Linear rheology of viscoelastic emulsions with interfacial tension

Emulsions of incompressible viscoelastic materials are considered, in which the addition of an interfacial agent causes the interfacial tension to depend on shear deformation and variation of area. The average complex shear modulus of the medium accounts for the mechanical interactions between inclusions by a self consistent treatment similar to the Lorentz sphere method in electricity. The resulting expression of the average modulus includes as special cases the Kerner formula for incompressible elastic materials and the Oldroyd expression of the complex viscosity of emulsions of Newtonian liquids in time-dependent flow.     

Concentration dependence of the linear viscoelastic properties of particle suspensions

The response under small amplitude oscillatory deformations of a suspension of non-Brownian spheres dispersed in a viscoelastic fluid is investigated. The correspondence principle of linear viscoelasticity is used to derive a simple constitutive model from a model for a suspension in a Newtonian liquid. The theory predicts that for a specific particulate system the concentration dependence of the viscoelastic properties should collapse to a single master curve when the values are normalized with those of the carrier fluid alone. Measurements with the micro-Fourier rheometer using oscillatory squeeze flow are carried out on two suspensions of 60 and 80 μm sized particles dispersed in polymeric fluid and in silicon oil, and the master curve is verified. Received: 27 April 1999/Accepted: 15 October 1999     

A differential model for the rheological properties of concentrated suspensions with weakly viscoelastic matrices

A model for the rheological properties of a concentrated suspension in weakly viscoelastic fluid matrices is proposed. The model is derived according to the Roscoe differential procedure described in 1952. The analytical results produced recently by Greco et al. (J Non-Newton Fluid Mech 147:1–10, 2007) and Housiadas and Tanner (J Non-Newton Fluid Mech 162:88–92, 2009) for dilute suspensions of neutrally buoyant, non-Brownian rigid spheres in weakly viscoelastic matrix fluids are the key results which are used as a base to predict the properties of concentrated suspensions. The results are compared with the few available experimental data from the literature, showing promising trends for the viscometric properties of the suspensions. In particular, one sees the rapidly increasing value of −N₂/N₁ as concentration increases.     

Linear viscoelastic analysis using frequency-domain algorithm on oscillating circular shear flows for bubble suspensions

To achieve a stable evaluation of the linear viscoelasticity of bubble suspensions, which have difficulties for conventional rheometers from spatial distributions of rheological properties with bubble deformations, we proposed a novel rheometry based on spatio-temporal velocity data obtained by ultrasonic velocity profiling (UVP). A frequency-domain algorithm was adopted to overcome a critical influence of measurement noise on the rheological assessment, which is inferred from error propagation characteristics through the equations of motion in discretized form. Applicability and advantage of the present rheometry with the frequency-domain algorithm were verified by two kinds of fluids: high viscous oil as a Newtonian fluid and polyacrylamide aqueous solution as a shear thinning, viscoelastic fluid. The rheometry was finally adopted for bubble suspensions subject to high oscillatory shear, and it could validly extract elasticity-originated momentum transfer as a function of space.     

The normal stress behaviour of suspensions with viscoelastic matrix fluids

 We investigate the variations in the shear stress and the first and second normal stress differences of suspensions formulated with viscoelastic fluids as the suspending medium. The test materials comprise two different silicone oils for the matrix fluids and glass spheres of two different mean diameters spanning a range of volume fractions between 5 and 25%. In agreement with previous investigations, the shear stress–shear rate functions of the viscoelastic suspensions were found to be of the same form as the viscometric functions of their matrix fluids, but progressively shifted along the shear rate axis to lower shear rates with increasing solid fraction. The normal stress differences in all of the suspensions examined can be conveniently represented as functions of the shear stress in the fluid. When plotted in this form, the first normal stress difference, as measured with a cone and plate rheometer, is positive in magnitude but strongly decreases with increasing solid fraction. The contributions of the first and the second normal stress differences are separated by using normal force measurements with parallel plate fixtures in conjunction with the cone-and-plate observations. In this way it is possible for the first time to quantify successfully the variations in the second normal stress difference of viscoelastic suspensions for solid fractions of up to 25 vol.%. In contrast to measurements of the first normal stress difference, the second normal stress difference is negative with a magnitude that increases with increasing solid content. The changes in the first and second normal stress differences are also strongly correlated to each other: The relative increase in the second normal stress difference is equal to the relative decrease of the first normal stress difference at the same solid fraction. The variations of the first as well as of the second normal stress difference are represented by power law functions of the shear stress with an unique power law exponent that is independent of the solid fraction. The well known edge effects that arise in cone-and-plate as well as parallel-plate rheometry and limit the accessible measuring range in highly viscoelastic materials to low shear rates could be partially suppressed by utilizing a custom- designed guard-ring arrangement. A procedure to correct the guard-ring influence on torque and normal force measurements is also presented. Received: 20 December 2000 Accepted: 7 May 2001     

