J. Mellema

MICRORHEOLOGICAL MODELING OF WEAKLY AGGREGATED DISPERSIONS

A microrheological model of aggregating dispersions is proposed in which the shear stress is estimated as the sum of hydrodynamic and structural parts. The former is attributed to the hydrodynamic cores of fractal aggregates, which behave as a suspension of impermeable spheres. The latter accounts for the forces transmitted by chains of particles linking neighboring aggregates into a transient network. To calculate the structural part the concept of fractal aggregation is incorporated into a transient network theory, to account for the creation and breakup of chains of colloidal particles connecting the aggregates. Rigid and soft chains are distinguished. The former have multiply connected backbones which deform as contorted elastic rods, while the latter have at least one soft junction and deform without elastic resistance until fully loaded. The contribution of the soft chains to the stress tensor is neglected. The calculations treat two different mechanisms for the evolution of rigid chains: a purely m...

Steady shear viscosity of weakly aggregating polystyrene latex dispersions

In order to describe the steady shear behavior of weakly aggregating dispersions a microrheological model is developed. This model combines the concept of fractal aggregation in shear flow with the transient network modeling originally developed for polymer dynamics. The former accounts for the hydrodynamic stress in the aggregates, while the latter is employed to calculate the stress component arising from the forces transmitted by chains of particles combining the neighboring aggregates into a network. The contribution of this network is shown to be significant for steady shear behavior at low volume fractions of solid and low shear rates. The validity of the model is tested by fitting it to experimental data on a well characterized weakly aggregating polystyrene latex dispersion. In this way a number of relevant parameters, among which the fractal dimension df of the aggregates and the capture efficiency of particle chains belonging to neighboring aggregates, are determined. The best agreement of the c...

Steady-shear viscosity of stirred yogurts with varying ropiness

Stirred yogurt was viewed as a concentrated dispersion of aggregates consisting of protein particles. The steady-shear behavior of three types of stirred yogurt with varying ropiness was investigated experimentally. To describe the shear-dependent viscosity, a microrheological model was used which was developed for weakly aggregating dispersions. This model was capable of successfully describing the steady-state viscosity as a function of shear rate of the stirred yogurts, the protein concentration of which ranged between 2.0% and 3.9%. The value of the fractal dimensionality df, following from the model for the aggregates is about 2.24, which was similar to the value of df found with other methods. Moreover, realistic values were found for the interaction forces (energies) describing interaction between the aggregates. The calculated size of the aggregates was close to the size found before by applying different experimental techniques. Using this model, the interpretation of the measured curves suggests that the exopolysaccharides, produced by the lactic acid bacteria in yogurt, play a significant role in the rheology of stirred yogurt.

The influence of particle size on the magnetorheological properties of an inverse ferrofluid

The dependence of magnetorheological properties on particle size is studied, using a model magnetorheological fluid consisting of nonmagnetic silica particles suspended in a ferrofluid. For small particles a strong increase of magnetorheological properties with particle size was found. At a certain particle size and field strength a crossover occurs to a regime where there is only a very limited size dependence. This can be understood in terms of the length of the chains in relation to the gap size of the geometry. Crossover occurs when the average chain length becomes comparable to the gap size. The remaining size dependence may be explained by polydispersity, variations in the morphology, variations in the sterically stabilizing layer of the particles and surface roughness of the geometry.

Shear-induced diffusion and rheology of noncolloidal suspensions: Time scales and particle displacements

The shear-induced self-diffusion and rheology of concentrated suspensions of noncolloidal hard spheres have been studied experimentally. The combined results provide an interesting physical picture. The projection of the trajectories of individual particles on the vorticity (z)–velocity (x) plane were determined through particle tracking. The particle trajectories turned out to be very useful for gaining qualitative insight into the microscopic particle motion. However, the technique is less suitable to obtain quantitative information. For a quantitative analysis of the particle displacements we measured the evolution of the ensemble averaged displacements as a function of time. The statistical analysis revealed two diffusion regimes, where 〈ΔzΔz〉 ∼ Δt. For large strain values (Δt>1) long-time self-diffusion was observed. The associated diffusion coefficient ∞ is in excellent agreement with literature data on shear-induced self-diffusion. On very short times (Δt≪1) a novel diffusive regime was discovered, characterized by a diffusion coefficient 0, which is significantly smaller than ∞ and grows monotonically with ϕ. 0 is detected on time scales on which the particle configuration is not changed significantly and thus it must represent the fluctuating motion of particles in the “cage” formed by their nearest neighbors. Finally, the rheology was studied with steady shear and oscillatory rheometry. The dynamic measurements in a controlled stress rheometer revealed that the viscoelastic response of the suspension is determined mainly by the amplitude of deformation. At small strain amplitudes γ0<1, the response is linear and a dynamic viscosity η′ is found, which is in excellent agreement with the high frequency limit η∞′ as reported in literature for colloidal hard sphere suspensions. Around γ0 = 1 the “cage” around a particle is deformed and a shear-induced microstructure is built. This leads to O(a) displacements of the particles and the viscoelastic response becomes strongly nonharmonic. Although the effect persists at large amplitudes, it becomes relatively small for γ0≫1. The microstructure is rearranged immediately after flow reversal and remains unchanged for the larger part of the period of oscillation. As a result a pseudolinear viscoelastic regime is found with a viscosity close to steady shear viscosity. Experiments show a correlation between the time scales controlling the 0/∞ diffusive behavior and the ones controlling the shear-induced changes in particle configuration as probed by the rheological measurements.

