Effect of interfacial modifier on single drop deformation and breakup in step increasing shear flow

This work deals with in situ visualisation of deformation and breakup of a copolymer modified single Newtonian drop immersed in a Newtonian homogenous matrix. The experiments were carried out on a model system made of poly-isobutylene as the suspending fluid and two poly-dimethylsiloxanes with different molecular weights as the drop phase with viscosity ratios 0.036 and 1.13, below and above but close to unity. Three weight concentrations 0.5%, 2% and 10% of the block copolymer laying below, close to and above the critical concentration of the total drop surface coverage were examined. Single drop deformation experiments were carried out in a home-designed Couette quartz cell connected to a home-modified Paar Physica Rheometer. The variation in the length-to-diameter ratio (L/D) versus shear rate and capillary number was measured both in steady and in transient regimes till breakup. The results indicated a weaker resistance of copolymer modified drops against hydrodynamic stresses at both viscosity ratios as compared to the clean drop. However, the drop deformation was found to be complex and depends on the copolymer concentration and the viscosity ratio.     

Shear rheometry and visualization of glass fiber suspensions

The nonlinear rheological behavior of short glass fiber suspensions has been investigated in this work by rotational rheometry and flow visualization. A Newtonian and a Boger fluid (BF) were used as suspending media. The suspensions exhibited shear thinning in the semidilute regime and weaker shear thinning in the transition to the concentrated one. Normal stresses and relative viscosity were higher for the BF suspensions than for the Newtonian ones presumably due to enhanced hydrodynamic interactions resulting from BF elasticity. In addition, relative viscosity of the suspensions increased rapidly with fiber content, suggesting that the rheological behavior in the concentrated regime is dominated by mechanical contacts between fibers. Visualization of individual fibers and their interactions under flow allowed the detection of aggregates, which arise from adhesive contacts. The orientation states of the fibers were quantified by a second order tensor and fast Fourier transforms of the flow field images. Fully oriented states occurred for shear rates around 20 s^− 1. Finally, the energy required to orient the fibers was higher in step forward than in reversal flow experiments due to a change in the spatial distribution of fibers, from isotropic to planar oriented, during the forward experiments.     

Effects of viscosity ratio on deformation of a viscoelastic drop in a Newtonian matrix under steady shear

Deformation of an Oldroyd B drop in a Newtonian matrix under steady shear is simulated using a front tracking finite difference method for varying viscosity ratio. For drop viscosity lower than that of the matrix, the long-time steady deformation behavior is similar to that of the viscosity matched system—the drop shows reduced deformation with increasing Deborah number due to the increased inhibiting viscoelastic normal stress inside the drop. However for higher viscosity ratio systems, the drop response is non-monotonic—the steady drop deformation first decreases with increasing Deborah number but above a critical Deborah number, it increases with further increase in Deborah number, reaching higher than the viscous case value for some viscosity ratios. We explain the increase in deformation with Deborah number by noting that at higher viscosity ratios, strain rate inside the drop is reduced, thereby reducing the inhibiting viscoelastic stress. Furthermore, similar to the viscosity matched system, the drop inclination angle increases with increasing Deborah number. A drop aligned more with the maximum stretching axis at 45 degree of the imposed shear, experiences increased viscous stretching. With increased ratio of polymeric viscosity to total drop viscosity, the drop deformation decreases and the inclination angle increases. Our simulation results compare favorably with a number of experimental and computational results from other researchers.     

The rheology of suspensions of porous zeolite particles in polymer solutions

We present data and predictive models for the shear rheology of suspended zeolite particles in polymer solutions. It was found experimentally that suspensions of zeolite particles in polymer solutions have relative viscosities that dramatically exceed the Krieger–Dougherty predictions for hard sphere suspensions. Our investigations show that the major origin of this discrepancy is due to the selective absorption of solvent molecules from the suspending polymer solution into zeolite pores. The effect raises both the polymer concentration in the suspending medium and the particle volume fraction in the suspension. Consequently, both the viscosity of the polymer solution and the particle contribution to the suspension viscosity are increased. We propose a predictive model for the viscosity of porous zeolite suspensions by incorporating a solvent absorption parameter, α, into the Krieger–Dougherty model. We experimentally determined the solvent absorption parameter by comparing viscosity data for suspensions of porous and nonporous MFI zeolite particles. Our results are in good agreement with the theoretical pore volume of MFI particles.     

