Squeeze flow of soft solids between rough surfaces

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 were measured for different amplitudes of plate roughness in the range 0.3–31 m. Newtonian liquids obeyed the relation Vh 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 m), 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).     

Yield stress of structured fluids measured by squeeze flow

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 ^*. Received: 13 December 1999/Accepted: 4 January 2000     

Flow of soft solids squeezed between planar and spherical surfaces

The force to squeeze a Herschel–Bulkley material without slip between two approaching surfaces of various curvature is calculated. The Herschel–Bulkley yield stress requires an infinite force to make plane–plane and plane–concave surfaces touch. However, for plane–convex surfaces this force is finite, which suggests experiments to access the mesoscopic thickness region (1–100 m) of non-Newtonian materials using squeeze flow between a plate and a convex lens. Compared to the plane–parallel surfaces that are used most often for squeeze flow, the dependence of the separation h and approach speed V on the squeezing-time is more complicated. However, when the surfaces become close, a simplification occurs and the near-contact approach speed is found to vary as V h⁰ if the Herschel–Bulkley index is n<1/3, and V h^(3n-1)/(2n) if n 1/3. Using both plane–plane and plane–convex surfaces, concordant measurements are made of the Herschel–Bulkley index n and yield stress ₀ for two soft solids. Good agreement is also found between ₀ measured by the vane and by each squeeze-flow method. However, one of the materials shows a limiting separation and a V(h) behaviour not predicted by theory for h<10 m, possibly owing to an interparticle structure of similar lengthscale.     

Radial filtration during constant-force squeeze flow of soft solids

Various soft solid suspensions were squeezed at constant force between polished and roughened circular glass plates and the time-dependence of the interplate separation was measured. The filterability of suspensions was quantified by their desorptivity S obtained from measurements of capillary suction time. The squeeze flow (SF) of suspensions for which S < 2 μm s^−1/2 was largely consistent with rheological theory, which neglected radial filtration: the relative motion between the liquid and solid phases of the suspension in the radial pressure gradient. Suspensions having S > 2 μm s^−1/2 showed SF behavior that was consistent with the presence of radial filtration.     

Rheometry for large-particulated fluids: analysis of the ball measuring system and comparison to debris flow rheometry

For large-particulated fluids encountered in natural debris flow, building materials, and sewage treatment, only a few rheometers exist that allow the determination of yield stress and viscosity. In the present investigation, we focus on the rheometrical analysis of the ball measuring system as a suitable tool to measure the rheology of particulated fluids up to grain sizes of 10 mm. The ball measuring system consists of a sphere that is dragged through a sample volume of approximately 0.5 l. Implemented in a standard rheometer, torques exerted on the sphere and the corresponding rotational speeds are recorded within a wide measuring range. In the second part of this investigation, six rheometric devices to determine flow curve and yield stress of fluids containing large particles with maximum grain sizes of 1 to 25 mm are compared, considering both rheological data and application in practical use. The large-scale rheometer of Coussot and Piau, the building material learning viscometer of Wallevik and Gjorv, and the ball measuring system were used for the flow curve determination and a capillary rheometer, the inclined plane test, and the slump test were used for the yield stress determination. For different coarse and concentrated sediment–water mixtures, the flow curves and the yield stresses agree well, except for the capillary rheometer, which exhibits much larger yield stress values. Differences are also noted in the measuring range of the different devices, as well as for the required sample volume that is crucial for application.     

Squeeze flow of a Bingham-type fluid with elastic core

The squeeze flow of a Bingham-type material between finite circular disks is considered. The material is modelled assuming that the unyielded region behaves like a linear elastic core. A lubrication approximation is considered. It is shown that no paradox can arise, such as that has been pointed out for many years by various authors when the unyielded region in the fluid is supposed to be perfectly rigid. The unyielded region is shown to be always detached from the axis of symmetry. Some numerical simulations are worked out for different squeezing rates.     

Squeeze flow of Bingham fluids under slip with friction boundary condition

This paper develops a theoretical analysis of a Bingham fluid in slipping squeeze flow. The flow field decomposition consists in combining a central extensional flow zone in the plane of symmetry and shear flow zones near the plates. It is also considered that the slipping zone is located around a central sticking zone as previously shown from experiments. It is assumed that the shear stress at the plates is constant in the slipping zone and equals a fixed friction yield value. The squeeze force required to compress a Bingham fluid under the slipping behaviour as well as the radial evolution of the transition point between both sticking and slipping zones are finally determined.     