Shear history dependence of the viscosity of aggregated colloidal dispersions

The shear history dependence of the viscosity of a depletion flocculated dispersion of colloidal spheres was studied using two different rheometrical geometries. The observed rheological behavior is found to depend on the geometry, due to effects of thixotropy and sedimentation. By comparing the results of a cone‐plate and a Couette geometry, we were able to obtain reliable data. The shear history dependence is explored by measuring a flow curve before and after subjecting the aggregated dispersion to a constant shear rate for one hour. The viscosity values of the flow curve after this hour turned out to be considerably lower than the initial flow curve. The results were interpreted with a microrheological model for fractal aggregation in shear flow. The drop in viscosity is attributed to a shear induced compaction of the aggregates. Combination of this model and the concept of compaction results in a satisfactory description of the experimental results.The shear history dependence of the viscosity of a depletion flocculated dispersion of colloidal spheres was studied using two different rheometrical geometries. The observed rheological behavior is found to depend on the geometry, due to effects of thixotropy and sedimentation. By comparing the results of a cone‐plate and a Couette geometry, we were able to obtain reliable data. The shear history dependence is explored by measuring a flow curve before and after subjecting the aggregated dispersion to a constant shear rate for one hour. The viscosity values of the flow curve after this hour turned out to be considerably lower than the initial flow curve. The results were interpreted with a microrheological model for fractal aggregation in shear flow. The drop in viscosity is attributed to a shear induced compaction of the aggregates. Combination of this model and the concept of compaction results in a satisfactory description of the experimental results.

A new transient network model for associative polymer networks

A new model for the linear viscoelastic behavior of polymer networks is developed. In this model the polymer system is described as a network of spring segments connected via sticky points (as in the Lodge model). [Lodge, A. S., “A network theory of flow birefringence and stress in concentrated polymer solutions,” Trans. Faraday Soc. 52, 120–130 (1956).] An important extension (with respect to previous models) is that chain connectivity is taken into account. All segments that are located in between connected stickers are supposed to carry stress. The attachment and detachment of stickers is described with kinetic equations in which activation energies play a role. Simultaneous transitions involving groups of stickers are allowed. The model shows a strong dependence upon the number of segments per chain. Broad relaxation spectra can be obtained. The storage modulus can have more than one plateau corresponding with the fact that stress relaxation may need the breakup of several bonds.

Linear viscoelastic properties of ordered latices

The frequency‐dependent behavior of the storage modulus G′ and loss modulus G″ has been measured for an ordered latex at different volume fractions. From these measurements the volume fraction dependency of the static shear modulus was obtained. The theoretical static shear modulus has been deduced from a stress tensor expression which only takes into account the electrostatic pair interactions between nearest neighbors. The electrostatic pair interaction is modeled adequately to account for the multiparticle environment of a particle and for high surface charges. The interactions are described by the linear superposition approximation for the pair interaction energy between two particles given by Bell et al. [J. Colloid Interface Sci. 33, 335 (1970)]. The apparent surface potential and the effective Debije screening length used in this expression are determined from the electrostatic potential which is numerically determined from the Poisson–Boltzmann equation in a spherical cell. The theoretical model i...

The viscosity and sedimentation of aggregating colloidal dispersions in a Couette flow

In order to interpret the time dependence of the measured torque in a steady shear experiment on an aggregating dispersion, a microrheological model has been used in which two existing models are integrated. In this microrheological model, a theory for fractal aggregation in shear flow is combined with a theory for the sedimentation and resuspension of non‐colloidal hard spheres. The former theory describes the viscosity as a function of shear rate, while the latter predicts the stress increase in a Couette device due to sedimentation. The connection between the two theories is made by identifying the aggregate parameters with the hard sphere parameters (size and volume fraction). The parameters of the aggregates as a function of shear stress are obtained by measuring a flow curve before sedimentation effects become significant and fitting this curve with the fractal aggregation theory. During the sedimentation, the aggregate size and volume fraction become a function of both time and position in the rheo...

A counter-rotating Couette apparatus to study deformation of a sub-millimeter sized particle in shear flow

We describe a new counter-rotating Couette apparatus that has been developed for deformation studies of single sub-millimeter sized particles in shear flow. New features are the adaption to the low viscosities of water-based systems and temperature control of the device. The inner to outer radius ratio of the cylinders used is 0.9785 and the height to width aspect ratio of the gap is 4.0, while the inner radius is 100 mm. Because of the limited particle size a high mechanical accuracy of the Couette geometry is necessary. The swing of the inner cylinder is less than 2 μm and that of the outer cylinder less than 4 μm. We achieved this by carefully choosing the design parameters of the aerostatic bearing and the coupling between cylinder and motor unit. Furthermore, special drive units give a shear rate resolution of 0.018 s−1, while the maximum shear rate is 100 s−1. For a liquid viscosity on the order of 1 mPas the effective maximum shear rate is 30 s−1. We have shown that deformations as small as (L−B)/(L+B) ≈ 0.01 of giant bilayer vesicles (typical radius 10 μm) with length L and width B can be observed with our device.