In this presentation, I summarize recent experimental and theoretical studies from my group on the breakup and coalescence of polymer drops in a second immiscible polymeric fluid. A particular focus is the role of “compatibilizers” in these processes. Compatibilizers are typically di-block copolymers of the two bulk polymers, and thus they act as large surfactants insofar as the breakup and coalescence processes are concerned. Compatibilizers inhibit coalescence, and lead to major changes in the distribution of drop sizes when a drop is stretched by a flow and then breaks by capillary instability when the flow is stopped.
The effects of fluid elasticity in the flow of non-Newtonian fluids in microfluidic converging/diverging geometries are investigated. We investigate the structure and dynamics of inertio-elastic flow instabilities and elastic corner vortices which develop upstream of the contraction plane, and explore their dependence on the relative magnitudes of inertia and elastic stress generated by the high deformation rates in the contraction geometry. The results show that the shape, size and evolution of these flow structures varies with the elasticity number, which is independent of the flow kinematics and is only dependent on fluid properties (viscosity, density and polymer relaxation time) and the characteristic size of the channel.
We consider developments in small amplitude oscillatory-shear testing, from the advent of the first post second world war commercial rheometers to the present day. To facilitate such a survey, we concentrate on the case where the test fluid is contained between two plates, which are initially parallel and horizontal. In the earliest experiments, the bottom plate performed small amplitude torsional oscillations about a vertical axis, with the motion of the upper plate constrained by a torsion wire. Somewhat later, a new kind of rheometer appeared, in which both plates rotated with the same angular velocity about two axes, which were both normal to the plates, but not coincident, (the so-called ‘Orthogonal Rheometer’). This led to an impressive (but relatively short-lived) period of research activity, before the device fell out of favour. At about the same time, a ‘tilted-plate rheometer’ was proposed and the basic theory developed. However, there is no evidence that such a technique was ever investigated experimentally. In recent years, there has been a growing interest in the so called ‘Compressional’ technique, in which the bottom plate is stationary, while the top plate performs small amplitude oscillations in the vertical direction. Such a device is shown to have some advantages over the earlier techniques, especially at high frequencies. Of particular interest in the present study is the way that the effect of ‘fluid inertia’ has been accommodated in the various experimental techniques and some recent theoretical and experimental work carried out at the author’s laboratory on the Compressional instrument is discussed in detail.
A continuum theory of constitutive equation of co-rotational type is developed for the anisotropic viscoelastic fluid-liquid crystalline (LC) polymer. According to the new concept of anisotropic viscoelastic simple fluid, the stress tensor is considered as a functional on whole history of deformation gradient and hole history of spin tensor measured with respect to co-rotational coordinates. Using the concept and generalizing the co-rotational Oldroyd fluid B model, a continuum theory of constitutive equation of co-rotational type is developed for the fluid. The theory is specialized to constitutive equations of LCP-H model and LCP-Qs model. The orientational motion and the anisotropic material functions are introduced in the equation to describe behaviour of the anisotropic effects of LC polymer fluid. Using the equation analytical expressions of apparent viscosity, first and second normal stress differences and extensional viscosity are given which are in a good agreement with the experimental results. The bifurcation of extrusion-extensional flow is observed for the fluid flow.
The functional for minimization following from the upper bound theorem depends on the constitutive law chosen. The effect of simultaneous deformation of viscoplastic and rigid perfectly plastic materials on the mathematical formulation of upper bound solutions is studied. The results show that, in contrast to the conventional formulation in the theory of rigid perfectly plastic solids, it is in general impossible to get an upper bound of the load applied. Instead, an approximate value of this load can be found. The theory is illustrated by a solution for plane-strain compression of a three-layer strip between two parallel, rough plates.
To identify rheological constitutive model of geo-materials, one generalized constitutive law is applied. So, the problem of model identification is transformed to the problem of traditional parameters identification. According to the relationship of objective function and optimization methods, the global optimization method, such as evolutionary algorithm, is very suitable to solve parameter identification problems. A new fast-convergent genetic algorithm is applied in this study. In this new algorithm, there are only two individuals in one population. So, the whole computation efficiency of optimization back analysis will be very high. Using this new back analysis method, a real engineering example of one underground coal mine roadway is used to verify the computing ability of the algorithm to real problems. The results show that the efficiency of optimization back analysis can be improved greatly with this new algorithm.
