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.

Fluid Mechanical Aspects of Antisymmetric Stress

Abstract: Basic fluid mechanical concepts are reformulated in order to account for some structural aspects of fluid flow. A continuous spin field is assigned to the rotation or spin of molecular subunits. The interaction of internal spin with fluid flow is described by antisymmetric stress while couple stress accounts for viscous transport of internal angular momentum. With constitutive relations appropriate to a linear, isotropic fluid we obtain generalized Navier‐Stokes equations for the velocity and spin fields. Physical arguments are advanced in support of several alternative boundary conditions for the spin field. From this mathematical apparatus we obtain formulas that explicitly exhibit the effects of molecular structure upon fluid flow. The interactions of polar fluids with electric fields are described by a body‐torque density. The special case of a rapidly rotating electric field is examined in detail and the induction of fluid flow discussed. The effect of a rotating electric field upon an ionic solution is analyzed in terms of microscopically orbiting ions. This model demonstrates how antisymmetric stress and body torque can arise in ``structureless'' fluids.

Flow of non‐Newtonian fluids in a magnetic field

Abstract: The analytical solution to the equation of motion is given for the steady laminar flow of a uniformly conducting incompressible non-Newtonian fluid between two parallel planes. The fluid is under the influence of a constant pressure gradient and is subjected to a steady magnetic field perpendicular to the direction of motion. Two non-Newtonian models are considered: the Bingham plastic model and the power-law model. Flow rates and the velocity profiles for various values of the Hartmann number and the generalized Hartmann number are presented and compared with those corresponding to Newtonian fluids.

Navier–Stokes revisited

Abstract: A revision of Newton's law of viscosity appearing in the role of the deviatoric stress tensor in the Navier–Stokes equation is proposed for the case of compressible fluids, both gaseous and liquid. Explicitly, it is hypothesized that the velocity v appearing in the velocity gradient term ∇ v in Newton's rheological law be changed from the fluid's mass-based velocity v m , the latter being the velocity appearing in the continuity equation, to the fluid's volume velocity v v , the latter being a stand-in for the fluid's volume current (volume flux density n v ). A similar v m → v v alteration is proposed for the velocity v appearing in the no-slip tangential velocity boundary condition at solid surfaces. These proposed revisions are based upon both experiment and theory, including re-interpretation of the following three items: (i) experimental “near-continuum” thermophoretic and other low Reynolds number phoretic data for the movement of suspended particles in fluids under the influence of mass density gradients ∇ ρ , caused either by temperature gradients in single-component fluids undergoing heat transfer or by species concentration gradients in inhomogeneous two-component mixtures undergoing mass transfer; (ii) the hierarchical re-ordering of the Burnett terms appearing in the Chapman–Enskog gas-kinetic theory perturbation expansion of the viscous stress tensor from one of being based upon small Knudsen numbers to one of being based upon small Mach numbers; (iii) Maxwell's (1879) ubiquitous v m -based “thermal creep” or “thermal stress” slip boundary condition used in nonisothermal gas-kinetic theory models, recast in the form of a v v -based no-slip condition. The v v vs. v m dichotomy in the case of compressible fluids is shown to lead to a fundamental distinction between the fluid's tracer velocity as recorded by monitoring the spatio-temporal trajectory of a small non-Brownian particle deliberately introduced into the fluid, and the fluid's “optical” or “colorimetric” velocity as monitored, for example, by the introduction of a dye into the fluid or by some photochromic- or fluorescence-based scheme in circumstances where the individual fluid molecules are themselves responsive to being probed by light. Explicitly, it is argued that the fluid's tracer velocity, representing a strictly continuum nonmolecular notion, is v v , whereas its colorimetric velocity, which measures the mean velocity of the molecules of which the fluid is composed, is v m .