Heterogeneous/homogeneous and inclined magnetic aspect of infinite shear rate viscosity model of Carreau fluid with nanoscale heat transport

The study of the inclined flow along with the heterogeneous/homogeneous reactions in the fluid has been widely used in many industrial and engineering applications, such as petrochemical, pharmaceutical, materials science, heat exchanger design, fluid flow through porous media, etc. The purpose of this study is to present an infinite shear rate viscosity model using the inclined Carreau fluid with nanoscale heat transport. The model considers the effect of inclined angle on the fluid’s viscosity and the transfer of heat at the nanoscale. The result shows that the viscosity of the fluid decreases by increasing the inclination angle and the coefficient of heat transfer also increases with the inclination. The model can be used to predict the viscosity and heat transfer fluid’s behavior in the inclined systems that is widely used in the industrial and engineering applications. The results provide a better understanding of the inclined flow behavior of fluids and the heat transfer at the nanoscale, which can be useful in heat exchanger design, fluid flow through porous media, etc. Greater Infinite shear rate viscosity parameter gives the higher magnitude of Carreau fluid velocity. Moreover, inclined magnetic field reduces the velocity due to Lorentz force. Two numerical schemes are used to solve the model, BVP4C and Shooting.     

The mechanism of the self-assembly of associating DNA molecules under shear flow: Brownian dynamics simulation

A shear flow induces the assembly of DNAs with the sticky spots. In order to strictly interpret the mechanism of shear-induced DNA assembly, Brownian dynamics simulations with the bead-spring model were carried out for these molecules at various ranges of the Weissenberg numbers (We). We calculate a formation time and analyze the radial distribution function of end beads and the probability distribution of fractional extension at the formation time to understand the mechanism of shear-induced assembly. At low Weissenberg number the formation time, which is defined as an elapsed time until a multimer forms for the first time, decreases rapidly, reaching a plateau at We = 1000. A shear flow changes the radial distribution of end beads, which is almost the same regardless of the Weissenberg number. A shear flow deforms and stretches the molecules and generates different distributions between end beads with a stickly spot. The fractional extension progresses rapidly in shear flow from a Gaussian-like distribution to a uniform distribution. The progress of the distribution of fractional extension increases the possibility of meeting of end beads. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. We also calculate properties such as the radius of gyration, stretch, and so on. As the Weissenberg number increases, the radius of gyration at the formation time also increases rapidly, reaching a plateau at We = 1000.     

Analysis of shear-induced and extensional-induced associating polymer assemblies: Brownian dynamics simulation

In order to examine the difference between shear-induced and extensional-induced associating polymer assemblies at the molecular level, Brownian dynamics simulations with the bead-spring model were carried out for model DNA molecules with sticky spots. The radial distribution of molecules overestimates from that in the absence of flow and increases with increasing Weissenberg number in extensional flow, but slightly underestimates without regard to shear rate in shear flow. The fractional extension progresses more rapidly in extensional flow than in shear flow and the distribution of fractional extension at the formation time has a relatively sharper peak and narrower spectrum in extensional flow than in shear flow. In shear flow, the inducement of the assembly mainly results from the progress of the probability distribution of fractional extension. However, in extensional flow, the assembly is induced by both the progress of the probability distribution and increasing the values of the radial distribution.     

Numerical Analysis of 3‐D Flow Past a Stationary Sphere with Slip Condition at Low and Moderate Reynolds Numbers

Computations are performed to determine the steady 3‐D viscous fluid flow forces acting on the stationary spherical suspended particle at low and moderate Reynolds numbers in the range of 0.1≤Re≤200. A slip is supposed on the boundary so that the slip velocity becomes proportional to the shear stress. This model possesses a single parameter to account for the slip coefficient λ (Pa.s/m), which is made dimensionless and is called Trostel number (Tr=λ a/μ). Decreasing slip, increases drag in all Reynolds limits, but slip has smaller effects on drag coefficient at lower Reynolds number regimes. Increasing slip at known Reynolds number causes to delay of flow separation and inflect point creation in velocity profiles. At full slip conditions, shear drag coefficient will be zero and radial drag coefficient reaches to its maximum values. Flow around of sphere at full‐slip condition is not equal to potential flow around a sphere. Present numerical results corresponding to full slip (Tr→0) are in complete accord with certain results of flow around of inviscid bubbles, and the results corresponding to no‐slip (Tr→∞) have excellent agreement with the results predicted by the no‐slip boundary condition.     

