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.

Steady‐shear rheological behavior of the suspension of spherical particles in a second‐order fluid

Abstract: In this paper we study the rheological behavior of a dilute suspension of rigid spherical particles in a second-order fluid. We extend the results of viscous fluids to discuss the expression for the bulk stress tensor of a second-order fluid and also obtain an approximate solution to the shear flow problem of this fluid. By combing these results, we write an approximate constitutive equation for the bulk stress tensor for such a suspension and study it in a shear flow. It is found that the new equation predicts no variation in the shear viscosity, but predicts enhancement of the pre-existing non-Newtonian nature of the suspending fluid with regard to the normal stress functions.

The effect of yield stress on pipe flow turbulence for generalised newtonian fluids

Abstract: The effect of modifying yield stress on turbulent pipe flow of generalised Newtonian fluids at a friction Reynolds number of 323 is investigated using direct numerical simulations. Simulations are carried out for Bingham and Herschel–Bulkley fluids with the yield stress varying from 0% to 20% of the mean wall shear stress. Results show that the effect of increasing yield stress is mostly similar to shear thinning in power-law fluids. The turbulent viscous stress which arises due to viscosity fluctuations is negative for a yield stress fluid and is higher in magnitude for higher yield stress. An analysis of the turbulent kinetic energy budget showed that the effect of yield stress is mainly significant near the wall for y + ≲ 60 which was also seen for shear-thinning power-law fluids at similar Re τ . Additional shear thinning enhances the yield stress effect. The main difference between shear thinning and yield stress is that the effect of yield stress is maximum outside the viscous sublayer whereas shear thinning has a more significant effect inside the viscous sublayer.

Analysis of von Kármán’s swirling flow on a rotating disc in Bingham fluids

Abstract: In this article, the flow above a rotating disc, which was first studied by von Karman for a Newtonian fluid, has been investigated for a Bingham fluid in three complementary but separate ways: by computational fluid dynamics (CFD), by a semi-analytical approach based on a new transformation law, and by another semi-analytical approach based on von Karman’s transformation. The full equations, which consist of a set of partial differential equations, are solved by CFD simulations. The semi-analytical approach, in which a set of ordinary differential equations is solved, is developed here by simplifying the full equations invoking several assumptions. It is shown that the new transformation law performs better and reduces to von Karman’s transformation as a limiting case. The present paper provides a closed-form expression for predicting the non-dimensional moment coefficient which works well in comparison with values obtained by the full CFD simulations. Detailed variations of tangential, axial, and radial components of the velocity field as a function of Reynolds number (Re) and Bingham number (Bn) have been determined. Many subtle flow physics and fluid dynamic issues are explored and critically explained for the first time in this paper. It is shown how two opposing forces, viz., the viscous and the inertial forces, determine certain important characteristics of the axial-profiles of non-dimensional radial velocity (e.g., the decrease of maxima, the shift of maxima, and the crossing over). It has been found that, at any Re, the maximum value of the magnitude of non-dimensional axial velocity decreases with an increase in Bn, thereby decreasing the net radial outflow. A comparison between the streamline patterns in Newtonian and Bingham fluids shows that, for a Bingham fluid, a streamline close to the disc-surface makes a higher number of complete turns around the axis of rotation. The differences between the self-similarity in a Newtonian fluid flow and the non-similarity in a Bingham fluid flow are expounded with the help of a few compelling visual representations. Some major differences and similarities between the flow of a Newtonian fluid above a rotating disc and that of a Bingham fluid, deduced in the present investigation, are brought together in a single table for ready reference. Two limiting cases, viz. Bn → 0 and Re → ∞, are considered. The present results show that the Bingham fluid solution progressively approaches the von Karman’s solution for a Newtonian fluid as the Bingham number is progressively reduced to zero (Bn → 0). It is also established here that, for finite values of Bn, the Bingham fluid solution progressively approaches the von Karman’s solution for a Newtonian fluid as the non-dimensional radius and Reynolds number increase. The higher the value of Bn, the higher is the required value of Re at which convergence with the solution for Newtonian fluid occurs.

An application of Bingham model to viscous fluid modeling of solid flow in moving bed

Abstract: Solid flow plays important roles in a moving bed reactor, for example, it determines the path and the residence time of the solid reactants as well as the stress distribution. The continuum models are useful for the kinetic based process analysis since their simplicity and computation load, although the discrete element approach is capable of estimating not only the particle motion but also the stress distribution in the bed. One of the continuum approaches is viscous fluid model. It is able to estimate solid flow pattern although it needs to appropriately determine the shape of stagnant region and viscosity before the simulation. In this study the Bingham model, which is the simplest shear rate-shear stress model of plastic fluid, is applied to the viscous fluid model of bulk solid flow within packed bed. This model successfully reproduce solid flow pattern in packed bed without setting stagnant zone, and the rheological properties can be obtained from simple preliminary experiments. Therefore, the viscous fluid model with the Bingham model is considered as a useful solid flow model for process analysis of moving bed reactors.

Determination of the flow curve of complex fluids using the Rabinowitsch–Mooney equation in sensorless microrheometer

Abstract: In this work, we present a way to make rheological measurements on a microfluidic chip. The originality of our approach relies on the determination of the flow curve of a fluid using the Rabinowitsch–Mooney equation. For this purpose, we use a parallel flow between a reference fluid and a studied fluid to measure the pressure drop inside the channel. Using a Newtonian fluid of known viscosity, knowing the flow rates of the two liquids and measuring the geometrical features of the two-phase flow allows determining the pressure drop in the channel. The Rabinowitsch–Mooney equation is used to calculate the local shear rate and shear stress at the wall for the studied sample. We validate our method for several complex fluids.