1. Introduction to colloid science and rheology 2. Hydrodynamic effects 3. Brownian hard spheres 4. Stable colloidal suspensions 5. Non-spherical particles 6. Weakly flocculated suspensions 7. Thixotropy 8. Shear thickening 9. Rheometry of suspensions 10. Suspensions in viscoelastic media 11. Advanced topics.

Colloidal Suspension Rheology

The deformations and stresses during squeeze flows are evaluated for a wider class of materials than previously covered in articles on this subject. These include generalised Newtonian fluids, yield stress fluids, as well as elastic and viscoelastic materials. Wherever possible, results are given in a compact mathematical form. The effect of different boundary conditions (no slip, perfect slip and partial slip) and how these interact with different types of material behaviour to give a variety of macroscopic responses is also discussed. The significance of this in using squeeze flow as a rheometry method is highlighted and a state-of-the-art view of squeeze flow rheometry is given.

Squeeze flow theory and applications to rheometry: A review

Yield stress fluids are encountered in a wide range of applications: toothpastes, cements, mortars, foams, muds, mayonnaise, etc. The fundamental character of these fluids is that they are able to flow (i.e., deform indefinitely) only if they are submitted to a stress above some critical value. Otherwise they deform in a finite way like solids. The flow characteristics of such materials are difficult to predict as they involve permanent or transient solid and liquid regions that are generally hard to locate a priori. Here we review the present state of the art as it appears from experimental data for flows of simple (non-thixotropic) yield stress fluids under various conditions, viz., uniform flows in straight channels or rheometrical geometries, complex stationary flows in channels of varying cross-section such as extrusion, expansion, flow through a porous medium, transient flows such as flows around obstacles, spreading, spin-coating, squeeze flow, and elongation. The effects of surface tension, confinement, and secondary flows are also reviewed. We focus especially on experimental work identifying internal flow characteristics that can be compared with numerical predictions. It is shown in particular that: (i) deformations in the solid regime can play a critical role in transient flows; (ii) the yield character is not apparent in the flow field when the boundary conditions impose large deformations; (iii) the yield character is lost in secondary flows.

Yield stress fluid flows: A review of experimental data

Microgel pastes and concentrated emulsions are shown to exhibit a generic slip behavior at low stresses when sheared near smooth surfaces. The magnitude of slip depends on the applied stress. Well above the yield stress, slip is negligible compared to the bulk flow. Just above the yield stress, slip becomes significant and the total deformation results from a combination of bulk flow and slip. At and below the yield stress, the bulk flow is negligible and the apparent motion is entirely due to wall slip. By directly imaging the deformation of pastes and from rheological measurements, we show that slip is characterized by universal scaling properties, which depend on solvent viscosity, bulk shear modulus, and particle size. A model based on elastohydrodynamic lubrication between the squeezed particles and the shearing surface explains these properties quantitatively.

https://sor.scitation.org/doi/pdf/10.1122/1.1795171

Slip and flow in pastes of soft particles: Direct observation and rheology

Food rheology focuses on the flow properties of individual food components, which might already exhibit a complex rheological response function, the flow of a composite food matrix, and the influence of processing on the food structure and its properties. For processed food the composition and the addition of ingredients to obtain a certain food quality and product performance requires profound rheological understanding of individual ingredients their relation to food processing, and their final perception.

Rheology of food materials

Various structured fluids were placed between the parallel circular plates of a squeeze-flow rheometer and squeezed by a force F until the fluid thickness h was stationary. Fluid thickness down to a few microns could be measured. Most fluids showed two kinds of dependence of f on h according to an experimentally-determined thickness h*. If h > h* then F varied in proportion to h−1 as predicted by Scott (1931) for a fluid with a shear yield stress τ0. The magnitude of τ0 from squeeze-flow data in this region was compared with the yield stress measured by the vane method. For some fluids τ0 measured by squeeze flow was less than the vane yield stress, suggesting that the yield stress of fluid in contact with the plates was less than the bulk yield stress. If h < h* then F varied approximately as h−5/2 and the squeeze-flow data in this region analysed with Scott's relationship gave a yield stress which increased as the fluid thickness decreased. This previously unreported effect may result from unconnected regions of large yield stress in the fluid of size similar to h* which are not sensed by the vane and which become effective in squeeze flow only when h < h*.