Non-linear viscoelastic behavior of fumed silica suspensions

Suspensions of fumed silica exhibit a wide range of rheological properties depending on the nature and magnitude of the interparticle forces. In a non-polar fluid, the particles interact through hydrogen bonding and can form a three-dimensional network. The microstructure formation is responsible for the non-linear viscoelastic behavior of fumed silica suspensions, even at very small strain. These non-linear rheological properties have been studied in small amplitude oscillatory experiments as a function of particle size, surface treatment of particles, suspending medium polarity and solids concentration. The non-linear viscoelastic behavior is characterized by a non-sinusoidal waveform of the signal response. For suspensions in a non-polar fluid, both the elastic and the loss moduli are shown to be sensitive to the strain amplitude: the elastic modulus is decreasing with increasing strain whereas the loss moduli is initially increasing with strain. We have chosen to examine the dissipated energy which is clearly related to the breakup of the suspension structure. A comparison of model predictions and the experimental data shows the limitations of these models, recently proposed in the literature to describe the behavior of colloidal suspensions. Received: 9 March 1998 Accepted: 17 November 1998     

Linear and non-linear viscoelastic properties of ethylene vinyl acetate/nano-crystalline cellulose composites

This paper reports on the melt rheological properties of ethylene vinyl acetate containing between 0 and 10 wt.% of nano-crystalline cellulose (NCC). A complete set of rheological tests including frequency sweeps, shear transients, and uniaxial elongations was performed. Frequency sweeps showed that at low frequencies, a pseudo solid-like behavior was obtained for NCC concentrations higher than 5%. This behavior was related to hydrogen bonding between NCC particles and the creation of particle networks as the result of particle–particle interactions. For transient shear tests, all compositions presented a stress overshoot at high shear rates before reaching a steady state. It was found that the amplitude of this overshoot depends on both NCC content and shear rate. On the other hand, the time to reach the maximum was found to be highly shear rate dependent but concentration dependence was rather weak. For uniaxial extensional flow, higher extensional viscosity was observed with increasing NCC content. On the other hand, strain hardening was found to decrease with increasing NCC content.     

Electrorheology of dilute suspensions induced by hydrodynamic instability

The viscosity behavior in electric fields was measured for dilute suspensions of p-[perfluoro(2-isopropyl-1,3-dimethyl-1-butenyl)oxy]benzoic acid particles (PFNA) in silicone oils. The application of electric fields causes a viscosity increase in a wide range of shear rates. Since the electrorheological (ER) effect is much stronger at low shear rates, the flow becomes shear-thinning. However, contrary to conventional ER suspensions which are reversibly converted between Newtonian fluids and Bingham solids, the PFNA suspensions are fluids even in electric fields. When the particle concentration is increased to 5 wt.%, the ER effect reaches saturation. Further increase does not contribute to additional viscosity enhancement. These results cannot be explained through the chain formation mechanism established for conventional systems. After the ER experiments, the bob surface of the rheometer is covered with several stripes of aggregated particles. Although the strength of electric and shear fields is constant in the rheometer, the periodic structure may be formed in the flow of electrified suspensions. When a dielectric liquid is subjected to high electric fields, the secondary motion of liquid can be induced by the Coulomb force acting on free charge. The electrohydrodynamic (EHD) convection is responsible for the periodic distribution of particles concentration. The ER effect of PFNA suspensions may be generated by a combined effect of EHD convection and external shear.     