Experimental and numerical study of the rotation and the erosion of fillers suspended in viscoelastic fluids under simple shear flow

When a porous agglomerate immersed in a fluid is submitted to a shear flow, hydrodynamic stresses acting on its surface may cause a size reduction if they exceed the cohesive stress of the agglomerate. The aggregates forming the agglomerate are slowly removed from the agglomerate surface. Such a behaviour is known when the suspending fluid is Newtonian but unknown if the fluid is viscoelastic. By using rheo-optical tools, model fluids, carbon black agglomerates and particles of various shapes, we found that the particles had a rotational motion around the vorticity axis with a period which is independent on shape (flat particles not considered), but which is exponentially increasing with the elasticity of the medium expressed by the Weissenberg number (We). Spherical particles are always rotating for We up to 2.6 (largest investigated We in this study) but elongated particles stop rotating for We>0.9 while orienting along the flow direction. Erosion is strongly reduced by elasticity. Since finite element numerical simulation shows that elasticity increases the local stress around a particle, the origin of the erosion reduction is interpreted as an increase of cohesiveness of the porous agglomerate due to the infiltration of a viscoelastic fluid.     

Überlegungen zur Scherviskosität von Suspensionen aufgrund einer Dimensionsanalyse

Dimensional analysis of the motion of solid particles suspended in a fluid phase shows that the macroscopic relative shear viscosity of suspensions generally depends not only on the volume concentration and particle shape but also on two Reynolds numbers and a dimensionless sedimentation number. These dimensionless numbers are formed using parameters characterizing the structure and motion of the suspension at the microscopic level. The analysis was based on the assumptions that the dispersed particles are rigid and sufficiently large that Brownian motion may be neglected, that the continuous fluid phase is Newtonian and that the interactions between particles and between particles and fluid phase are only hydrodynamic. The Reynolds numbers describe the influence of the inertial forces at the microscopic level, and the sedimentation number the influence of gravity. The dimensionless numbers can be neglected if their values are much smaller than one. For each of the dimensionless numbers both the shear rate and the particle size influence the shear viscosity. Thus sedimentation number is large for low shear rates, whereas the Reynolds numbers are large for high shear rates. The viscosity function for one suspension can be transformed into the viscosity function for another suspension with geometrically similar particles but of a different size. The scale-up rules are derived from the requirement that the relevant dimensionless numbers must be constant. The influence of non-hydrodynamic effects at the microscopic level on the shear viscosity can be detected by deviations from the derived scale-up rules.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 1. Theory and experiment

The rheological behavior of stable slurries is shown to be characterized by a bimodal model that represents a slurry as made up of a coarse fraction and a colloidal size fine fraction. According to the model, the two fractions behave independently of each other, and the non-Newtonian behavior of the viscosity is solely caused by the colloidal fraction, while the coarse fraction increases the viscosity level through hydrodynamic interactions. Data from experiments run with colloidal coal particles of about 2–3 µm average size dispersed in water show the viscosity of these colloidal suspensions to exhibit a highly shearrate-dependent behavior and, in the high shear limit, to match very closely the viscosity of suspensions of uniform size rigid spheres although the coal volume fraction must be determined semi-empirically. Different amounts of coarse coal particles are added to the colloidal suspension and the viscosity of the truly bimodal slurries measured as a function of shear rate. In agreement with the bimodal model, the measured shear viscosities show the coarse fraction to behave independently of the colloidal fraction and its contribution to the viscosity rise to be independent of the shear rate. It is shown that the shear rate exerted on the colloidal fraction is higher than that applied by the viscometer as a result of hydrodynamic interactions between the coarse particles, and that it is this effective higher shear rate which is necessary to apply in the correlations. For determining the coal volume fraction a relatively simple and quite accurate measurement technique is developed for determining the density and void fraction of coarse porous particles; the technique directly relates volume fraction to mass fraction.     

