Herschel–Bulkley fluid

About: Herschel–Bulkley fluid is a research topic. Over the lifetime, 1946 publications have been published within this topic receiving 49318 citations.

Debye-Hückel solution for steady electro-osmotic flow of micropolar fluid in cylindrical microcapillary

Abstract: Analytic expressions for speed, flux, microrotation, stress, and couple stress in a micropolar fluid exhibiting a steady, symmetric, and one-dimensional electro-osmotic flow in a uniform cylindrical microcapillary were derived under the constraint of the Debye-Huckel approximation, which is applicable when the cross-sectional radius of the microcapillary exceeds the Debye length, provided that the zeta potential is sufficiently small in magnitude. Since the aciculate particles in a micropolar fluid can rotate without translation, micropolarity affects the fluid speed, fluid flux, and one of the two non-zero components of the stress tensor. The axial speed in a micropolar fluid intensifies when the radius increases. The stress tensor is confined to the region near the wall of the microcapillary, while the couple stress tensor is uniform across the cross-section.

A new utility calculation model for axial flow of non-Newtonian fluid in concentric annuli

Abstract: A new utility approach that is independent of the rheological model is presented for the flow of non-Newtonian fluids in concentric annulus. The novel model was developed without assuming that the generalised flow index remains constant over all shear rate ranges. Based on the slot model, the flow rate expressions for all common rheological models flowing in annuli were obtained, such as the Herschel–Bulkley model, the Robertson–Stiff model, and the Four-parameter model, and they all can be solved numerically to obtain accurate wall shear rate and shear stress. Following Metzner and Reed's study, we defined a generalised flow index for non-Newtonian fluid flow in annuli. Through a theoretical analysis, we also defined a new effective diameter for non-Newtonian fluid flow in annuli, which accounts for the effects both of annulus geometry and fluid rheology but which is different from that was proposed by Reed and Pilehvari. Through the generalised effective diameter we linked non-Newtonian annular flow with Newtonian pipe flow. A general annular Reynolds number expression was derived from this method for conditions under which the generalised flow index is variable. A theoretical calculation method for the generalised flow index and a uniform pressure loss calculation model for non-Newtonian flow in concentric annuli were developed, which are applicable to all time-independent non-Newtonian fluid. The predictions of this model have been compared with an extensive set of data from the literature. The comparisons of different fluids in different size annuli show very good agreement over the entire range of flow types.

The influence of viscometer dynamics on the characterization of an electrorheological fluid under sinusoidal electric excitation

Abstract: The dynamic response of a controlled‐strain, Couette viscometer employed for the characterization of the frequency response of an electrorheological (ER) fluid is studied both numerically and experimentally. In the numerical model, the ER fluid flow between the cup and bob elements of the viscometer is coupled with the mechanical response of the cup–torque sensor system. The Bingham model is used for describing the ER fluid, with various functional forms for relating the electric field strength to the Bingham stress. Variation in the shear‐rate dependency of the Bingham stress response is also represented. Dynamic resonance tends to dominate the cup rotation response and the shear rate of the fluid. The Bingham stress response contains higher harmonic components whenever it does not follow a second power‐law relationship exactly with the electric field strength. Higher harmonics induce their own resonances at relatively lower values of excitation frequency. Experimental results obtained with zeolite‐based ER fluids generally agree with those predicted through the numerical analysis. The characterization of an ER fluid will be reasonably accurate only if the excitation frequency of the electric field is low, say less than 0.1 times the natural frequency of the cup–torque sensor assembly.

Stability of plane Poiseuille–Couette flows of a piezo-viscous fluid

Abstract: We examine stability of fully developed isothermal unidirectional plane Poiseuille–Couette flows of an incompressible fluid whose viscosity depends linearly on the pressure as previously considered in Hron et al. [J. Hron, J. Malek, K.R. Rajagopal, Simple flows of fluids with pressure-dependent viscosities, Proc. R. Soc. Lond. A 457 (2001) 1603–1622] and Suslov and Tran [S.A. Suslov, T.D. Tran, Revisiting plane Couette–Poiseuille flows of a piezo-viscous fluid, J. Non-Newtonian Fluid Mech. 154 (2008) 170–178]. Stability results for a piezo-viscous fluid are compared with those for a Newtonian fluid with constant viscosity. We show that piezo-viscous effects generally lead to stabilisation of a primary flow when the applied pressure gradient is increased. We also show that the flow becomes less stable as the pressure and therefore the fluid viscosity decrease downstream. These features drastically distinguish flows of a piezo-viscous fluid from those of its constant-viscosity counterpart. At the same time the increase in the boundary velocity results in a flow stabilisation which is similar to that observed in Newtonian fluids with constant viscosity.

Thermal elastohydrodynamic lubrication of rolling/sliding line contacts using a mixture of Newtonian and power law fluids

Abstract: Thermal elastohydrodynamic lubrication (EHL) behaviour of rolling/sliding line contacts is investigated numerically using a mixed rheological fluid model. The lubricant used is a homogeneous mixture of Newtonian base oil and power law fluid with varying volume fraction, viscosity ratio (VR), and power law index. The velocity distribution across the fluid film for the mixed rheological fluid model is obtained using perturbation method to derive Reynolds and mean temperature equations. The TEHL characteristics computed for the mixture are found to depend upon the effective viscosity of the lubricant which, besides thermal effect, is governed by the superposition of shear thinning and piezo-thickening effects of the non-Newtonian fluid additive. Thermal effect is found to be a function of additive volume fraction, VR, and power law index. The mixtures yield thicker fluid films along with an increase in coefficient of friction in most of the cases. Therefore, a judicious selection of additive fluid with an ap...