelled as a periodic array of cells consisted of a fluid part and a solid one. Solid parts of the domain present impermeable obstacles, whose impact on fluid flow may be seen as a slowing factor through averaged quantities such as the permeability function, obtained by the homogenization process. In that way, the influence of the microstructure is implemented in the homogenized equations through a kind of nonlinear Darcy's law. Our goal is to find more explicitly the dependence of the permeability function on the size η of the obstacle in the unit cell and the so-called low-volume-fraction limit. Main difficulties arise from the nonlinear character of the power-law viscosity and the apparent weak convergence of the solutions involved.

Heat transfer in pseudo-plastic non-Newtonian fluids with variable thermal conductivity

This paper endeavors to complete a numerical analysis for heat transfer in pseudo-plastic non-Newtonian fluids aligned with a semi-infinite plate by extending the study in two directions. On one hand, viscous dissipation are included in the energy equation, and on the other hand, unlike most classical works, the effects of power-law viscosity on temperature field are taken into account by assuming that the thermal diffusivity varies as a function of velocity gradient. The solutions are presented numerically by using the similarity transformation and shooting technique. The associated transfer characteristics are discussed in some domains of parameters, including the power-law index n , the generalized Prandtl number N Pr and the Zheng number ZH .

Temporal analysis of power law liquid jets

In this paper we investigate the breakup mechanisms of power law liquid jets. The viscosity of the liquid is represented the Carreau–Yasuda model, and the surface tension of the liquid jet has a variation (gradient) along the jet axial direction. The surface tension gradient may be introduced by the thermal disturbance of the jet surface as it comes of out an orifice. The Carreau–Yasuda fluid has a power law viscosity bounded by two plateaus, the higher plateau at zero strain rate, μ 0, and the lower plateau at the infinite strain rate, μ ∞. The governing equation for the surface profile of the liquid jet is derived in the forms of a partial differential equation (PDE), as well as an ordinary differential equation (ODE). The PDE and ODE are solved for various cases of Carreau–Yasuda fluid to study the effect of fluid properties on jet breakup. The effects of various parameters on the instability behavior are studied in comparison with two Newtonian jets with upper and lower bound viscosities, μ 0 and μ ∞. A number of quantitative conclusions and sensitivities on the instability behavior of non-Newtonian jets are investigated. It is found that the jet breakup mechanism depends on the properties of the fluid as well as the wave number of the thermal disturbance that causes the surface tension gradient. In contrast to the Newtonian liquid where the jet surface profile has the same frequency as the surface tension gradient, the nonlinear nature of the Carreau–Yasuda constitutive behavior may enable the jet surface profile at frequencies higher than that of the surface tension gradient. This leads to significant surface profile oscillation within one wavelength of the surface tension gradient and the generation of small satellite drops. It is worth noting that at a small wave number the breakup time for the Carreau–Yasuda fluid maybe shorter than that of the Newtonian jet with μ ∞, although the Newtonian jet has a lower viscosity.

The Rate of Intramolecular Loop Formation in DNA and Polypeptides: The Absence of the Diffusion-Controlled Limit and Fractional Power-Law Viscosity Dependence

The problem of determining the rate of end-to-end collisions for polymer chains has attracted the attention of theorists and experimentalists for more than three decades. The typical theoretical approach to this problem has focused on the case where a collision is defined as any instantaneous fluctuation that brings the chain ends to within a specific capture distance. In this paper, we study the more experimentally relevant case, where the end-to-end collision dynamics are probed by measuring the excited state lifetime of a fluorophore (or other lumiphore) attached to one chain end and quenched by a quencher group attached to the other end. Under this regime, a "contact" is defined not by the chain ends approach to within some sharp cutoff but, instead, typically by an exponentially distance-dependent process. Previous theoretical models predict that, if quenching is sufficiently rapid, a diffusion-controlled limit is attained, where such measurements report on the probe-independent, intrinsic end-to-end collision rate. In contrast, our theoretical considerations, simulations, and an analysis of experimental measurements of loop closure rates in single-stranded DNA molecules all indicate that no such limit exists, and that the measured effective collision rate has a nontrivial, fractional power-law dependence on both the intrinsic quenching rate of the fluorophore and the solvent viscosity. We propose a simple scaling formula describing the effective loop closure rate and its dependence on the viscosity, chain length, and properties of the probes. Previous theoretical results are limiting cases of this more general formula.

An experimental study on the effect of ultrasonication on viscosity and heat transfer performance of multi-wall carbon nanotube-based aqueous nanofluids

Four samples of 1 wt% multi-walled carbon nanotube-based (MWCNT) aqueous nanofluids prepared via ultrasonication were thermally characterized. Direct imaging was done using a newly developed wet-TEM technique to assess the dispersion state of carbon nanotubes (CNT) in suspension. The effect of dispersing energy (ultrasonication) on viscosity, thermal conductivity, and the laminar convective heat transfer was studied. Results indicate that thermal conductivity and heat transfer enhancement increased until an optimum ultrasonication time was reached, and decreased on further ultrasonication. The suspensions exhibited a shear thinning behavior, which followed the Power Law viscosity model. The maximum enhancements in thermal conductivity and convective heat transfer were found to be 20% and 32%, respectively. The thermal conductivity enhancement increased considerably at temperatures greater than 24 °C. The enhancement in convective heat transfer was found to increase with axial distance. A number of mechanisms related to boundary layer thickness, micro-convective effect, particle rearrangement, possible induced convective effects due to temperature and viscosity variations in the radial direction, and the non-Newtonian nature of the samples are discussed.