Nearly 30 years ago the PTT constitutive equation for molten polymers and solutions was published, and since then it has been widely used. In the intervening time much progress has been made in polymer science and mechanics, especially via network and tube theories. It is natural to unite these points of view in a revisitation of PTT-type models. We show that a new improved form of the PTT model, called the PTT-X model, can closely describe, in particular, the rheological behaviour of low-density polyethylene in (steady and transient) shear and elongational flow and in recoil from an elongational stretch. The results of an attempt to reduce the number of parameters are also described and we place the new model within the context of general network theory and tube theory.
A general nonlinear slip of fluid flow at a solid surface is proposed in the present paper. The theoretical prediction shows that the slip length keeps as a constant (an initial slip length) at a small shear rate, then increases with the shear rate, and finally is approximately proportional to the slip velocity at a high shear rate. The nonlinear slips occurring at both of the simple flow in a parallel sliding system and a complex flow between two approaching spheres are investigated. It is found that the initial slip length controls the slip behavior at a small shear rate, but a critical shear rate controls the boundary slip at the high shear rate. Our theoretical predictions are in well agreement with the experimental measurements of boundary slips for both a simple fluid and a complex fluid.
The objective of this study is to well understand the migration and orientation of thin micro-particles, such as talc and mica, in a suspension flow by means of both experiments and numerical simulations as well as to obtain the knowledge of the processing operations of thin micro-particle reinforced composites. A slit channel was mounted on the sidewall of a large reservoir in the experimental setup. For this reason, the thin disk-like particles were subjected by a planar extensional flow in a reservoir, then by a simple shear flow through a slit channel. The evolution of the orientation of thin disk-like particles was studied in both a planar extensional and simple shear flows by numerical calculation of the Jeffery equation: thin disk-like particles aligned in the parallel orientation to the upper- and lower-walls of the slit channel in a planar extensional flow through the reservoir, then entered into the inlet of the slit channel. On the other hand, in a simple shear flow through the slit channel, the disk-like particles kept this parallel orientation except the occurrence of flip-over. The period of the flip-over became longer with a decrease in aspect ratio (thickness/diameter) of the disk-like particles. Furthermore, the measurements of the orientation of the talc particles in a suspension flow through the slit channel clearly showed that almost the same period of the flip-over was found in spite of different particle size. The experimental result arises from complex geometries and no accurate data of the thickness of talc particles.
Some distinctive computer technologies, which lead to multiscale computational experiments and investigations of peculiarities of micromechanical behavior of heterogeneous composite media, taking into consideration of atomic-molecular formations, were discussed. The results calculated by Monte-Carlo approach were considered as a perspective method for description of the important features of atomic and molecular texture and energetics of heterogeneous polymer media. The quantum-mechanical approach was discussed as the method for solutions of top problems of micromechanics of polymer composites, namely, an investigation of the interaction of soot model particle with non-terminated and H-terminated surface with segments of polymer chain with different chemical structures. The parallel technologies of calculations and supercomputer were used. Optimization of viscoelastic behavior of composite media such as rubbers leads to the procedure of identification. Validity of reinforcement effect on the basis of the relaxation properties analysis of materials seems very perspective.
The thixotropy-loop tests of a LDPE (PE-FSB-23D022/Q200) melt were described in the present paper by using the simplified Acierno-type constitutive equation, which was formed by a modified upper convected Maxwell model and a kinetic equation. The simplified Acierno model is a single-mode equation and only contains three parameters. The descriptions of the simplified Acierno model show partial agreements with the triangular-form thixotropy loop tests of the LDPE melt, in which the calculations of the model show agreement with the tests experiencing short- and medium-time shearing, but show some deviation with the experiment experiencing long-time shearing. The simplified Acierno model can reflect some typical viscoelastic properties of the melt.
The blood and tissue liquid flow are studied by microcirculation method or porous flow model. The blood flow in capillaries is studied by used the porous media flow model in this paper. The advantage of the model is to research the whole flow characteristics, and it can be used to study the blood flow in animal viscera. By used the Casson constitutive model, the differential equation of blood flow in capillaries is derived, and the characteristics of steady flow and transient flow are solved by numerical method. The result shows that the more threshold stress is, the bigger flow resistance is, and the flow is different from the newtonian fluid flow. This method is a new useful approach to study the biological fluid mechanics.
