Step Changes In Shear Rate Research Articles

Measurement of Drilling Fluid Rheology and Modeling of Thixotropic Behavior

AbstractDrilling fluids perform a number of important functions during a drilling operation, including that of lifting drilled cuttings to the surface and balancing formation pressures. Drilling fluids are usually designed to be structured fluids exhibiting shear thinning and yield stress behavior, and most drilling fluids also exhibit thixotropy. Accurate modeling of drilling fluid rheology is necessary for predicting friction pressure losses in the wellbore while circulating, the pump pressure needed to resume circulation after a static period, and how the fluid rheology evolves with time while in static or near-static conditions. Although modeling the flow of thixotropic fluids in realistic geometries is still a formidable future challenge to be solved, considerable insights can still be gained by studying the viscometric flows of such fluids. We report a detailed rheological characterization of a water-based drilling fluid and an invert emulsion oilbased drilling fluid. The micro structure responsible for thixotropy is different in these fluids which results in different thixotropic responses. Measurements are primarily focused at transient responses to step changes in shear rate, but cover also steady state flow curves and stress overshoots during start-up of flow. We analyze the shear rate step change measurements using a structural kinetics thixotropy model.

Flow and evolution of ice-sucrose crystal mushes.

We study the rheology of suspensions of ice crystals at moderate to high volume fractions in a sucrose solution in which they are partially soluble, a model system for a wide class of crystal mushes or slurries. Under step changes in shear rate, the viscosity changes to a relaxed value over several minutes, in a manner well fitted by a single exponential. The behavior of the relaxed viscosity is power-law shear thinning with shear rate, with an exponent of -1.76±0.25, so that shear stress falls with increasing shear rate. On longer time scales, the crystals ripen (leading to a falling viscosity) so that the mean radius increases with time to the power 0.14±0.07. We speculate that this unusually small exponent is due to the interaction of classical ripening dynamics with abrasion or breakup under flow. We compare the rheological behavior to mechanistic models based on flow-induced aggregation and breakup of crystal clusters, finding that the exponents can be predicted from liquid phase sintering and breakup by brittle fracture.

Thixotropic Flow Behaviour in Chemical Pulp Fibre Suspensions

This paper presents results on the thixotropic behaviour of hardwood and softwood pulp fibre suspensions. Three rheological tests including hysteresis-loops, creep tests, and step-wise experiments were used to investigate the thixotropic rheology. Both suspensions exhibited a plateau in their flow curves where a slight change of the applied shear stress led to a dramatic change in the corresponding shear rates. During creep experiments under controlled stress, they evolved either towards a rapid shear (liquid regime) or stoppage (solid regime), depending on the relative values of the imposed stress, leading to a viscosity bifurcation around a critical stress. The transient response of pulp to step changes in shear rate was marked by a characteristic time, which can be used to understand the rate of structural change for pulp suspensions. Moreover, the yielding and thixotropic behaviour of the pulp suspensions were highly dependent on shear history and the time of rest prior to the measurement.

Blood viscosity modelling: Influence of aggregate network dynamics under transient conditions

This paper reports on a theoretical examination of the hypothesis that red blood cell network characteristics influence the mechanical properties of the fluid. For this purpose a newly developed energy-rate based blood viscosity model, which incorporates network dynamics, was used to predict the transient behaviour of blood viscosity (steady-state results of this model have been reported in Biorheology 46 (2009), 487-508). The main network characteristic examined in the present work was the inter-aggregate branch size and its relationship to the evolving aggregates. Branch size was used to define a network integrity index that accounted for the strength of the developed network. For the development and validation of the model, experiments performed with an optical shearing microscope, with different step-changes in shear rate, were utilised, as well as viscosity measurements under similar flow conditions performed in a double wall Couette instrument. The experimental data were compared with the response of the model, which incorporated the network integrity index. The results suggest that network characteristics may influence the viscosity of blood at low shear rates and exhibit good agreement with experimental observations.

Micron-scale origin of the shear-induced structure in Laponite–poly(ethylene oxide) dispersions

We study the transient response to simple shear of aqueous dispersions of Laponite clay particles and poly(ethylene oxide) at concentrations for which shear induces structure in the form of a network of polymer–clay bonds. We examine the effects of shear on the structure at the micrometer length scale. Bulk rheometric measurements give the material’s response to step changes in shear rate. We find that a critical value of the shear rate separates two regions with different rheological behaviors. Static small-angle light scattering shows a corresponding qualitative change in the anisotropy of the dispersion under shear at the micron scale. We interpret our results in terms of the effects of shear on the interactions between clay particles and polymer chains and on the aggregation mechanisms in the dispersion.

