A simple model for the nonlinear collective transport of interacting particles in a random medium with strong disorder is introduced and analyzed. A finite threshold for the driving force divides the behavior into two regimes characterized by the presence or absence of a steady-state particle current.Below this threshold, transient motion is found in response to an increase in the force, while above threshold the flow approaches a steady state with motion only on a network of channels which is sparse near threshold. Some of the critical behavior near threshold is analyzed via mean field theory, and analytic results on the statistics of the moving phase are derived. Many of the results should apply, at least qualitatively, to the motion of magnetic bubble arrays and to the driven motion of vortices in thin film superconductors when the randomness is strong enough to destroy the tendencies to lattice order even on short length scales. Various history dependent phenomena are also discussed. 05.60.+w, 74.60.Ge, 62.20.Fe Typeset using REVT E X

this phenomenon has nothing to do with the rheological complexities of the ambient liquids, and its interpretation must be sought in the different behavior of bubbles and drops in liquids. The larger the bubble is, the larger the contact area between the concave face of the leading and the convex face of the trailing bubble cap. Thus, the area of the film to be drained increases with the increasing basal diameter of the bubble. On the other hand, drops in the region of diameters between 0.004 and 0.007 m remain essentially spherical. CONCLUSIONSThe elasticity of polymer solutions has a tendency to increase both the collision and the coalescence times of gas bubbles and liquid drops. Thus, polymer additives with strong elastic component may reduce the overall coalescence rate considerably.Greek Letters a y = shearrate o = angular velocity = material parameter, Equation (3) = material parameter, Equation ( 3 ) = basal diameter of a bubble/drop = axial thrust between the cone and the plate of the R18 rheogoniometer = acceleration due to gravity = material parameter, Equation (3) = material parameter, Equation (3) = radius of the cone and plate setup = torque between the cone and the plate of the R18 rheogoniometer = initial separation of bubbles/drops = complementary apex angle between the cone and the plate in the R18 rheogoniometer 7 = apparent viscosity p = density k u1 = characteristic time of a viscoelastic liquid = primary normal stress difference A three-phase fluidized bed consists of solid phase particles fluidized by a gas and liquid flow. Although many Begovich. schemes for contacting the three phases are possible, a common method is to fluidize the solid phase by the upward concurrent flow of gas and liquid. The liquid forms Correspondence concerning this note should be addressed to J. M.

A simple model of the driven motion of interacting particles in a two-dimensional random medium is analyzed, focusing on the critical behavior near to the threshold that separates a static phase from a flowing phase with a steady-state current. The critical behavior is found to be surprisingly robust, being independent of whether the driving force is increased suddenly or adiabatically. Just above threshold, the flow is concentrated on a sparse network of channels, but the time scale for convergence to this fixed network diverges with a larger exponent than that for convergence of the current density to its steady-state value. This is argued to be caused by the ''dangerous irrelevance'' of dynamic particle collisions at the critical point. Possible applications to vortex motion near to the critical current in dirty thin-film superconductors are discussed.

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