Characteristic rheological behaviors of polymer nanocomposites were studied in shear flow and uniaxial elongational flow. Solid-like plateau storage modulus, strong shear thinning at low frequency regions, and strain hardening at elongational flow were observed. Especially, strain hardening was clearly observed for polymers without long chain branches if nanoparticles were homogeneously dispersed in the polymer matrix and interactions between nanoparticles and surrounding polymer molecules were sufficiently strong. Reptation models were used to model the nanoscale dynamics of nanoparticles and macromolecular chains, and the characteristic rheological behavior of nanocomposites could be explained. Brownian dynamics simulation of Doi-Edwards reptation model was applied and two particle constraint coefficients were introduced to express the influence of nanoparticles on molecular orientation and reptational diffusion of polymer chains. In the simulation, stress tensor including link tension coefficient which characterizes anisotropic friction coefficient of the molecular chain was used to obtain material functions by assuming that the anisotropy of friction was altered by the presence of nanoparticles. Additional frictional force between polymer chains and nanoparticles was considered and the suitable relaxation process and chain stretch were incorporated by considering the full chain geometry of polymer molecular chains. All the reptation models considering the effect of nanoparticles were verified by comparing the theoretical results with experimental data for polymer nanocomposites in shear and elongational flows.
A mathematical model of the polymer solution flow in porous media is established with the different concentration distribution. The polymer solution is treated as the power law non-Newtonian fluid with its power law index depended on the concentration of the solution. The finite element method is used to solve the problem by considering the effects of the concentration distributions and the different boundary conditions on the process of pressure conduction. The wellbore pressure and pressure distribution have been determined. For the different case, the type curve of pressure and its derivate have been analyzed. Some in situ test data are analyzed to verify the new model by using the type curve matching method. The results show that the concentration distribution of the polymer solution in the porous media is clearly reflected by the power law indexes changed along the distance. The characteristic parameters of the porous media and the polymer solution distribution can be determined by analyzing the in situ test data. The new model has been extended to more complicated boundary cases.
Three-dimensional flows of liquid crystalline polymers in rectangular abrupt contraction and expansion channels were numerically analyzed using a modified Doi model as a constitutive equation. The orientational behavior of molecules was mainly investigated using the director and the orientational order parameter, and the relation between the orientational field and the velocity field was analyzed at several Deborah numbers De. In the contraction flow, flow aligning of molecules occurred in the main flow near the contraction owing to elongational flow. In the expansion flow, molecules near the mid-plane were aligned perpendicular to the flow direction just downstream of the expansion and this alignment related to a concave velocity profile appeared in this region. The order parameter increases just downstream of the expansion and the orientation more slowly relaxes along the flow for larger De. In addition, negative elongational flow downstream of the expansion causes a highly three-dimensional structure of directors called a twist structure.
A continuum theory of constitutive equation of co-rotational derivative type was developed for anisotropic viscoelastic fluid—liquid crystalline(LC) polymer. The theory was specialized to a constitutive equation of co-rotational type LCP-H model and LCP-Qs model. Using the constitutive equation of LCP-Qs model, the shear-extensional flow was studied for the extrusion process near the die exit of the fiber spinning of liquid crystalline polymer melt. Bifurcation of extensional viscosity was observed in the case without orientation and the two cases when the directors were parallel to flow and vertical to flow for the LC polymer melts. The extensional viscosity increases when the director rotates from the flow direction to that vertical to flow. Based on the LCP-Qs model a computational analytical theory was developed for extrusion process of LC polymer melt, contraction of the extrudate was predicted by the theory. The computational symbolic manipulation such as computer software Maple was used for the problem solution. An important conclusion can be drawn that the director tumbling has remarkable influence on extensional viscosity but no principal one on LC polymer melt extrusion.
A long-standing question is readdressed as to whether the viscoelasticity can have a measurable effect on lubrication characteristics in thin-film flows. Specifically, a perturbation method based on the upper convected Maxwell constitutive equation is employed to analyze thin-film flows of a non-Newtonian fluid between two surfaces. The results show that there is a significant enhancement on the pressure field in the presence of viscoelasticity when the minimum thin-film thickness is sufficiently small. This mechanism suggests that viscoelasticity does indeed produce a beneficial effect on lubrication characteristics, which is consistent with experimental observations.
A new variational principle is used to establish more reasonable finite element method, which set no limits to physical equations, that is, appropriate to general situations including elasticity, plasticity and rheology. According to theory of finite element method, tanking the Lagrange multiplier as unknown variables with unit joint stress, the corresponding calculating formula of the finite element method is derived. Through solving the equations about basic unknown variables, all unknown variables such as the strains and stresses in the whole solving area, can be work out. A problem about elastic body and a problem about Maxwell body are given and work out, and the results are both identical with the results in the corresponding literature. So the finite element calculating formula can be used to solve the problem of structure analysis with different stress-strain relations and may offer a new alternative way for some more complex problems, for example, the study on the elasticity-plasticity interface. And the other difference with the finite element calculation of common generalized variational principles is: the Lagrange multipliers are not determined beforehand, but to join in the calculating of finite element to get their physical meaning, the train of thought is more natural and the range for solving is expanded.