Bulk rheology of dilute suspensions in viscoelastic liquids

A theoretical relation is derived for the bulk stress in dilute suspensions of neutrally buoyant, uniform size, spherical drops in a viscoelastic liquid medium. This is achieved by the classic volume-averaging procedure of Landau and Lifschitz which excludes Brownian motion. The disturbance velocity and pressure fields interior and exterior to a second-order fluid drop suspended in a simple shear flow of another second-order fluid were derived by Peery [9] for small Weissenberg number (We), omitting inertia. The results of the averaging procedure include terms up to orderWe ². The shear viscosity of a suspension of Newtonian droplets in a viscoelastic liquid is derived as $$\eta _{susp} = \eta _0 \left[ {1 + \frac{{5k + 2}}{{2(k + 1)}}\varphi - \frac{{\psi _{10}^2 \dot \gamma ^2 }}{{\eta _0^2 }}\varphi f_1 (k, \varepsilon _0 )} \right],$$ whereη ₀, andω ₁₀ are the viscosity and primary normal stress coefficient of the medium,ε ₀ is a ratio typically between ?0.5 and ?0.86,k is the ratio of viscosities of disperse and continuous phases, and \(\dot \gamma \) is the bulk rate of shear strain. This relation includes, in addition to the Taylor result, a shear-thinning factor (f ₁ > 0) which is associated with the elasticity of the medium. This explains observed trends in relative shear viscosity of suspensions with rigid particles reported by Highgate and Whorlow [6] and with drops reported by Han and King [8]. The expressions (atO (We ²)) for normal-stress coefficients do not include any strain rate dependence; the calculated values of primary normal-stress difference match values observed at very low strain rates.     

On viscous flow and effective viscosity of concentrated suspensions and emulsions

Summary Previous analysis byHappel (3) of viscous flow in concentrated solid suspensions has been extended to include concentrated emulsions of slightly deformable fluid particles in the presence or absence of surfactant impurities.General expressions were obtained for viscous flow in multi-particle systems when arbitrary shear fields are imposed. Specific relations were then derived for uniform,Couette and hyperbolic fields. The behavior is found to be strongly dependent upon particle concentration and surfactant concentration. The theoretical expressions obtained for effective viscosity of emulsions compare favorably with experimental data ofNeogy andGhosh (18),Sibree (15),Sherman (17), andBroughton andWindebank (16). These results support other studies on ensemble velocities [(10), (12), and in particular (22)], which strongly indicate the practical value and factual reliability of cell models in predicting the behavior of suspensions and emulsions.     

Behavior of viscoelastic glass bead suspensions under superposed flows

Parallel superposed flows may be useful in order to explain the rheological behavior of viscoelastic suspensions. It has been shown that relaxation times of molecules are affected by a combined flow, and the rheological behavior of glass bead suspensions in a viscoelastic medium is explaned in terms of such variations.     

Singularity solutions for ellipsoids in low-Reynolds-number flows: With applications to the calculation of hydrodynamic interactions in suspensions of ellipsoids

The disturbance velocity fields due to translational and rotational motions of an ellipsoid in a uniform stream. constant vorticity and constant rate-of-strain. required in fundamental studies of behavior of suspensions. have been obtained by the singularity method. These solutions extend earlier solutions for prolate spheroids. Although equivalent solutions problems were obtained by Oberbeck. Edwardes and Jeffery by separation of variables in ellipsoidal coordinates. the singularity solutions are far more simple in form. Other significant results obtained by the singularity method include the exposition of the unified structure shared by the three boundary value problems and the construction of new forms of the Faxen laws for ellipsoids through application of the reciprocal theorem. The disturbance solutions and Faxen laws. the basis for Smoluchowski's method-of-reflections technique. are used to calculate hydrodynamic interactions between two or more arbitrarily oriented ellipsoids. In particular. mobility problems are solved directly to orderR⁻⁵. whereR is the centroid-to-centroid separation between the ellipsoids.     

Rheology of polymer blends: linear model for viscoelastic emulsions

 Kerner's model for flow of composite elastic media is extended to an emulsion of viscoelastic phases with interfacial tension undergoing deformations of small amplitude. A privileged internal structure inside the suspended drops is discussed in terms of fluid circulation across the interface. It is shown that for usual drop radius and interfacial tension values of emulsions, the rheological behavior predicted by the model, with very simple expression for the complex shear modulus, is quantitatively similar to that predicted by Palierne's model. Predictions of the model are compared with experimental data obtained on a polystyrene/polyethylene blend sheared in a small-amplitude oscillatory mode. Received: 10 August 1998 Accepted: 18 December 1998     

Linear viscoelastic behavior of the Hookean dumbbell with internal viscosity

The linear viscoelastic modulus G(t) predicted by the analytical formulations of Schieber (1993), Wedgewood (1993), Dasbach et al. (1992), and Booij and van Wiechen (1970) for the free-draining Hookean dumbbell with internal viscosity (IV) are compared with exact analytical results and exact numerical results obtained from Brownian dynamics simulations. All of these analytical formulations employ the Booij and van Wiechen expression for the IV force, thereby eliminating errors associated with linearization of the deformational velocity, however the theories differ in the approximations employed to solve configuration moment equations. Comparison with the exact G(t) results provides a means of testing these approximations. The approximate theories all correctly predict the singular part of G(t) at t = 0, providing correct predictions of , however deviations from the exact G(t) are seen in all cases for t > 0.     