The effect of temperature and shear rate upon the aggregation of whey protein and its implications for milk fouling

In milk fouling, the rate of production and composition of the fouled layer is controlled by reactions in the bulk fluid which lead to the creation of aggregates which are deposited on heated surfaces. The influences of temperature (70 °C–90 °C) and shear rate (111 s −1–625 s −1) upon the rate of growth and size of aggregates in whey protein concentrate solutions (WPC35) have been investigated using a Couette apparatus with and without the addition of mineral Calcium and Phosphorous. At temperatures below 75 °C, the aggregates formed are small and weakly bonded, whilst aggregates formed at higher temperatures (and higher shear rates) were denser and more rigid. This was attributed to weak van der Waals bonding between the particles at low temperatures and the formation of stronger covalent disulphide bonds at higher temperatures. Growth of the aggregates is due to both protein denaturation and aggregation; temperature step-change experiments have verified that denaturation is a strong function of temperature whilst aggregation is a function of the applied shear field and the strength of the particles. Step-changes in shear rate have shown that both denaturation and particle growth rate are enhanced by increasing shear rate due to an increase in the number of particle collisions, yet the final particle size showed a complex behaviour with the increase in shear rate. The addition of minerals to the WPC solution resulted in the formation of much smaller aggregates and increased deposition onto the surface of the Couette apparatus. This was attributed to interactions between Ca and β-lactoglobulin both in the bulk and at the heated surface.

Rheo-optical studies of the response of entangled polymer solutions to step changes in shear rate

Experimental birefringence data are reported for an entangled 4.86 wt % polystyrene solution involving a narrow molecular weight distribution, 8.42×106 g/mol polymer in tricresyl phosphate. The average number of entanglements per chain was estimated to be approximately 22. The flows considered involve step changes in shear rate from one steady value to another (including the case in which the two shear rates have the same sign and that in which the sign changes and the flow direction is reversed). Comparisons were also made for these flows with data obtained for the same polymer/solvent combination, but at 3.00 wt % where the estimated number of entanglements per chain was approximately 10. The range of shear rates was chosen to span Weissenberg numbers based on the longest Rouse time of O(1) and thus provide data that can be used to explore the effects of modest chain stretching on the dynamics. Although the long-time behavior was found to be qualitatively similar to a startup flow, the short-time dynami...

The influence of initial deformation on drop breakup in subcritical time-dependent flows at low Reynolds numbers

Transient effects associated with the deformation and breakup of a drop following a step change from critical to suberitical flow conditions are studied experimentally and numerically. In the experiments, we consider step changes in both the shear rate and flow type for two-dimensional linear flows generated in a four-roll mill. Numerically we consider step changes in shear rate only for a uniaxial extensional flow. Depending upon the degree of deformation prior to the change in flow conditions, the drop may either return to a steady deformed shape, or continue to stretch at a reduced rate, or, for intermediate cases, the drop may break without large-scale stretching. This behaviour is a consequence of the complicated interaction between changes of shape due to interfacial tension and changes of shape due to the motion of the suspending fluid. This mode of breakup is most pronounced for high viscosity ratios, because very large extensions are necessary to guarantee breakup if the flow is stopped abruptly. For drops that are not too deformed, the sudden addition of vorticity to the external flow is characterized by rapid rotation of the drop to a new steady orientation followed by deformation and/or breakup according to the effective flow conditions at the new orientation. Finally, for viscous drops in flows with vorticity, it is demonstrated experimentally that breakup can be achieved if the initial shape is sufficiently non-spherical even though the same drop could not be made to break in the same flow at any capillary number when beginning with a near-spherical shape.

Characteristics of Thixotropic Behavior

The shear stress-shear rate behavior of a thixotropic hectorite clay-water suspension was studied in a Couette viscometer under a wide variety of rest and shear rate histories. Shear stress decay and build-up transients resulting from step changes in shear rate were measured. The transient stress data were used to construct equilibrium and constant structure flow curves. The constant structure curves could be described by the Power Law model with a constant exponent but varying coefficient. Normalized stress transients could be described by an exponential time series similar to those used in stress relaxation studies on viscoelastic polymers. This method was applicable to literature data and to data obtained for other fluids in our laboratory. The transient behavior of thixotropic fluids is heavily influenced by past history of deformation. Structural rebuilding during rest seemed to begin with the formation of a weak gel structure. Structural rebuilding was also observed under shear rate. In experiments with a short rest period, stresses measured after reapplication of shear rate returned quickly to the values measured before the rest period.