A new statistical approach to assessing the friction factor correlations was presented. Fourteen correlations, published from 1959 to 2003, were collected to calculate friction factors for power law fluids in turbulent pipe flow. A series of Fanning friction factors, f, were computed from these equations. Then the relations between the calculated values of f and ReMR (Metzner-Reed Reynolds number) were analyzed, when the rheological behavior index, n, was given. To verify the foregoing analysis result, in addition, the relations between the calculated values of f and n were analyzed, when ReMR was given. The f value calculated from each equation was compared with each mean value of all the f values from the 14 equations, when each combination (n, ReMR) (n ranging from 0.4 to 1.4 and ReMR from 4 000 to 100 000) was set. The comparison results were surveyed in the relative deviation table of the calculated f values. It shows that the overall mean relative deviation (OMRD) of the Dodge-Metzner correlation is the minimum, 1.5%. Therefore, the Dodge-Metzner correlation is recommended for predicting the friction factors for the turbulent pipe flow of power law fluids.
Translational motion of a single tiny spherical gas bubble subject to a weak acoustic standing wave field is studied both analytically and numerically assuming that the liquid surrounding the bubble is a viscoelastic fluid obeying the second-grade rheological model. Equations of motion are derived in radial and translational directions for this particular fluid model and shown to be coupled through the virtual mass effect. A perturbation analysis is carried out first to show that the natural frequency of a gas bubble is increased the higher the fluid’s elasticity. Fourth-order Runge-Kutta method is used to investigate the effects of a fluid’s elasticity on the bubble dynamics in the translational direction. It is shown that bubbles exhibiting erratic behavior in the translational direction for the case of Newtonian fluids can be stabilized provided that the liquid surrounding the bubble is sufficiently elastic.
The nonlinear iteration method of compelling displacement of boundary support was presented, combined with the nonlinear element method of space beam and Newton-Raphson nonlinear iteration, which can succeed flexibly in finding equilibrium configuration under complicated external loads. The relationship between space configuration of flexible pipe, constraint forces and active load by mining machine was studied. The result shows that the computing method is important to engineering.
The rheological properties of water-based magnetic fluids (MFs) were measured using rotating and capillary rheometers. It is found that the rheological behaviors of MFs with high solid content under an applied magnetic field can be described using the Herschel-Bulkley (H-B) model. Two-dimensional numerical simulation was performed to investigate ejection phenomena of the MF from a capillary with the H-B model. Experiments was conducted to observe drop formations. The measured numerical results are validated by the experimental findings.
Based on the widely used second-order essentially non-oscillatory(ENO) scheme, a modifying coefficient approach was defined on non-uniform mesh. By modifying its coefficient, without extending modifying coefficient ENO scheme’s stencil, a new scheme was obtained. The new scheme gives the accuracy of one higher order, and preserves most of the properties (Upwind, TVD and TVD etc) of the primitive ENO scheme. The numerical experiments show that modifying coefficient ENO scheme is more efficient and of higher accuracy in smooth regions when compared with ENO scheme.
Flow properties such as viscosity and gel point of waxy crude oils, particularly the beneficiated waxy crude oils, are sensitive to shear history that the crude oil experienced, called the shear history effect. To understand quantitatively this shear history effect is necessary to oil pipeline design and operation. For experimental simulation of the shear process during pipelining, shear rates of turbulent pipe flow, and flow through centrifugal pumps and throttle valves are necessary. Stirred vessels are usually used for shear simulation in laboratory, therefore, shear rate in the stirred vessels has to be known before shear simulation. Based on relationship between energy dissipation rate and the shear rate, approaches are developed and presented for calculation of shear rates in the above-mentioned specific flows. Combined with the entropy generation due to viscous flow in the shear process, which has been proved to be a proper parameter for simulation of the shear history effect, the shear history effect on viscosity and gel point of the beneficiated waxy crude oils has been experimentally simulated accurately.
An experimental study was performed on two-phase pressure drop of gas/non-Newtonian liquid systems in co-current horizontal flow. The effects of superficial velocities and polymer concentrations on two-phase pressure drop were investigated. A total of 180 experimental tests were conducted for the following conditions: superficial liquid velocity from 0.18 m/s to 1.42 m/s, and superficial gas velocity from 0.13 m/s to 2.59 m/s. The results show that the drag reduction will occur when the value of flow behavior index, n, is smaller than 0.6, and the lower the value of n is, the greater the effect of drag reduction will be.
