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.

The viscous squeeze-film behaviour of shear-thinning fluids

Abstract: A finite element technique is proposed to predict the purely viscous squeeze-film behaviour of an arbitrary shear-thinning fluid confined between parallel discs and subjected to a constant load The technique requires establishment of the distribution of viscosity in the gap The variable viscosity is modelled by a discrete number of Newtonian fluids, with each fluid lying in a region bounded by lines of constant shear rate Each of these Newtonian regions is further divided into regions which appear as “finite element” rectangles in the r-z plane The equations governing squeeze-film flow are applied to this finite element network and an ordinary differential equation is ultimately derived which governs the gap decrease with time Solving this equation is not simple because the coefficients of two terms change as the gap decreases When the number of Newtonian fluids is sufficient, the technique predicts the squeeze-film time of a power-law fluid to within a fraction of a percent Application of the technique to synovial fluid viscosity prevents the cartilage surfaces from touching for only a fraction of a second

Energy growth in Hagen–Poiseuille flow of Herschel–Bulkley fluid

Abstract: Linear stability of Poiseuille flow of Herschel–Bulkley fluid in a cylindrical pipe is studied using modal and non-modal approaches. The first part of the present study thus deals with the classical normal mode approach in which the resulting eigenvalue problem is solved using a Chebyshev collocation method. Within the considered range of parameters, the modal-linear theory predicts that perturbations are dumped exponentially. In the second part, the effect of the rheological behavior of the fluid on the pseudospectra and the most amplified perturbations is investigated. At very low Herschel–Bulkley number (Hb H b , the optimal perturbation is oblique. The amplification of such perturbation is due to a synergy between Orr and lift-up mechanisms. In the last part of the study, the maximal value of the Reynolds number, RecE, below which the perturbation energy decreases monotonically with time is computed for a large range of Hb. Asymptotic behaviors of RecE for Hb >1 are established. The influence of the terms arising from the viscosity perturbation is highlighted throughout this study.

On the rectilinear flow of a second-order fluid and the role of the second normal stress difference in edge fracture in rheometry

Abstract: Assuming that a rectilinear flow is possible in an incompressible simple fluid, the vanishing of the shear stress on a free surface in the flow is shown to lead to one of three restrictions: the second normal stress is zero, or either the velocity gradient is orthogonal to the external, unit normal to the surface, or it is parallel to the unit normal. The consequences of the last two are investigated when the fluid is the second-order fluid and the flow occurs between two parallel plates and the free surface has a small semi-circular indentation in it and when the edge crack in the free surface is almost parallel to the plates. It is found that when there is a small semi-circular indentation, the normal stress at the midway point is tensile, causing the free surface to move into the fluid. The proof depends on obtaining a lower bound to the shear rate at this point and is based on an application of the maximum principle to harmonic functions. Hence, the Tanner-Keentok calculation of the stress at this point is in accord with the present proof; indeed, the magnitude found by them is the lower bound to the true tensile stress and equals the true tensile stress if the ratio of the radius of the indentation to the semi-gap between the parallel plates vanishes. When the edge fracture has moved into the fluid, driven by the above tensile stress and has become almost flat, it is shown that the velocity gradient is parallel to the unit normal to the surface and that the normal stress is compressive, forcing the edges together and preventing the crack from moving further into the fluid.