No abstract

When a flat plate is withdrawn from a liquid bath, a liquid film will adhere to it. Knowledge of the thickness of this film and the amount of liquid withdrawn (the flux) are important to many practical applications, some examples of which are coating of photographic films (2), metal coating (hot tinning, enamelling, etc.), and lubrication of moving machine parts ( 1 ) . Another example requiring the knowledge of fluid dynamics of liquid films is the drainage of paints after deposition on a vertical support during painting.In many cases, the fluids involved in drainage and withdrawal operations are non-Newtonian. Although the equivalent Newtonian case has been studied extensively, both theoretically (2, 10, 16) and experimentally (2, 12, 1 5 ) , the results cannot, in general, be applied to nonNewtonian fluids. This article presents the results of a study for non-Newtonian fluids. Both drainage and withdrawal cases are considered theoretically. Experiments are reported for the withdrawal case only.For this analysis, the fluids were assumed to be simple non-Newtonian fluids without elastic properties or memory. In the drainage case, the fluid used in the theoretical description was the three-constant Ellis model. For the withdrawal case, the power law fluid was employed. Although the influence of elastic properties was not investigated theoretically, a viscoelastic fluid [ carboxymethyl cellulose (CMC) solution] was tested. This test was made to estimate deviations both from the simple theory and from the experiments with inelastic fluids, such as aqueous Carbopol solutions. ASSUMPTIONS

Shock wave propagation arising from steady one-dimensional motion of a piston in a granular gas composed of inelastically colliding particles is treated theoretically. A self-similar long-time solution is obtained in the strong shock wave approximation for all values of the upstream gas volumetric concentration v0. Closed form expressions for the long-time shock wave speed and the granular pressure on the piston are obtained. These quantities are shown to be independent of the particle collisional properties, provided their impacts are accompanied by kinetic energy losses. The shock wave speed of such non-conservative gases is shown to be less than that for molecular gases by a factor of about 2.The effect of particle kinetic energy dissipation is to form a stagnant layer (solid block), on the surface of the moving piston, with density equal to the maximal packing density, vM. The thickness of this densely packed layer increases indefinitely with time. The layer is separated from the shock front by a fluidized region of agitated (chaotically moving) particles. The (long-time, constant) thickness of this layer, as well as the kinetic energy (granular temperature) distribution within it are calculated for various values of particle restitution and surface roughness coefficients. The asymptotic cases of dilute (v0 [Lt ] 1) and dense (v0 ∼ vM) granular gases are treated analytically, using the corresponding expressions for the equilibrium radial distribution functions and the pertinent equations of state. The thickness of the fluidized region is shown to be independent of the piston velocity.The calculated results are discussed in relation to the problem of vibrofluidized granular layers, wherein shock and expansion waves were registered. The average granular kinetic energy in the fluidized region behind the shock front calculated here compared favourably with that measured and calculated (Goldshtein et al. 1995) for vibrofluidized layers of spherical granules.

No abstract

A finite element method is proposed for solving two dimensional flow problems in complex geometrical configurations commonly encountered in polymer processing. The method is applicable to flow in relatively narrow gaps of variable thickness and any desired shape. It was developed for analyzing flow in injection molding dies and certain extrusion dies. The fluid can be any non-Newtonian fluid which is incompressible, inelastic, and time independent. The flow field is divided into an Eulerian mesh of cells. Around each node, located at the center of the cell, a local flow analysis is made. The analysis around all nodes results in a set of linear algebraic equations with the pressures at the nodes as unknowns. The simultaneous solution of these equations results in the required pressure distribution, from which the flow rate distribution is obtained. Solution for the isothermal Newtonian flow problem is obtained by a one-time solution of the equations, whereas solution of a non-Newtonian problem requires iterative solution of the equations.