A set of experimental equipment was established for falling film evaporation. The aqueous CMC (carboxymethylcellulo) solution was used to simulate the non-Newtonian fluid that obeys the power law model. Effects of rheology of the non-Newtonian fluid on heat transfer were investigated experimentally. A theoretical model was developed and coupling characteristics between rheology and heat transfer were described in non-Newtonian environmental fluid falling film in evaporation process. The different theoretical models were established for the developing region and the fully developed region in this evaporation process, respectively. Using finite difference method and shooting method, the simulated calculations were obtained. Furthermore, by introducing the generalized Reynolds number and the Prandtl number, which includes the necessary physical properties of the non-Newtonian fluid, a correlation about the Nusselt number was proposed for non-Newtonian fluid falling film in evaporation process.
The rheological properties of solution of polyethersulfone(PES) in dimethyl sulfoxid(DMSO) were investigated on a HAAK RS150 cone-and-plate rheological instrument, including the dependence of non-Newtonian Index, apparent viscosity, zero shear viscosity on concentration and temperature of the solutions. Apparent viscosity ηa at same shear rate increases with increasing PES concentration. Non-Newtonian Index n decreases with increasing concentration and increases with increasing temperature. Zero shear viscosity decreases in an index manner with increasing temperature. When PES content is 24%(mass fraction), amount of macromolecule tangling points of solution is near saturation value. Tangling points do not increase or increase little with increasing PES concentration so that the flow activation energy Eη changes little.
A capillary rheometer operating at prescribed temperature and pressure was set up. The measurement principles of the capillary rheometer were introduced. The equipment constant was obtained using standard liquids (e.g. water with known viscosity), and the rheometer was thus calibrated. The different carrier liquids viscosities of Fe3O4 magnetic fluid (MF) were measured at different flow rates. The experimental data were compared with the results of a theoretical equation derived in this study. Finally, the effect of temperature was investigated. Due to the effect of different carrier liquids, xylene-based and silicon oil-based MF show Newton behavior, but the hydroxyethyl-cellulose (HXC)-based MF shows non-Newton behavior of shear thinning. The difference between the experimentally measured viscosity and the theoretical prediction is lower for dilute MF, whereas, the difference is large for highly concentrated MF. The viscosity decreases quickly with the increase of temperature.
Polycrystalline PbZr0.52Ti0.48O3 (PZT) thin films with different thicknesses were prepared by metal-organic decomposition (MOD) at different thermal decomposition temperatures, and their effective elastic constants were evaluated with X-ray diffraction (XRD) techniques. The relative intensities of textures in the thin films were analyzed from XRD patterns, and the effective elastic constants were calculated by averaging over orientations according to the relative intensities. On the other hand, Gaussian distribution functions were used to fit the normalized intensities of (001) pole figures, and the effective elastic constants of PZT thin films were calculated according to the grains’ orientation distribution described by Gaussian distribution functions. The results show that the effective elastic constants of PZT polycrystalline thin films evaluated by XRD patterns are in good agreement with those evaluated by pole figures, and the differences are within 10%. The effective elastic constants of PZT thin films are greatly affected by the thermal decomposition temperature, while the effects of thickness of thin films are relatively small.
The focus of rheology is generally on shearing because shear is the dominant mode of deformation in most transport processes. At the same time, there are processes in which extension is the dominant motion, and then the rheological challenge is to characterize fluid resistance to extensional deformation. While extensional motion is important in polymer processes such as film blowing and extrusion, this work focuses on extensional motion of solutions and suspensions primarily because extensional motion of these fluids is all printing and coating processes, including roll coating and inkjet printing. In this paper, the state of extensional rheometry is briefly reviewed and then a new technique to measure extensional flow resistance is introduced.
New methods must be developed in order to access rheology’s full potential. The tools that allow a researcher (or student) to move freely and rapidly between the most advanced rheological theories, or between experimental data and theory are envisioned. This combination would enable him/her to reach a deeper understanding of rheology. The Amherst rheology platform(ARP) intends to facilitate this valuable process. ARP connects dedicated software modules, which perform calculations and return the corresponding results to the graphics screen of ARP. The experimental part of ARP has been completed, and the ARP implements the most powerful tools of data analysis. In addition, rheology experts have begun to write theory modules that seamlessly connect into ARP; several modules are complete and more are in progress.
For describing anisotropic behaviour of the material, thermotropic and lyotropic liquid crystalline polymers were investigated by polariscope to take microstructural photos. Experimental investigation on the rheological and rheo-optical behaviour of the HPC was reported. The HPC was used in a extrusion test, a small contraction, nearly planar extrudate and resonance instability due to shear disturbance were observed when the lyotropic LC polymer HPC solution was extruded. A simple stability theory of orientational motion of director vector was developed for the LC polymer fluid that extended flow of thermotropic LC polymer melts is very effective in producing a high degree of macroscopic orientation.
