Suspension (vehicle)

Abstract: Einstein's viscosity equation for an infinitely dilute suspension of spheres is extended to apply to a suspension of finite concentration. The argument makes use of a functional equation which must be satisfied if the final viscosity is to be independent of the sequence of stepwise additions of partial volume fractions of the spheres to the suspension. For a monodisperse system the solution of the functional equation is ƞ τ = exp 2.5φ 1 − kφ where ηr is the relative viscosity, φ the volume fraction of the suspended spheres, and k is a constant, the self-crowding factor, predicted only approximately by the theory. The solution for a polydisperse system involves a variable factor, λij, which measures the crowding of spheres of radius rj by spheres of radius ri. The variation of λij with r i r j is roughly indicated. There is good agreement of the theory with published experimental data.

Abstract: The purpose of the paper is to consider in general terms the properties of the bulk stress in a suspension of non-spherical particles, on which a couple (but no force) may be imposed by external means, immersed in a Newtonian fluid. The stress is sought in terms of the instantaneous particle orientations, and the problem of determining these orientations from the history of the motion is not considered. The bulk stress and bulk velocity gradient in the suspension are defined as averages over an ensemble of realizations, these averages being equal to integrals over a suitably chosen volume of ambient fluid and particles together when the suspension is statistically homogeneous. Without restriction on the type of particle or the concentration or the Reynolds number of the motion, the contribution to the bulk stress due to the presence of the particles is expressed in terms of integrals involving the stress and velocity over the surfaces of particles together with volume integrals not involving the stress. The antisymmetric part of this bulk stress is equal to half the total couple imposed on the particles per unit volume of the suspension. When the Reynolds number of the relative motion near one particle is small, a suspension of couple-free particles of constant shape is quasi-Newtonian; i.e. the dependence of the bulk stress on bulk velocity gradient is linear. Two significant features of a suspension of non-spherical particles are (1) that this linear relation is not of the Newtonian form and (2) that the effect of exerting a couple on the particles is not confined to the generation of an antisymmetrical part of the bulk stress tensor. The role of surface tension at the particle boundaries is described.In the case of a dilute suspension the contributions to the bulk stress from the various particles are independent, and the contributions arising from the bulk rate of strain and from the imposed couple are independent for each particle. Each particle acts effectively as a force doublet (i.e. equal and opposite adjoining ‘Stokeslets’) whose tensor strength determines the disturbance flow far from the particle and whose symmetrical and antisymmetrical parts are designated as a stresslet and a couplet. The couplet strength is determined wholly by the externally imposed couple on the particle; but the stresslet strength depends both on the bulk rate of strain and, for a non-spherical particle, on the rate of rotation of the particle relative to the fluid resulting from the imposed couple. The general properties of the stress system in a dilute suspension are illustrated by the specific and complete results which may be obtained for rigid ellipsoidal particles by use of the work by Jeffery (1922).

Abstract: A critical analysis was made of the extensive experimental data on the relative viscosity of suspensions of uniform spherical particles. By appropriate extrapolation techniques, non-Newtonian, inertial, and nonhomogeneous suspension effects were minimized. As a result, the scatter of the data was reduced from ±75% to ±13% at a volume fraction solids of 0.50. The coefficients of different power series relating relative viscosity and volume fraction solids were determined using a nonlinear least squares procedure. It was shown that a new expression containing three terms of a power series with coefficients determined from previous theoretical analyses and an exponential term with two adjustable constants fit the data as well as a power series with six terms, either three or four of which were adjustable constants with the remaining coefficients being theoretical values.

Abstract: Tire and rim fundamentals.- Forward vehicle dynamics.- Tire dynamics.- Driveline dynamics.- Applied kinematics.- Applied mechanisms.- Steering dynamics.- Suspension mechanisms.- Applied dynamics.- Vehicle planar dynamics.- vehicle roll dynamics.- Applied vibrations.- Vehicle vibrations.- suspension optimization.- Quarter car.