Natural convection heat transfer of non-Newtonian fluids in porous media from a vertical cone under mixed thermal boundary conditions

This work studies the problem of the steady natural convection boundary layer flow over a downward-pointing vertical cone in porous media saturated with non-Newtonian power-law fluids under mixed thermal boundary conditions. A similarity analysis is performed, and the obtained similar equations are solved by cubic spline collocation method. The effects of the power-law viscosity index and the similarity exponent on the heat transfer characteristics under mixed thermal boundary conditions have been studied. Under mixed thermal boundary conditions, both the surface heat flux and the surface temperature are found to decrease when the power-law viscosity index of the non-Newtonian power-law fluid in porous media is increased. Moreover, an increase in the similarity exponent tends to increase the boundary layer thickness and thus decreases the surface heat flux under mixed thermal conditions. The generalized governing equations derived in this work can be applied to the cases of prescribed surface temperature and prescribed heat flux.

Non-Newtonian Natural Convection Along a Vertical Flat Plate With Uniform Surface Temperature

Natural-convection boundary-layer flow of a non-Newtonian fluid along a heated semi-infinite vertical flat plate with uniform surface temperature has been investigated using a four-parameter modified power-law viscosity model. In this model, there are no physically unrealistic limits of zero or infinite viscosity that are encountered in the boundary-layer formulation for two-parameter Ostwald–de Waele power-law fluids. The leading-edge singularity is removed using a coordinate transformation. The boundary-layer equations are solved by an implicit finite-difference marching technique. Numerical results are presented for the case of a shear-thinning fluid. The results indicate that a similarity solution exists locally in a region near the leading edge of the plate, where the shear rate is not large enough to induce non-Newtonian effects; this similarity solution is identical to the similarity solution for a Newtonian fluid. The size of this region depends on the Prandtl number. Downstream of this region, the solution of the boundary-layer equations is nonsimilar. As the shear rate increases beyond a threshold value, the viscosity of the shear-thinning fluid is reduced. This leads to a decrease in the wall shear stress compared with that for a Newtonian fluid. The reduction in the viscosity accelerates the fluid in the region close to the wall, resulting in an increase in the local heat transfer rate compared with the case of a Newtonian fluid.

The Numerical Analysis of a Mold Cavity Filling Using the Finite Control Volume Method and Comparison to the Experimental Results

One of the most complicated subjects of the injection molding is the flow analysis. The flow of the plastic depends on the structure of the plastic material and the geometry of the mold cavity and the injection process parameters. The flow analysis and the simulations are achieved according to the numerical solution of the non linear differential governing equations. In this study, the Navier-Stokes equations are solved using the Finite Control Volume Method. The staggered grid system is used for the Full Implicit discretization method and SIMPLE algorithm is preferred for the calculation of the pressure. The Boussinesq approach is applicated to determine the density variations and the Power Law viscosity model is choosen. The melt flow is analyzed by Phoenics code. Both numerical analysis and the experiments have been realized for the same processing conditions and the same plastic material. HDPE is studied as a plastic material. It is shown that the theoretical and the experimental results are in good agreement.

Mixed convection of non-Newtonian fluids along a heated vertical flat plate

Mixed convective heat transfer of non-Newtonian fluids on a flat plate has been investigated using a modified power-law viscosity model. This model does not contain physically unrealistic limits of zero or infinite viscosity as are encountered in the boundary-layer formulation with traditional models of viscosity for power-law fluids. These unrealistic limits can introduce an irremovable singularity at the leading edge; consequently, the model is physically incorrect. The present modified model matches well with the measurement of viscosity, and does not introduce irremovable singularities. Therefore, the boundary-layer equations can be solved by marching from the leading edge downstream as for Newtonian fluids. The numerical results are presented for a shear-thinning fluid in terms of the velocity and temperature distribution, and for important physical properties, namely the wall shear stress and heat transfer rates.

Non-Newtonian Natural Convection Along a Vertical Plate with Uniform Surface Heat Fluxes

Natural convection of non-Newtonianfluids along a verticalflat platewith the heating condition of uniform surface heat flux was investigated using a modified power-law viscosity model. In this model, there are no physically unrealistic limits in the boundary-layer formulation for power-law non-Newtonian fluids. The governing equations are transformed into parabolic coordinates and the singularity of the leading edge is removed; hence, the boundarylayer equations can be solved straightforwardly by marching from the leading edge downstream. Numerical results are presented for the case of shear-thinning as well as shear-thickening fluids for two limits. The numerical results demonstrate that a similarity solution for natural convection exists near the leading edge, where the shear rate is not large enough to trigger non-Newtonian effects. After the shear rate increases beyond a threshold value, nonNewtonian effects start to develop and a similarity solution no longer exists. This indicates that the length scale is introduced into the boundary-layer formulation by the classical power-law correlation.