Melt of a segmented block copolymer constituting of poly (lauryl lactam) as the hard segment and poly (tetramethylene oxide) as the soft segment was investigated by rheological techniques. Storage modulus of the polymer melt exhibits the non-terminal behavior resembling those of diblock and triblock copolymer melts, indicating the existence of a microphase separated structure. Contrarily to most block copolymers, the melt of the segmented block copolymer transforms from a weak structure to a stiff one upon raising temperature. Atomic force microscopic data in tapping mode reveal that at low temperatures the structure of the melt is constituted of small spherical soft domains dispersed in a hard matrix and the hardness of the matrix differs slightly from that of the domains; at high temperatures the spherical domain structure preserves but the domain becomes larger and so does the hardness difference between the domain and the matrix. Infrared spectrum analysis shows that the temperature induced structural change is related to the dissociation of hydrogen bonding between the hard and the soft segments.
The stress relaxation behavior of polypropylene (PP) was investigated at room temperature. Displacement controlled experiment was simulated using engineering computational software ANSYS and performed on PP. Both results were compared with each other. The utility of numerical simulation was also discussed. The experiment results are well in agreement with the numerical ones.
The current models for the entanglement dynamics of flexible polymers are mostly based on the molecular picture of dynamic tube dilation (DTD). The full-DTD picture, assuming the equivalence of the relaxed portions of the chains and a simple solvent at any time t, fails for binary blends of long and short linear polyisoprene (PI) chains at intermediate t, as revealed from comparison of viscoelastic and dielectric data. In contrast, the partial-DTD picture considering the extent of DTD determined by the constraint release (CR) process gives much better description of the data. The failure of the full-DTD picture and success of partial-DTD picture are noted also for star-branched PI chains. The partial-DTD picture, achieving consistent coarse-graining of the length and time scales, would serve as a good starting point for constructing refined models.
Melt compounding with a twin-screw extruder was used to prepare exfoliated polypropylene (PP) nanocomposites of organophilic montmorillonite clay compatibilized with maletaed polypropylene (PPgMA). Several grades of PPgMAs of different melt flow indices (MI) and molecular masses were analyzed for the effectiveness of melt exfoliation of organoclay. The extent of clay exfoliation in the nanocomposites was confirmed by X-ray diffraction spectroscopy. It was found that the nanoscale dimensions of the dispersed clay platelets led to significantly increased oscillatory shear flow properties. At a clay loading of 5%(mass fraction), which is much smaller than that of conventional macrocomposites, the hybrid materials exhibited unbound increase of shear viscosity at low frequencies; and nonterminal low-frequency plateau in the linear storage modulus. The relative dynamic properties revealed a systematic trend with the state of exfoliation and dispersion in the nanocomposites.
The linear Mohr-Coulomb and nonlinear Hoek-Brown failure criteria, which neglect the effects of intermediate principal stress, are widely used in soil and rock engineering. However, much experimental data shows that the failure envelope relates to the intermediate principal stress. Employing the failure criterion and the generalized plastic potential function, the stability of rock cavity driven in an isotropic and homogeneous medium was investigated under the condition of plane strain considering the effects of intermediate principal stress. The closed-form solutions for stresses and displacement around a rock cavity were given in the elastic and plastic zones. Based on the closed-form solutions, the intermediate principal stress has an important effect on cavity stability.
The rheological behavior and wall slip phenomena in the shear flow of a commercial polymethylvinylsiloxane (PMVS) and a high density polyethylene (HDPE) were studied by using a rotary rheometer with parallel plates fixtures. The damping function obtained from the stress relaxation experiment was compared with the prediction results of Doi-Edwards theory with the independent alignment approximation (IAA) and that of Marrucci et al model. Wall slip phenomena in the steady shear flow for PMVS and HDPE were studied by checking the gap dependence of the shear-stress and shear-rate relation. The results show that when strain grows, the discrepancy between the experiment and theory increases probably in that single reptation considered is not enough for polydisperse systems. As the strain applied in stress relaxation increases, more than one peak stress values are obtained, suggesting that strain localization or stratified strain may occur inside the samples. In the shear stress range from 100 to 5 000 Pa, anomalous slip behavior can be observed for PMVS, while no obvious slip for HDPE.