Effect of Coriolis and buoyancy forces on three-dimensional flow of chemically reactive tangent hyperbolic fluid subject to variable viscosity

Thermophoresis effect has wide range of applications in electro-static precipitators and in biology for calculating single biological macro molecules, such as genomic-length DNA and HIV virus in the micro channels. Current study deal with effects of Coriolis and buoyancy forces on the three-dimensional boundary layer flow of tangent hyperbolic fluid with thermo-migration and haphazard motion of nano-sized particles. Arrhenius kind of chemical reaction is taken along an exponentially stretchable surface. The main focus of current exploration is to execute shear thinning nano-liquid flow past an exponentially rotating stretchable surface under the influence of variable viscosity, mixed convection and activation energy. We are motivated to explore the features of three-dimensional shear thinning model combined under the features of mixed convention, variable viscosity, and activation energy. The mathematical model is designed to generate PDEs and converted them into ODEs by employing fractious transformation. The numerical outcomes are exhibited via graphs by employing Bvp4c numerical technique whereas the values of skin friction coefficient are calculated by monopolizing shooting method. Characteristics of the parameters appearing in modeling like the viscosity parameter, power-law index, local Weissenberg number, mix convection parameter, rotation parameter, Prandtl number and chemical reaction parameter are comprehensively analyzed through graphical behavior. The impact of governing parameters on skin friction, heat and mass transfer rates is illustrated through tables. The detail analysis anticipates that the elevation in Weissenberg number and porosity caused decline in velocity. Further, the temperature behaves doppositely analogous to development Prandtl besides the thermophoresis parameter.     

Entanglement junctions in melts and concentrated solutions of flexible-chain polymers: Macromodeling

The effect of deformation on the behavior of intermolecular entanglements in melts and in concentrated solutions of polymers is simulated with the use of knots formed by long flexible threads. Two cases are discussed: the behavior of individual junctions and the pattern of change in the entanglements in a network of statistically entangled threads. It is shown that, at low strain rates, the junctions disentangle and threads slip out of the entanglements. This situation simulates an irreversible flow of macromolecules in the classical tube model. At high rates, the junctions tighten, a phenomenon that simulates the impossibility of irreversible motion of macromolecules. The transition from slipping to tightening of entanglements simulates the change in the pattern of behavior of the melt, i.e., from flow to rubberlike deformations. A generalized dependence of elastic deformations on the Weissenberg number is constructed; it shows that the transition occurs at Weissenberg numbers on the order of 3–5, which correspond to the characteristic lifetimes of an entanglement junction. At high strain rates, redistribution and local accumulation of entanglements are observed.     

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.     

Self-organization in the flow of complex fluids (colloid and polymer systems). Part 2: Theoretical models

Flow induced transitions in complex fluids are usually accompanied by changes in the internal media structure and the flow symmetry. In this review paper, we discuss the theoretical models and approaches that have been used for the analysis of different types of flow instabilities and flow patterns. The main attention is focused on the basic fluid models which reveal vortex and banding flow structures at high shear rates. The Oldroyd-B fluid is one of such models. The Reynolds and the Weissenberg (or Deborah) numbers are the parameters governing its flow behavior. For this model, the secondary flow patterns arising in viscometric flows of different geometries at the bifurcation point are described. Complex fluids which are able to exist in multiple states can form coexisting bands of different structures with different rheological properties and flowing with different shear rates at the same shear stress. Shear banding is typical for fluids demonstrating non-monotonous flow curves described by such models as the diffusive Johnson-Segalman fluid model, for example. Recent progress in exploring this phenomenon is discussed.     

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow with hydrodynamic interaction

The adsorption of single polyelectrolyte molecules in shear flow is studied using Brownian dynamics simulations with hydrodynamic interaction (HI). Simulations are performed with bead-rod and bead-spring chains, and electrostatic interactions are incorporated through a screened Coulombic potential with excluded volume accounted for by the repulsive part of a Lennard-Jones potential. A correction to the Rotne-Prager-Yamakawa tensor is derived that accounts for the presence of a planar wall. The simulations show that migration away from an uncharged wall, which is due to bead-wall HI, is enhanced by increases in the strength of flow and intrachain electrostatic repulsion, consistent with kinetic theory predictions. When the wall and polyelectrolyte are oppositely charged, chain behavior depends on the strength of electrostatic screening. For strong screening, chains get depleted from a region close to the wall and the thickness of this depletion layer scales as N(1/3)Wi(2/3) at high Wi, where N is the chain length and Wi is the Weissenberg number. At intermediate screening, bead-wall electrostatic attraction competes with bead-wall HI, and it is found that there is a critical Weissenberg number for desorption which scales as N(-1/2)kappa(-3)(l(B)|sigmaq|)(3/2), where kappa is the inverse screening length, l(B) is the Bjerrum length, sigma is the surface charge density, and q is the bead charge. When the screening is weak, adsorbed chains are observed to align in the vorticity direction at low shear rates due to the effects of repulsive intramolecular interactions. At higher shear rates, the chains align in the flow direction. The simulation method and results of this work are expected to be useful for a number of applications in biophysics and materials science in which polyelectrolyte adsorption plays a key role.     