Yield stress of structured fluids measured by squeeze flow

Experiments are described in which the time-dependence of the sample thickness h(t) was measured for various soft solid materials squeezed between two parallel glass plates by a constant squeezing force F applied at t=0. A yield stress for each material was also measured using rotational vane and serrated parallel-plate tools. Initially, the squeeze-rate V(t)=–dh/dt of all materials was fast and resembled that of a viscous fluid. Later, most materials showed a very small squeeze-rate, and h seemed to approach a finite plate-separation limit, characteristic of a yield-stress material. For some materials h appeared not to approach a finite limit, attributed to creep or thixotropy not evident in the more rapid vane and serrated parallel-plate measurements. Expressions which relate F to h(t) and V(t) for a Herschel-Bulkley material with stick or slip at the sample-plate interface were reviewed. No materials made frictionless contact with the sample-plate interfaces, and most were best-described by the Herschel-Bulkley squeeze-flow model of Sherwood and Durban (1998). The squeeze-flow data at very low shear rate did not support the existence of Newtonian high viscosity plateaux. A soft solid of closely-packed water-swollen particles swelled when F was decreased after a period of squeeze flow, suggesting relative motion between the constituent phases. The advantages and problems of using squeeze flow as a rheometrical technique are described and discussed.

Constant-force squeeze flow of soft solids

Newtonian liquids and non-Newtonian soft solids were squeezed between parallel glass plates by a constant force F applied at time t=0. The plate separation h(t) and the squeeze-rate % MathType!MTEF!2!1!+- % feaafaart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOvaiabg2 % da9iabgkHiTiqadIgagaGaaaaa!39AF! $$ V = - \dot h $$ were measured for different amplitudes of plate roughness in the range 0.3–31 μm. Newtonian liquids obeyed the relation V∝h
 3
 of Stephan (1874) for large plate separations. Departures from this relation that occurred when h approached the roughness amplitude were attributed to radial liquid permeation through the rough region. Most non-Newtonian materials showed boundary-slip that varied with roughness amplitude. Some showed slip that varied strongly during the squeezing process. Perfect slip (zero boundary shear stress) was not approached by any material, even when squeezed by optically-polished plates. If the plates had sufficient roughness amplitude (e.g. about 30 μm), boundary slip was practically absent, and the dependence of V on h was close to that predicted by no-slip theory of a Herschel-Bulkley fluid in squeeze flow (Covey and Stanmore 1981, Adams et al. 1994).

Squeeze flow of soft solids between rough surfaces

Experiments are described in which a constant force F squeezed a fluid, either between two parallel circular plates, or between a plate and convex spherical lens. Newtonian fluids obeyed the relation of Stefan (1874) for plates, and the relation of Adams et al. (1994) for plate and lens. The non-Newtonian yield stress fluids Brylcreem, Laponite and Sephadex were squeezed between plates of various diameter D to attain a stationary separation h. Only for separations greater than h
* (which depended on the fluid) did Brylcreem and Laponite obey the relation F/D
3 ∝ h
−1 of Scott (1931) and give a yield stress in agreement with the vane method. For Sephadex the dependence of F/D
3 on h disagreed with Scott's relation, but varied as h
−5/2 for h > 0.6 mm and h
−3/2 for h < 0.6 mm. On rotating one plate in its plane the yield stress fluids at a fixed F suffered a marked decrease of h. This, and the existence of h
*, are discussed in terms of the soft glassy material model of Sollich et al. (1997) and Sollich (1998). Brylcreem and Laponite were squeezed between a plate and lenses of various curvature and their yield stress obtained using the relation of Adams et al. (1994) was compared with measurements by plate-plate squeeze-flow and vane methods.

Squeeze flow between plane and spherical surfaces

Two principal squeeze flow modes are investigated for yield stress and Newtonian materials squeezed by a constant force, F, between plates of equal or unequal diameters. In mode A, the material fills the space between the plates and is extruded at their periphery as their separation decreases. Experiments are described to measure the contribution to F from the extrudate. In mode B, all the material remains in contact with the planes of the plates as their separation decreases; there is no extrudate. The results of mode B experiments agree closely with the predictions of theory and give rheological parameters in fair agreement with those measured by the rotational vane method. The material properties and extrusion behaviour which complicate mode A experiments are discussed.

Gerald Henry Meeten

Papers

Yield stress of structured fluids measured by squeeze flow

Constant-force squeeze flow of soft solids

Squeeze flow of soft solids between rough surfaces

Squeeze flow between plane and spherical surfaces

Comparison of squeeze flow and vane rheometry for yield stress and viscous fluids