Flow of a yield stress fluid over a rotating surface

We study the flow of yield stress fluids over a rotating surface when both the viscoelastic solid behavior below a critical deformation (γ _c) and liquid properties beyond γ _c can play a significant role. We review the detailed characteristics of the flow in the solid regime in the specific case of a pure elongational strain (large height to radius ratio). We, in particular, show that there exists a critical rotation velocity (ω _c) associated with the transition from the solid to the liquid regime. We then consider the specific case of lubricational regime (small height to radius ratio) in the liquid regime. In that case we describe the different possible evolutions of the equilibrium shape of the material as a function of the rotation velocity (ω), from which we extrapolate the transient shape evolutions as ω increases. We show that for a sufficiently large rotation velocity the sample separates into two parts, one remaining at rest around the rotation axis, the other going on moving radially. These predictions are then compared with systematic spin-coating tests under increasing rotation velocity ramps followed by a plateau at ω _f with typical yield stress fluids. It appears that there exists a critical velocity below which the material undergoes a limited elongation and beyond which it starts to spread significantly over the solid surface. For a larger ω _f value the sample forms a thick peripheral roll, leaving behind it a thin layer of fluid at rest relatively to the disc. These characteristics are in qualitative agreement with the theoretical predictions. Beyond a sufficiently large ω _f value this roll eventually spreads radially in the form of thin fingers. Moreover, in agreement with the theory in the lubricational regime, the different curves of deformation vs ω fall along a master curve when the rotation velocity is scaled by ω _c for different accelerations, different sample radii, or different material yield stress. The final thickness of the deposit seems to be mainly governed by the displacement of the roll, the characteristics of which take their origin in the initial stage of the spreading, including the solid–liquid transition.     

An investigation of squeeze flow as a viable technique for determining the yield stress

A systematic study of squeeze flow (SF) was performed on different concentrations of Carbopol with varying yield stresses. A sample of constant volume was placed between two parallel plates and a series of constant force steps applied, following the plate separation as a function of time. Precise rheological measurements of the model yield stress fluids were performed in addition to the well-controlled SF tests. These rheological measurements were used in conjunction with the SF equations to determine the time-dependent plate separation, allowing a direct comparison of theory and experiment throughout the entire test. The limiting height achieved during constant force SF reveals information about the yield stress of the fluid as predicted by the theory. It appears that by carefully controlling the experimental conditions of the squeeze test one can obtain yield stress values that agree with the rheological measurements within 10%. Additionally, the validity of the lubricational theory was tested; not only for the determination of the yield stress but throughout the flow as well.     

Stability of a Rayleigh-Bénard Poiseuille flow for yield stress fluids—Comparison between Bingham and regularized models

A linear stability analysis of a Rayleigh-Bénard Poiseuille flow is performed for yield stress fluids whether we use the Bingham or regularized models. A fundamental difference between those models is that the effective viscosity is not defined in the plug zone for the Bingham model, while it is defined in the whole domain for the regularized models. For these models, the viscosity depends highly on a parameter ? near the axis and increases drastically in an intermediate region. The convergence of the critical conditions between the simple and the Bingham models is not obtained. However, we show that the Bercovier and Papanastasiou models can tend to the exact Bingham results.     

Squeeze-flow and vane rheometry of a gas–liquid foam

The rheology and slip of a dry shaving foam are investigated using squeeze-flow and rotating-vane methods. Constant-force squeeze flow between planar surfaces is used to study the effect of surface roughness on slip and to obtain the yield stress. Non-slip vane measurements are used to obtain the linear shear viscosity and elasticity at small strains, and the yield stress and strain at large strains. Data are compared with the small-strain Maxwell and Kelvin–Voigt linear-viscoelastic models. An apparent dependence of the yield stress and elasticity on the rotational speed of the vane is shown to result from time-dependent rheological parameters as the foam ages. The effect of viscosity in the pre-yield region may give an erroneous identification of yield.     

Comparative yield stress determination for pure and interstratified smectite clays

Different experimental devices and operative procedures were used to obtain the main properties of suspensions of two purified clays, a pure smectite and an interstratified illite-smectite natural clay, at different concentrations. The yield stress values derived from flow and creep tests were found to be very consistent, while those derived from dynamic tests were observed to be much more sensitive to experimental conditions. Qualitatively, the two clays exhibit the same rheological behaviour, which can be modelled using the Herschel-Bulkley model; their yield stress increases with clay concentration and they present a thixotropic character for low concentrations, with an inversion of the curves when the clay concentration increases. However, significant differences were observed when considering numerical values. For the same clay concentration in the suspension, the yield stress of the pure smectite is distinctly higher than that of the interstratified one. The rheological properties of the pure smectite clay can be related to the swelling properties and the organisation of the minerals in water, leading to three-dimensional strong but deformable structures. On the other hand, the presence of a small percentage of illite in the natural clay gives it a brittle behaviour which collapses more easily under stress.     