A boundary‐only approach to the deformation of a shear‐thinning drop in extensional Newtonian flow

The influence of shear thinning on drop deformation is examined through a numerical simulation. A two‐dimensional formulation within the scope of the boundary element method (BEM) is proposed for a drop driven by the ambient flow inside a channel of a general shape, with emphasis on a convergent–divergent channel. The drop is assumed to be shear thinning, obeying the Carreau–Bird model and the suspending fluid is Newtonian. The viscosity of the drop at any time is estimated on the basis of a rate‐of‐strain averaged over the region occupied by the drop. The viscosity thus changes from one time step to the next, and it is strongly influenced by drop deformation. It is found that small drops, flowing on the axis, elongate in the convergent part of the channel, then regain their spherical form in the divergent part; thus confirming experimental observations. Newtonian drops placed off‐axis are found to rotate during the flow with the period related to the initial extension, i.e. to the drop aspect ratio. This rotation is strongly prohibited by shear thinning. The formulation is validated by monitoring the local change of viscosity along the interface between the drop and the suspending fluid. It is found that the viscosity averaged over the drop compares, generally to within a few per cent, with the exact viscosity along the interface.     

Rheology of coal suspensions

Proper design of operations encountered in preparation, transport and employment of suspensions like coal slurries and coal-oil mixtures require an accurate knowledge of their rheological behaviour.Such concentrated suspensions generally exhibit non-Newtonian behaviour (shearthinning) which is more pronounced at higher coal concentrations. The nature of the dispersing medium influences the aggregation state of the disperse phase and, consequently, affects the stability and the rheology of the systems. In the present paper coal suspensions prepared with different dispersing media and covering a wide range in solid phase concentration are studied, by using a rotational coaxial cylinders viscometer.Different models have been taken into consideration for correlating experimental data. In particular, in order to describe the dependence of viscosity on shear rate and solid phase concentration, the suitability of the model suggested by Smith and Bruce is evaluated. Accordingly, the aggregation state of the disperse phase as well as its dependence on shear rate and dispersing medium can be estimated.     

Shear Rate Determination from Pore-Scale Flow Fields

Aqueous solutions with polymer additives often used to improve the macroscopic sweep efficiency in oil recovery typically exhibit non-Newtonian rheology. In order to predict the Darcy-scale effective viscosity \(\mu _{\mathrm{eff}} \) required for practical applications often, semi-empirical correlations such as the Cannella or Blake–Kozeny correlation are employed. These correlations employ an empirical constant (“C-factor”) that varies over three orders of magnitude with explicit dependency on porosity, permeability, fluid rheology and other parameters. The exact reasons for this dependency are not very well understood. The semi-empirical correlations are derived under the assumption that the porous media can be approximated by a capillary bundle for which exact analytical solutions exist. The effective viscosity \(\mu _{\mathrm{eff}} (v_{\mathrm{Darcy}} )\) as a function of flow velocity is then approximated by a cross-sectional average of the local flow field resulting in a linear relationship between shear rate \(\gamma \) and flow velocity. Only with such a linear relationship, the effective viscosity can be expressed as a function of an average flow rate instead of an average shear rate. The local flow field, however, does in general not exhibit such a linear relationship. Particularly for capillary tubes, the velocity is maximum at the center, while the shear rate is maximum at the tube wall indicating that shear rate and flow velocity are rather anti-correlated. The local flow field for a sphere pack is somewhat more compatible with a linear relationship. However, as hydrodynamic flow simulations (using Newtonian fluids for simplicity) performed directly on pore-scale resolved digital images suggest, flow fields for sandstone rock fall between the two limiting cases of capillary tubes and sphere packs and do in general not exhibit a linear relationship between shear rate and flow velocity. This indicates that some of the shortcomings of the semi-empirical correlations originate from the approximation of the shear rate by a linear relationship with the flow velocity which is not very well compatible with flow fields from direct hydrodynamic calculations. The study also indicates that flow fields in 3D rock are not very well represented by capillary tubes.     