Effect of internal viscosity on Brownian dynamics of DNA molecules in shear flow

The results of Brownian dynamics simulations of a single DNA molecule in shear flow are presented taking into account the effect of internal viscosity. The dissipative mechanism of internal viscosity is proved necessary in the research of DNA dynamics. A stochastic model is derived on the basis of the balance equation for forces acting on the chain. The Euler method is applied to the solution of the model. The extensions of DNA molecules for different Weissenberg numbers are analyzed. Comparison with the experimental results available in the literature is carried out to estimate the contribution of the effect of internal viscosity.     

Effects of laterally heterogeneous slip on the resonance properties of quartz crystals immersed in liquids

A formalism is presented which predicts the influence of laterally heterogeneous slip (for instance, induced by nanoscopic air bubbles) on the shift of the resonance frequency and bandwidth of quartz crystal resonators immersed in liquids. The lateral heterogeneities are decomposed into their Fourier components. The distribution of slip lengths provides a boundary condition, giving rise to a small, secondary flow field. The mean stress exerted by this secondary field induces a shift in resonance frequency and bandwidth. If the slip length is much smaller than the penetration depth of the shear waves and smaller than the lateral correlation length, one finds that the effects of the heterogeneities scale as n(3/2), with n being the overtone order. The frequency, f, and half-band-half-width, Gamma, decrease by the same amount. These calculations match experimental results obtained with a gold-coated resonator in contact with various hydrophilic liquids.     

Rheology of chlorosulphonated polyethylene solutions

The viscosity behaviour of chlorosulphonated polyethylene was studied as a function of shear rate, concentration and temperature in three aromatic solvents viz. benzene, toluene and xylene. The Carreau model was used to correlate the data. The time constant t₁ arising from the Carreau model was compared with the Bueche time constant λ_H; there appears to be good agreement between them especially at lower temperatures and higher concentrations. A unified curve based on plots of η/η_O vs γλ_H correlated the data successfully. The temperaure dependence of the zero shear viscosity was studied. The apparent activation energy for viscous flow was linearly related to the polymer concentration.     

高分子/棒状纳米粒子复合物的分子动力学模拟

采用非平衡态分子动力学模拟研究了剪切场下棒状纳米粒子对高分子基体的结构、 动力学和流变性质的影响. 通过比较多种体积分数(0.8%~10%)的纳米复合物及纯熔体的模拟结果发现, 随着纳米粒子的增加, 高分子链的扩散和松弛逐渐受到抑制, 而链尺寸几乎保持不变. 从Weissenberg number(W_i)角度看, 在剪切流场下, 高分子链的结构性质(如归一化的均方回转半径、 回转张量和取向抑制参数)几乎与纳米粒子的体积分数无关, 而高分子链的Tumbling运动受到抑制. 研究还发现, 纳米复合物与纯熔体的剪切黏度曲线趋势基本一致, 即W_i=1将曲线分为平台区和剪切变稀区. 纳米棒的加入仅定量地改变了流体的剪切黏度.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

Reliable measurements of interfacial slip by colloid probe atomic force microscopy. III. Shear-rate-dependent slip

We present experimental evidence and theoretical models that demonstrate that the slip length, which is the departure from the hydrodynamic no-slip boundary condition, cannot be constant as commonly assumed, but must decrease with increasing shear rate to avoid an unphysical divergence in the velocity of the fluid adjacent to the surface at small separations. The molecular origin of the shear rate dependence of the slip length is discussed. A new theoretical model for slip (the saturation model) is obtained, and it is shown to describe accurately colloid probe atomic force microscopy force measurements for all separations down to a few nanometers in two partially wetting situations (di-n-octyl phthalate on silanized silicon and bare silicon). Previous observations of slip length increasing with shear rate are explained as due to an imprecise calculation of the drag force on the cantilever. A new way of plotting experimental data is also presented, which provides a useful way to illustrate the slip length dependence on the shear rate.     

