Martin Whittle

Stress overshoot in a model particle gel

Brownian dynamics simulation is used to investigate the large strain rheology of a model three-dimensional particle gel. The gel is formed from soft spherical particles incorporating flexible surface-to-surface bonds which restrict the angular reorganization of fractal aggregates resulting in a stable, percolating, network structure. Extending earlier work, bond breakage is introduced to the model allowing the study of structural disruption in response to large deformations. The accompanying interparticle stress response reveals a distinctive stress overshoot characteristic of viscoelastic materials. Hookean and non-Hookean bonding interactions have been studied, and for both cases the stress maximum scales as a power law close to the square root of the strain-rate, while the strain at which the stress maximum occurs is relatively invariant. The limiting aggregate size at high strain-rates is dependent on the bond force as well as the energetic barrier to breakage.

BROWNIAN DYNAMICS SIMULATION OF GELATION IN SOFT SPHERE SYSTEMS WITH IRREVERSIBLE BOND FORMATION

Brownian dynamics simulation is used to study the structure and small-deformation shear rheology of three-dimensional particle gels formed from a model of soft spherical particles incorporating a combination of flexible, irreversible bond formation and non-bonded interparticle interactions. An essential feature of the model is the restriction of angular reorganization of cross-linked aggregates during and after gelation. Numerical data relating to the fractal structure and porosity of the gels are compared with those from some related particle gel simulation models in two and three dimensions. Stress relaxation and frequency dependent rheological properties are determined as a function of the strength and nature of the interparticle interactions, and the results are discussed in relation to structural properties. A linear relationship is demonstrated between the high-frequency modulus and the number of bonds in the gel network.

Large deformation rheological behaviour of a model particle gel

We report on some aspects of the large deformation rheology of model three-dimensional networked particle gels. Model gels with a particle volume fraction of 5% are formed by aggregation in a Brownian dynamics simulation from soft spherical particles incorporating flexible surface-to-surface bonds that restrict the subsequent angular reorganization and infer structural stability on the resulting percolating, fractal structure. The interaction potential allows some control over the final fractal dimension of the gel and bonds may be either breakable or essentially permanent depending on the choice of parameters. The use of continuous potentials allows the rheology to be studied at constant strain-rate and at constant stress by the incorporation of a homogeneous strain algorithm. For systems with ‘permanent’ bonds, strain hardening is observed when the strain-rate is very low compared with the structural relaxation time. At relatively high strain-rates the stress response is more nearly proportional to the strain. These systems also show strain recovery when the stress is removed. For systems with short breakable bonds, a yield stress is observed at slow constant strain. Here, we have studied the yielding behaviour of these systems by applying a steadily increasing stress and we find that, under these conditions, the structure degrades in three distinct stages. The initial breakage of bonds does not immediately disrupt the gel but allows some viscoelastic flow. This is followed by breakdown into a small number of relatively large aggregates. The ensuing viscoplastic flow causes the further rupture of aggregates that culminates in a catastrophic break-up to smaller entities at a critical point that presages true viscous flow. These transitions between viscoelastic and viscoplastic flow and between viscoplastic and viscous flow correspond to the static and dynamic yield stresses that have been observed experimentally in colloidal systems at high volume fraction. The oscillatory response for systems with permanent bonds shows non-linear behaviour expressed as overtone modes for strain amplitudes in excess of 0.05. The effective modulus for these systems also increases with strain amplitude while for systems with breakable bonds the modulus decreases or passes through a maximum as a consequence of structural decay. This behaviour compares favourably with experimental studies on chemical and physical gels.

Dynamic colloidal interactions between protein-stabilised particles—experiment and simulation

Experimental n data are compared with computer simulation of interactions between two colloidal particles in a laminar n shear field, when one particle is fixed to a wall and a second particle is freely mobile in the shear field n in the narrow gap formed by a second parallel, moving wall. Both colloidal and hydrodynamic interactions n are taken into account in simulating the scattering of the mobile particle by the fixed particle. A detailed explanation is given of the experimental procedure required to perform and observe such particle collisions successfully, n in order to extract the information required to compare with the simulated results. Polystyrene latex particles and n oil droplets of diameter ca. 5 μm, stabilised by pure β-casein, αs1-casein, sodium caseinate or gelatine, were studied in water over a range of pH values and ionic strengths. Within experimental error, the scattering in these systems could not be detected as varying markedly, due mainly to random noise introduced by n Brownian motion, in agreement with the simulation results for a wide range of DLVO plus simple steric-type colloidal n interaction potentials. It is concluded that the dynamic n steric interactions for all the different protein layers, as measured by this technique, may n be quite similar, n or that a more complex n type of dynamic interaction may be involved.

Sticking of protein-coated particles in a shear field

The shear-driven formation of particle doublets at a wall, of latex and emulsion systems, has been studied using a colloidal particle scattering apparatus. In this technique, one particle is fixed on the wall while a second, mobile free particle is made to collide with the fixed particle by the application of the shear field. The effects of pH (in the range 5.5–4.8) and ionic strength (in the range 0.01–0.5 mol dm−3) on the efficiency of irreversible sticking (capture) of the mobile particle to the fixed particle have been studied for systems stabilised by adsorbed films of sodium caseinate, pure αs1-casein or pure β-casein. At low ionic strength (≤0.2 mol dm−3), the efficiency of capture increases with decreasing pH and increasing ionic strength in ways that are consistent with decreasing net charge on the protein and increased screening of the electrostatic repulsion between the particles. The increase in capture efficiency also agrees well with a previously observed increase in viscoelasticity of the corresponding concentrated protein-stabilised emulsions. However, a pronounced drop in the capture efficiency was found at higher ionic strength (0.5 mol dm−3). This effect at high ionic strength, combined with qualitative visual assessment of the behaviour of particles during collisions, conforms to the additional role of tangential interparticle forces in determining the sticking behaviour. It seems that, if the adsorbed protein layer becomes sufficiently thick, even if it has a very low net charge, then particle sticking can be prevented. The sticking phenomenon probably depends on entanglement of the adsorbed layers and on the strength of the protein–protein attractive interactions, as well as on the net particle charge.

Pore size in model particle gels

The porosity of model particle gel networks with a range of textures is investigated using some established methods. The pore-size distribution function distinguishes clearly between simulated gels of differing texture. The chord length distribution appears less useful, although clearly it does become bi-modal for coarse configurations, corresponding to the appearance of distinct high and low density regions. A box-counting analysis is presented for describing the fractal scaling properties of the voids.