Numerical simulation of entry flow of the IUPAC-LDPE melt

Numerical simulations have been undertaken for the creeping entry flow of a well-characterized polymer melt (IUPAC-LDPE) in a 4:1 axisymmetric and a 14:1 planar contraction. The fluid has been modeled using an integral constitutive equation of the K-BKZ type with a spectrum of relaxation times (Papanastasiou–Scriven–Macosko or PSM model). Numerical values for the constants appearing in the equation have been obtained from fitting shear viscosity and normal stress data as measured in shear and elongational data from uniaxial elongation experiments. The numerical solutions show that in the axisymmetric contraction the vortex in the reservoir first increases with increasing flow rate (or apparent shear rate), goes through a maximum and then decreases following the behavior of the uniaxial elongational viscosity. For the planar contraction, the vortex diminishes monotonically with increasing flow rate following the planar extensional viscosity. This kinematic behavior is not in agreement with recent experiments. The PSM strain-memory function of the model is then modified to account for strain-hardening in planar extension. Then the vortex pattern shows an increase in both axisymmetric and planar flows. The results for planar flow are compared with recent experiments showing the correct trend.     

向列相溶致液晶旋转黏度研究

溶致液晶具有良好的生物相容性、无毒性、生物降解性以及光学、电磁学各向异性等, 在细胞相互作用、神经刺激传递、脂肪吸收、药物智能输运等生命活动研究、医药工程和液晶显示等领域有广泛应用. 本文采用旋转磁场法测得溶致液晶日落黄在不同温度和溶液浓度下向列相时旋转黏度, 并结合溶致液晶分子自组装过程, 理论分析了溶致液晶向列相旋转黏度随温度和溶液浓度的变化规律. 研究结果表明: 溶致液晶旋转黏度与液晶分子自组装柱状体平均长度的平方呈正比增大关系, 随溶液浓度的增大而增大, 随温度的升高表现出指数减小的规律. 构建了与向列相溶致液晶温度和浓度相关的旋转黏度经验表达式, 经验表达式计算结果与实验值吻合较好, 最大误差仅为18.56${\%}$. 提出采用旋转流变仪间接获得溶致液晶剪切能的新方法, 溶致液晶剪切能随溶液浓度的增大而增大, 但在实验温度范围内, 溶致液晶剪切能几乎不随温度而改变. 利用旋转流变仪间接获得的溶致液晶剪切能与报道的利用X-Ray检测所得的结果之间最大误差仅为3${\%}$. 成功地利用了液晶分子自组装能力随温度的变化规律来研究柱状体长径比对旋转黏度的影响规律, 创新地提出了"一步法"测量研究, 大大减少相关实验研究的成本和复杂性.      

The effect of particle size and migration on the formation of flow-induced structures in viscoelastic suspensions

Flow-induced structures in suspensions containing spheres in viscoelastic suspending media were investigated by microscopy and rheo-optical methods. Suspensions of monodisperse polystyrene spheres with diameters ranging from 1.2 to 2.8 μm and dispersed in aqueous solutions of hydroxypropylcellulose were studied in simple shear flows. Optical microscopy observations as well as small-angle light-scattering (SALS) experiments were performed using a parallel plate geometry. In agreement with previous work, necklaces of particles aligned in the flow direction were observed when shearing faster then a critical shear rate, which was found to be independent of particle size. In contrast to earlier work, however, the role of particle migration was found to be of prime importance. Particles were shown to migrate toward the plates where the particles assembled and aligned in strings running in the flow direction. For the smallest particles (1 μm diameter), the formation of particle doublets or short strings along the vorticity direction was observed at low shear rates, which flipped to an orientation into the flow direction and grew into longer strings at higher shear rates. SALS experiments were used to quantify the degree of alignment and its dependence on particle size, shear rate, and gap. For the system under investigation, the degree of alignment was found to increase with increasing shear rate and particle size and with decreasing gap. The present results suggest that, depending on the details of the suspending medium and the size and nature of the suspended particles, the formation of aligned structures is affected by the relative magnitude of the colloidal and hydrodynamic forces and the kinetics of string formation versus the kinetics of migration.     