Friction between brush layers of charged and neutral bottle-brush macromolecules. molecular dynamics simulations

Using molecular dynamics simulations, we study the lubricating properties of neutral and charged bottle-brush coatings as a function of the compression and shear stresses and brush grafting density. Our simulations have shown that in charged bottle-brush systems under shear there is a layer with excess counterions located in the middle between brush-bearing surfaces. The main deformation mode of the charged bottle-brush layers is associated with the backbone deformation, resulting in the backbone deformation ratio, α, and shear viscosity, η, being universal functions of the Weissenberg number. In the case of neutral bottle-brush systems, in addition to the backbone deformation there is also side chain deformation. The coupling between backbone and side chain deformation violates universality in the deformation ratio, α, dependence on the Weissenberg number and results in scaling exponents varying with the compression stress and brush grafting density. The existence of different length scales controlling deformation of neutral bottle brushes manifests itself in the shear viscosity, η, dependence on the shear rate, ?γ. Shear viscosity, η, as a function of the shear rate, ?γ, has two plateaus and two shear thinning regimes. The low shear rate plateau and shear thinning regime correspond to the backbone deformation, while the second plateau and shear thinning regime at moderate shear rates are due to side chain deformation. For both systems the value of the friction coefficient increases with increasing shear rate. The values of the friction coefficient for charged bottle-brush systems are about ten times smaller than corresponding values for neutral systems at the same shear rate.     

Electrophoresis in a Carreau fluid at arbitrary zeta potentials

The electrophoresis of colloidal particles has been studied extensively in the past. Relevant analyses, however, are focused mainly on the electrophoretic behavior of a particle in a Newtonian fluid. Recent advances in science and technology suggest that the electrophoresis conducted in a non-Newtonian fluid can play a role in practice. Here, the electrophoresis of a concentrated colloidal dispersion in a Carreau fluid is investigated under the conditions of arbitrary electrical potential where the effect of double-layer polarization may be significant. A pseudo-spectral method coupled with a Newton-Raphson iteration scheme is used to solve the governing equations, which describe the electric, the flow, and the concentration fields. The results of numerical simulation reveal that, due to the effect of shear thinning, the electrophoretic mobility for the case of a Carreau fluid is greater than for that of a Newtonian fluid. Also, the higher the surface potential of a particle, the more significant the non-Newtonian nature of a Carreau fluid on its electrophoretic mobility.     

Sedimentation of a cylindrical particle in a Carreau fluid

The drag coefficient of an isolated, rigid cylindrical particle in a Carreau fluid is evaluated. The result of numerical simulation reveals that, in general, the shear-thinning nature of a Carreau fluid yields a drag coefficient smaller than that for the corresponding Newtonian fluid. Also, the smaller the Reynolds number, the more appreciable the decrease of the drag coefficient as the relaxation time constant of the Carreau fluid increases. The influence of the index parameter of a Carreau fluid on the drag coefficient depends largely on the magnitude of the relaxation time constant and is insensitive to the Reynolds number. Only if the relaxation time constant is sufficiently large is the influence of the index parameter on the drag coefficient significant. If the Reynolds number and/or the relaxation time constant is sufficiently large, the flow field upstream of a particle becomes asymmetric to that downstream. In general, the influence of the index parameter, the relaxation time constant, and the Reynolds number on the flow field follows the order index parameter相似文献   

The role of multi-walled carbon nanotubes in shear enhanced crystallization of isotactic poly(1-butene)

The flow-induced crystallization behavior of nanocomposites, containing isotactic poly(1-butene) (PB) and functionalized multi-walled carbon nanotubes (MWNT), was investigated. Three different MWNT concentrations (0.1, 1, 5 wt%) were used to prepare the nanocomposites. Effects of MWNT and shear flow on the crystallization parameters were evaluated separately. Rheological measurements based on oscillatory shear revealed induction time and crystallization half-time at the quiescent state, where both parameters exhibited the nucleating effect of MWNT on PB. Rheological measurements based on steady-state shear flow and short-time shear flow revealed the evolution of molecular orientation, which was studied in both PB and its nanocomposites. A small increase in crystallization kinetic was recorded in PB under shear having moderate values of the Weissenberg (We) number. On the other hand, a dramatic synergistic effect of MWNT and shear was detected under the same shear conditions for nanocomposites. The optical microscopic images exhibited a clear transition from isotropic to row-like morphology in the case of nanocomposites under shear.