Rheology of soft particle suspensions

Abstract

The purpose of this work is to investigate the effect of particle elasticity on suspension rheology and flow. Non-colloidal (~ 10 µm) spherical agarose microgels suspended in water are used as a model system. The advantage of these microgels is that they are manufactured to a specific elastic modulus, ranging from 8 to 300 kPa, determined from the modulus of an agarose gel disk. This is in contrast to routinely studied colloidal microgels where the particle modulus cannot be established. Colloidal microgel modulus and specific volume are variable as they are responsive to suspension conditions (such as, pH, temperature and osmotic pressure). Using experimental rheology, an investigation was carried out into the liquid and solid-like behaviour of agarose microgel suspensions. Suspension concentration regimes from dilute to densely packed were investigated to show explicitly the effect of particle modulus on rheology, which becomes increasingly more significant with increasing phase volume. In addition, particle modulus is shown to influence two shear flow characteristics – slip and shear thickening. To interpret suspension viscosity as a function of phase volume the model, developed by Maron and Pierce (1956) and popularised by Quemada (1977) (MPQ model), is applied. This model is based on a scaling relation of the pair distribution function and predicts the critical phase volume at which the viscosity tends to infinity, corresponding to when spherical particles are randomly close packed (Φrcp). Commonly, it is used empirically by free fitting of experimental data to obtain the critical phase volume. In this work, a method has been developed to use the MPQ model in accordance with its theoretical basis by independently predicting Φrcp from the particle size distribution. It is shown that this theoretical form of the MPQ model, with no adjustable parameters, results in an accurate prediction (within experimental uncertainty, ± 5 %) of the viscosity-phase volume relationship for hard spheres. In addition, alterations in suspension microstructure (for example, through particle aggregation) or rheological artefacts (such as, particle migration) are readily identified by plotting the MPQ model in a linear form. In contrast to hard spheres, the phase volume of agarose microgels is difficult to define accurately. The approach typically used in literature, and used here, is to define the specific volume from dilute suspension viscosity. This approach can be corroborated using the theoretical viscosity-phase volume model validated with hard sphere suspensions. The specific volume of agarose microgels is easily defined at Φrcp using the particle size distribution. From this approach it is discovered that, in the viscous regime, below Φrcp, particle elasticity does not explicitly affect suspension viscosity. However, it is shown that particle elasticity has an indirect effect on viscosity at phase volumes between ~ 0.4 and Φrcp due to limited re-swelling during microgel preparation procedures. When microgels come into close contact at Φrcp, the suspension becomes distinctly viscoelastic. The suspensions are purely viscous with no measurable viscoelasticity below Φrcp. However, just above Φrcp, the suspensions are shear thinning and viscoelastic with a measurable storage modulus (G’) less than the loss modulus (G’’). Further increases in suspension phase volume lead to a second transition, defined here as the jamming fraction (Φj), where G’ becomes greater than G” (evaluated at a frequency of 10 rad/s). In this concentrated region, viscoelastic solid-like behaviour is strongly dependent on particle elasticity; the behaviour is reasonably predicted using a cell model with particle contact given by Hertzian interaction of elastic spheres. The three regions of rheological behaviour—viscous, viscoelastic fluid and viscoelastic (soft) solid—are demonstrated experimentally and validated using theoretical models with no free fitting parameters. Two interesting shear flow characteristics—slip and shear thickening—are also investigated, both of which are found to depend on particle elasticity. Here, it is shown that the effect of particle elasticity on slip of non-colloidal microgels is described by a model based on elastohydrodynamic lubrication, analogous to colloidal microgels. In addition, a time dependent flow phenomenon is observed under constant shear that results in a transition for the microgel suspensions from a viscoelastic fluid to solid at certain phase volumes. Particle elasticity is shown to influence this shear induced structuring process, which is most pronounced for the hardest agarose microgel particles. The increase in G’ and thus the resulting structure are maintained when shear is removed. Such shear induced structuring is normally only seen in attractive particle or worm-like micelle suspensions. These studies use experimental data supported by theoretical models to provide insights into how mechanical properties at the particle scale affect microgel suspension rheology. The knowledge gained in this work, and the approach taken, have the potential to be used to interpret or tune rheological properties of complex soft particle systems that are widespread in both nature and industry.