Investigation of the effect of SSP in stabilizing the structure of condensation polymer blends via rheological measurements

We investigated the influence of solid-state polymerization (SSP) process on the reactions that could be taken place at the interphase of polycondensation polymer blends to stabilize the structure obtained after melt mixing. Polyethylene terephthalate (PET) and polyamide 66 (PA66) were melt blended in a mixer, and subsequent SSP process was performed for each sample. FTIR spectra indicated reactions between two polymers. Viscosity behavior and interfacial slip were investigated by measuring shear viscosity of components and blends before and after SSP and then compared with the viscosity calculated from the log-additivity model. The results showed that after SSP, there was no sign of interfacial slip, the slope of viscosity reduction with increasing shear rate became smaller, and the viscosity of blends showed positive deviation at all examined shear rate from the log-additivity model while this deviation was negative at higher shear rate before SSP. SEM micrographs, which were taken after shear stress was imposed on the samples, also indicated the morphological stability after SSP. Furthermore, we studied the effect of functional groups concentration on the reactions at the interphase by using hydrolyzed PET as a precursor for blends. The results showed that slip at the interface would decrease with increasing functional groups of the precursors. These results are particularly valuable for using recycled polymers.     

Sedimentation of particles in shear flows of viscoelastic fluids with fibers

We study the effect of fiber additives on rheology and sedimentation of particle suspensions in a base viscoelastic suspending fluid in the case when the suspension is subjected to shear flow. We found experimentally that fiber additives (3–6 mm in length and 8–12 μm in diameter at a mass fraction of 0–0.4%) increase the suspension viscosity and retard the particle sedimentation significantly. At the same mass concentration, long and thin fibers reduce the sedimentation velocity and increase the viscosity to a much greater extent than short and thick fibers. We revealed that both rheology and sedimentation are controlled by a single conformational parameter (overlap parameter) defined as the number of fibers per unit volume multiplied by fiber length cubed.     

Transient shear rheology of carbon nanofiber/polystyrene melt composites

We characterize the transient shear rheology of polystyrene/carbon nanofiber composites. Our experimental measurements of the composites show increasing stress overshoot responses to transient shear as the carbon nanofiber concentration increases. We also find the steady state viscosity reached at long times during application of a constant shear rate increases with increasing carbon nanofiber concentration. Flow reversal experiments show the effects of nanofiber orientation and structural evolution on the composite's rheological response.We present a microstructurally based constitutive model where all but two parameters are determined by rheological characterization of the pure polymer and the shape and concentration of the nanoparticles. The Folgar-Tucker constant, C_I, is treated as a fitting parameter, while several definitions for the shape factors A, B, C and F are evaluated. We make note of the effects each parameter has on the model's predictions. We find that the constitutive model is in agreement with our experimentally measured transient shear rheology of the PS/CNF melt composites for the CNF concentrations and shear rates presented.     

The effect of the hydrodynamic interaction on the rheological properties of Hookean dumbbell suspensions in steady state shear flow

The diffusion equation for the configurational distribution function of Hookean dumbbell suspensions with the hydrodynamic interaction (HI) was solved, in terms of Galerkin’s method, in steady state shear flow; and viscosity,first and second normal-stress coefficients and molecular stretching were then calculated. The results indicate that the HI included in a microscopic model of molecules gives rise to a significant effect on the macroscopic properties of Hookean dumbbell suspensions. For example, the viscosity and the first normal stress coefficient, decreasing as shear rate increases, are no longer constant; the second normal-stress coefficient, being negative with small absolute value and shear-rate dependent, is no longer zero; and an additional stretching of dumbbells is yielded by the HI. The viscosity function and the first normal-stress coefficient calculated from this method are in agreement with those predicted from the self-consistent average method qualitatively, while the negative second normal-stress coefficient from the former seems to be more reasonable than the positive one from the latter.     