Relaxation behavior and shear-induced isothermal crystallization of two commercial high-density polyethylenes (HDPE) were investigated by using a rotational rheometer with cone-plate configuration. The excessive free energy was estimated by the measured shear stress and the first normal stress difference, based on a model proposed by Marrucci, in which the molecular orientation brought about by shearing was responsible for the increase of free energy. The results show that a small change of free energy can significantly increase the crystallization rate, thus the induction time of crystallization decreases rapidly as the shear rate increases. The excessive free energy and the induction time of isothermal crystallization can be correlated by an exponential function.
This paper presents experimental observations and numerical simulations of six polyethylene melts with different molecular structures in the planar flow with a confined slit. The polyethylene melts investigated include three low-density polyethylene grades (LDPE), two high density polyethylene grades (HDPE), and one linear low density polyethylene (LLDPE). The objectives are to reveal the differences in the rheological and processing flow properties of these polyethylene melts, and correlate those properties with their molecular structures. Through this study, the author would also like to present a successful approach using simple shear data, in terms of a Wagner integral constitutive equation, to predict processing flow behaviors of polymer melts at a reasonable accuracy.
The influence of relative molecular mass (MM) of LLDPE on the rheological, thermal and mechanical properties of two sets of m-LLDPE/HDPE blends of low and high branch content (BC) was studied. Blends of m-LLDPE with linear HDPE reveal no influence of MM (60–100 kg/mol) on melt miscibility at low BC (about 20 branches/1 000 C). However, at high BC levels (about 40 branches/1 000 C), MM affects the melt miscibility of m-LLDPE/HDPE blends. The DSC results suggest that compatibility in the solid state is independent of MM and BC. For all blends studied, the HDPE-rich blends are found to contain single crystal populations, suggesting high degree of cocrystallization, whereas, m-LLDPE rich phase shows separate crystallization. Mechanical properties of these blends are found to be a strong function of blend compatibility and the specific properties of the blend components. In general, the high BC pairs show poor mechanical properties.
A tree gum which is mainly composed of natural heteropolysaccharides, namely PG gum, was presented. The rheological characteristics of PG gum based drilling fluids at different concentrations and aging temperatures were studied by means of a rotating rheometer. The effects produced by the addition of inorganic salts (NaCl and CaCl2) on the rheological properties of PG gum based drilling fluids were also studied. The results show that PG gum based drilling fluids investigated behaves as non-Newtonian shear-thinning fluids. With the increase of PG gum concentrations from 0.5% to 2.5%, the consistency coefficient increases while the viscosity behavior index decreases. The aging experimental data indicate that temperature has a slight effect on the rheological properties of PG gum based clay suspensions when the aging temperature is below 120 °C. Whereas, when temperature is above 120 °C, the rheological parameters of the suspensions, containing apparent viscosity, plastic viscosity and yield point, decrease significantly. The PG gum shows a better resistance to an increase in salinity or divalent cations concentration.
A thermotropic liquid crystalline polymer (TLCP) based on hydroxybenzoic acid, hydroquinone and sebacic acid was used as a processing aid in the extrusion of high molecular mass polyethylene (HMMPE)/clay nanocomposites. Clay/TLCP with optimal mass ratio loading in HMMPE matrix has better thermal stability than that of clay or TLCP blends. Capillary rheometry experiments were carried out at processing temperature 190 °C with TLCP in the full nematic phase. TLCP is an effective processing aid agent with viscosity reduction in excess of 95%. The mechanism is proposed and analyzed by morphological study and surface analysis. TLCP has been shown to act as both a compatiblizer between nanoclay and the HMMPE matrix and a processing aid for the nanocomposite.
Organoclay was dispersed in polystyrene of five different relative molecular mass by melt blending. Melt rheology was used to screen the resulting nanocomposite samples for a plateau in the elastic modulus G′. Presence of this plateau behavior indicates a solid-like network in the blend, brought about by dispersion of the organoclay. Using the values of the G′ plateaus for the PS blends, a percolation theory was tested for the nanocomposites and two solvent/organoclay blends. Lowering the blending temperature to take advantage of high mixing viscosity and subsequent high mixing stress allowed for stronger networks to be formed than when processing conditions favored increased diffusion. A constant viscosity mixing study shows that the relative molecular mass is the most prominent variable affecting dispersion in PS nanocomposites and has reaffirmed the importance of stress over diffusion. By applying high stress to 18 kg/mol PS with 1% organoclay, we were able to disperse the clay to an aspect ratio of 60. Several master batching methods and PS-NH2 compatibilizer were also considered.