An approximate solution considering flow inertia between spherical surfaces

In this paper, the analytical expressions of the pressure distribution, velocity distribution and discharge of the flow between spherical surfaces are found by using the method of iterative approximate solution when the inertia terms of Navier-Stokes equations in spherical coordinates are taken into consideration. Furthermore, using these expressions, we can directly obtain the corresponding analytical expressions of the laminar radial flow between parallel disks, which are fully identical with corresponding results presented by refs. [3,4].     

The oscillatory squeeze flow rheometer: comprehensive theory and a new experimental facility

In this paper, we give detailed attention to a relatively recent method for the determination of the linear dynamic properties of viscoelastic systems, namely, the so-called oscillatory squeeze flow (OSF) technique. We provide a comprehensive theory for the OSF rheometer, which includes a full discussion of the influence of fluid inertia. In the process, it is argued that, fortuitously perhaps, fluid inertia is more easily accommodated in the OSF rheometer than in the corresponding torsional-flow techniques. A new version of the OSF rheometer is described and experimental results on a set of viscoelastic systems are used to demonstrate the versatility of the technique. In the process, the potential use of the instrument within an industrial quality control environment is stressed.     

On the squeeze flow of a power-law fluid between rigid spheres

The lubrication solution for the squeeze flow of a power-law fluid between two rigid spherical particles has been investigated. It is shown that the radial pressure distribution converges to zero within the gap between the particles for any value of the flow index, n, provided that the gap separation distance is sufficiently small. However, in the case of the viscous force, it is useful to consider that there are two contributions. The first is developed in the inner region of the gap and corresponds to the lubrication limit. The second is due to an integration of the pressure in the adjacent outer region of the gap. The relative contribution to the force in this outer region increases as n decreases and the separation distance increases. In particular, for flow indices in the range n>1/3, the contribution in the outer region is negligible if the separation distance is sufficiently small. For n1/3, this is the dominant term and an accurate prediction of the viscous force is possible only for discrete liquid bridges.Based on “zero” pressure and lubrication criteria for the upper limits of integration, two closed-form solutions have been derived for the viscous force. Both are accurate for n>0.5 and are in close agreement with a previously published asymptotic solution in the range n>0.6. For smaller values of n, the asymptotic solution over-estimates the viscous force and predicts a singularity when n approaches 1/3. The two closed-form solutions show continuous and monotonic behaviour for all values of n. Moreover, the solution satisfying the lubrication limit is valid in the range n<1/3 provided that it is restricted to liquid bridges.     

The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.     

Squeeze flow of a power-law fluid between two rigid spheres with wall slip

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On flow and stability of a Newtonian fluid past a rotating plane

An exact solution is given for the steady flow of a Newtonian fluid occupying the halfspace past the plane z=0 uniformly rotating about a fixed normal axis (Oz). This solution is obtained in a velocity field of the form considered by Berker [2] and can be deduced as a limiting case, as h+, of the solution to the problem relative to the strip 0zh imposing at z=h either the adherence boundary conditions or the free surface conditions. Furthermore, the stability of this flow, subject to periodic disturbances of finite amplitude, is studied using the energy method and the result is compared with those corresponding to stability of flows in the strip 0zh.

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Sommario In questa nota si mostra che-oltre alla calssica soluzione di von Karman [1] — esiste, per opportuni valori del gradiente di pressione all'infinito, una soluzione esatta per il moto stazionario di un fluido Newtoniano posto nel semispazio limitato dal piano z=0 uniformemente rotante attorno ad un asse ad esso perpendicolare (Oz). Tale soluzione, ottenuta sulla scia del lavoro di Berker [2], si può dedurre anche come limite, per h+, della soluzione del problema relativo alla striscia 0zh quando sul piano z=h si assegnano o le condizioni di aderenza o le condizioni di frontiera libera. Si studia poi la stabilità di tale moto rispetto a perturbazioni spazialmente periodiche di ampiezza finita col metodo dell'energia e si confronta il risultato ottenuto con quelli relativi alla stabilità dei moti nella striscia 0zh.

     

Axial annular flow of plastic fluids: dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ _c, λ will be such that flow commences when τ(κR) = τ(R) = τ _c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.