Self-consistent particle simulation of model-stabilized colloidal suspensions

Dynamics of model-stabilized colloidal suspensions were investigated by the self-consistent particle simulation method (SC), a new simulation algorithm that takes into account the interaction between the particles and suspending fluid. In this method, the fluid-particle interaction is introduced self-consistently by combining the finite element method (FEM) for fluid motion with Brownian dynamics (BD) for particle dynamics. To validate the reliability of the proposed algorithm, the shear dynamics of the stable particle suspensions were investigated. Relative viscosity and microstructure as a function of dimensionless shear rate at different volume fractions were in good agreement with previous observations. The robustness of the method was also verified through numerical convergence test. The effect of the fluid-particle interaction was well represented in simulations of two model problems, pressure-driven channel flow and rotating Couette flow. Plug-shaped velocity profile was observed in pressure-driven channel flow, which arised from shear thinning behavior of the stable suspension. In rotating Couette flow, shear banded nonlinear flow profile was observed. Although full hydrodynamic interaction (HI) was not rigorously taken into account, it successfully captured the macroscopic structure-induced flow field. It also takes advantage of the geometrical adaptability of FEM and computational efficiency of BD. We expect this newly developed simulation platform to be useful and efficient for probing the complex flow dynamics of particle systems as well as for practical applications in the complex flow of complex fluids.     

Bimodal model of slurry viscosity with application to coal-slurries. Part 2. High shear limit behavior

It is shown that in a truly bimodal coal-water slurry the hydrodynamic interactions between the coarse particles impose on the fine fraction a shear rate higher than that applied externally by the viscometer walls. A semi-empirical function of the coarse volume fraction is obtained for this correction factor to the applied shear rate. The derivation of this shear correction factor is based on lubrication concepts and introduces the maximum packing fraction,ø _m, at which flow can take place.ø _m is obtainable from a simple dry packing experiment. It is shown that the contribution of the coarse particles to the viscosity rise can be successfully described by a viscosity model employing the same concepts used to derive the shear correction factor. The bimodal model is applied in the high shear limit to polymodal coal slurries with a continuous particle size distribution. In the model, the contribution of the coarse particles to the viscosity rise is taken from separate viscosity measurements for the coarse coal particles, while the contribution to the viscosity of the fine coal particles is taken to be that given by the measured viscosity of colloidal suspensions of monomodal rigid spheres. It is shown that there is a ratio of coarse to fine fraction volumes in the continuous size distribution, corresponding to a specific separating particle size, for which the measured viscosities of the polymodal slurries match almost perfectly over the whole solids volume fraction range with the viscosity values obtained using the bimodal approach. The match is found to be relatively insensitive to the precise value of the separating particle size.     

The effect of NaCl addition on the rheological behavior of cetyltrimethylammonium <Emphasis Type="Italic">p</Emphasis>-toluenesulfonate (CTAT) aqueous solutions and their mixtures with hydrophobically modified polyacrylamide aqueous solutions

In this paper, the influence of NaCl addition, up to very large concentrations, on the rheological properties of cetyltrimethylammonium p-toluenesulfonate (CTAT) solutions and their mixtures with two hydrophobically modified polyacrylamides (HMPAM) has been studied under simple shear. The CTAT concentrations employed were above the critical rod concentration. As salt is added to CTAT aqueous solutions, the zero-shear viscosity first increases, goes through a maximum, and at very high ionic strengths increases once more. The overlap concentration of worm-like micelles decreases as the concentration of NaCl increases. The results are explained by the salt addition-induced growth of worm-like micelles and salting out effects at the highest contents of NaCl. The influence of ionic environment on the rheological properties of CTAT with two HMPAM solutions with different contents of hydrophobic moieties was also studied under simple shear. When NaCl is added to HMPAM/CTAT solutions, the same trends observed in CTAT/NaCl solutions were repeated but the viscosity increases were largely magnified. The large viscosity enhancements with salt increments in HMPAM/CTAT solutions were explained by the formation of an interpenetrated network of hydrophobically modified polymer chains and worm-like micelles with hydrophobic sequences embedded within its structure.