An experimental study was carried out to investigate phase and flow behavior of hydrophobically modified hydroxyethyl cellulose (HMHEC) solution with or without nonionic surfactant C12E5. Shear thickening behavior is observed at moderate shear rates for pure HMHEC solutions at modest concentrations. Shear thickening becomes less significant with increasing temperature and disappears at temperature reaching 25 °C for 0.2%(mass fraction) HMHEC. Also, the shear rate at which the maximum viscosity occurs increases with temperature. Addition of a very small amount of C12E5, even below its critical micellar concentration, can promote the thickening and the strongest thickening occurs at around 6×10−5(mass fraction) C12E5. A further addition, however, can suppress the thickening phenomenon that eventually disappears at high enough C12E5 concentrations. It therefore implies that when the surfactant reaches a certain amount and starts to weaken the gel strength, the imposed flow can no longer enhance the networking. While the pure HMHEC solutions always remain a single phase, phase separation takes place for polymer-surfactant mixtures when the C12E5 concentration exceeds about 1.5×10−4.
The rheological characteristic of polymer solution directly influences the oil displacement efficiency in the process of polymer flooding, and it is necessary that rheological characteristics of polymer solution used in polymer flooding are researched. Loss modulus and storage modulus of polymer solution with different mass concentration and relative molecular mass are studied and the relationship between them is analyzed through steady and dynamic shear experiments. The first normal stress difference at low angular rate is calculated based on loss modulus and storage modulus, and combined with the first normal stress difference obtained by steady shear flow experiments at high shear rate. The first normal stress differences at a wider range of shear rate can be obtained and the relationship between the first normal stress difference and shear rate is set up. The results show that the relationship established between the first normal stress difference and shear rate at wide range shear rate is feasible. The higher the mass concentration or the relative molecular mass of polymer solution is, the higher the first normal stress difference coefficient is.
The small-deformation shear behavior at 25 °C of 1%–4%(mass fraction) cross-linked waxy corn starch (CWCS) and 0.5%(mass fraction) κC mixtures with and without KCl were studied. Dispersions were heated (1.5 °C/min) to 90 °C, held for 10 min, then cooled (1.5 °C/min) to 90 °C. When the volume fraction of CWCS is about 0.5 to 0.7, the rheological behavior is governed by the continuous phase, while above these values the disperse phase dominates the rheological behavior. When carrageenan is in a disordered state without KCl, the swollen granules are dispersed in a macromolecular solution. With KCl, the rigidity of the gels increases by effect of CWCS, carrageenan and salt concentrations. However, salt concentrations above 100 mmol/L lead to a marginal increase in rigidity. Results can be interpreted in terms of two types of systems: particles suspended in a macromolecular solution and composite gels of particles embedded in a network matrix when both κC and KCl were added.
An equimolar mixture of a cationic surfactant, cetylperidinium chloride (CPyCl) and the salt sodium salicylate (NaSal) forms wormlike micelles in aqueous solutions. Under shear, the solution shows a pronounced shear-thickening behavior, which is coupled with oscillations in shear rate and the apparent viscosity. In this shear-thickening regime the formation of shear-bands is observed, which also oscillate in position and intensity. Fast Fourier Transformations (FFT) of the oscillating shear rate and intensity signals show a single dominating frequency in the power spectrum analysis. This characteristic frequency as well as the amplitude of shear rate oscillation is found to increase with stress. Experiments performed in transparent parallel-plate geometry show dampening of the shear rate oscillations and increase in the characteristic frequency with decrease in the gap. Rheo-small angle light scattering and rheo-optical techniques confirm the formation of different kinds of structures at smaller gaps.
A theoretical analysis of the phenomenon of boundary layer separation flow in power law pseudoplastic non-Newtonian fluids was made. Bifurcation solutions for skin friction were numerically represented for parameters of velocity ratio and power law exponent. The results indicate that both superior and inferior solutions are noticeable and the solutions not only depend on the velocity ratio of the plate to the velocity of the free stream, but also on the power law parameter.
The steady-state rheological properties of poly (m-phenyleneisophthalamide)(PMIA) in 1-n-butyl-3-methylimidazolium chloride [Bmim]Cl and DMAc/LiCl solutions are presented. The polymer in the concentration range investigated exhibits very different behavior between [Bmim]Cl and DMAc/LiCl solutions. Unlike in DMAc/LiCl solvent, PMIA/[Bmim]Cl solution exhibits maxima in apparent viscosity-concentration plots in the range studied. PMIA shows wormlike chain model when dissolved in DMAc/LiCl while the rodlike chain model in [Bmim]Cl. The different rheological behavior shows polymer-ionic liquids interaction which leads to the supermolecular aggregates in PMIA/[Bmim]Cl solution.