Non-linear viscoelastic response of magnetic fiber suspensions in oscillatory shear

This paper reports the first study on the large amplitude oscillatory shear flow for magnetic fiber suspensions subject to a magnetic field perpendicular to the flow. The suspensions used in our experiments consisted of cobalt microfibers of the average length of 37 μm and diameter of 4.9 μm, dispersed in a silicon oil. Rheological measurements have been carried out at imposed stress using a controlled stress magnetorheometer. The stress dependence of the shear moduli presented a staircase-like decrease with, at least, two viscoelastic quasi-plateaus corresponding to the onset of microscopic and macroscopic scale rearrangement of the suspension structure, respectively. The frequency behavior of the shear moduli followed a power-law trend at low frequencies and the storage modulus showed a high-frequency plateau, typical for Maxwell behavior. Our simple single relaxation time model fitted reasonably well the rheological data. To explain a relatively high viscous response of the fiber suspension, we supposed a coexistence of percolating and pivoting aggregates. Our simulations revealed that the former became unstable beyond some critical stress and broke in their middle part. At high stresses, the free aggregates were progressively destroyed by shear forces that contributed to a drastic decrease of the moduli. We have also measured and predicted the output strain waveforms and stress–strain hysteresis loops. With the growing stress, the shape of the stress–strain loops changed progressively from near-ellipsoidal one to the rounded-end rectangular one due to a progressive transition from a linear viscoelastic to a viscoplastic Bingham-like behavior.     

Influence of disperse phase concentration upon the viscoelastic behaviour of emulsions

Rheology of soya oil-water emulsions in the linear region has been studied. The viscoelastic response consisted of three contributions. There was a purely elastic component, a purely viscous component and a contribution due to the retarded compliance. Emulsions became more viscous and elastic with increasing soya oil concentration. Sharp changes in rheology were observed as the concentration approached the random close packed limit. There was also a marked increase in zero-shear viscosity. Breakdown of coagulation structure was observed as the shear stress was increased into the non-linear region. The rheological behaviour of the emulsions in the linear region could be adequately described by the generalized Kelvin-Voigt model.     

Linear viscoelastic behavior of asphalt and asphalt based mastic

The rheological properties of an asphalt mastic and its matrix are investigated. For the purpose of comparison a sample of thermal aged asphalt matrix is also considered. Dynamic and creep shear measurements are reported. The reduced shear rate concept proposed by Ohl and Gleissle is used to correlate mechanical properties of the three materials at the same temperature. We found that the concept gives only qualitative trends. A similar conclusion is found concerning the applicability of the time-temperature superposition principle for each sample. Our experimental results show also that the increase in viscosity due to thermal treatment or to the inclusion of solid particles is not uniform with temperature. The differences in the increase of the Vogel temperature from the asphalt to the mastic, or to the thermally aged asphalt, relate to the different mechanisms involved. Sedimentation of steel spheres in asphalt and mastic, is studied next. The Newtonian wall correction factor for the Stokes drag law holds for the three samples. Despite the similar behavior observed in conventional shear tests, Stokes' law gives the correct trend for the two asphalts although it overestimates the experimental settling velocity by a factor of approximately two in the case of the mastic. Received: 8 June 1999/Accepted: 19 October 1999     

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.     

Structure and properties of sheared fiber suspensions with mechanical contacts

The properties of fiber suspensions are highly sensitive to the suspension microstructure. In dilute or semi-dilute suspensions, nL²d≪1, the fibers' orientation distribution is controlled by hydrodynamic interactions among the fibers. However, direct mechanical contacts among the fibers play an important role in semi-concentrated suspensions, nL²d=O(1). Here, n is the number of fibers per unit volume, L is the fiber length and d is the fiber diameter. We have performed dynamic simulations of fiber suspensions including contact forces that prevent any two fibers from passing through one another. Collisions between the fibers cause them to flip more frequently in the shear flow, leading to a spread of the orientation distribution away from the flow direction. Both this increased orientational dispersion and the direct stress transmitted through the contacts enhance the shear viscosity of the suspension significantly. The contacts also give rise to normal stress differences. The results of the simulation are compared with experiments and the relative importance of contacts and hydrodynamic interactions is discussed.