Professor Daniel Joseph's Lectures

Lubricated Pipelinig -- Nature's Gift - PUBLIC LECTURE
Wednesday, November 5, 4:00pm, Alumni Center Ballroom (refreshments to be served at 3:30 pm).

Abstract: I m going to talk about the issues posed by the science and technology for transporting heavy oils in a sheath of lubricating water. There is a strong tendency for two immiscible fluids to arrange themselves so that the low viscosity constituent in the region of high shears-at the wall where it lubricates the flow. Nature’s gift is such that the lubricated configuration is what you actually get. High viscosity liquids hate to work. Low-viscosity liquids are the victims of the laziness of high viscosity liquids because they are easy to push around. When a small amount of water is in a pipeline transporting thick oil, it will migrate to the wall. The oil is lighter than the water so it wants to float up but hydrodynamic forces keep it off the wall. The fluid dynamics of levitation of oil off the wall of great interest with different groups are at odds about what is going on. The downside is that the oil can foul the wall and the fouling can build up blocking the flow. Syncrude’s oil from the oil sands contains a lot of water with clay. This clay water arises when they take out the stones and dirt. They don’t have to put in water; the water is produced and it is magic clay water which prevents fouling. We call this self lubrication because water is in the oil already. Self lubricated pipelines are now used all over the Alberta oil sands. The oil is transported at a tiny fraction of what it would cost to transport the oil alone. I will show movies of lubricated lines, bamboo waves, snake waves and tiger waves.

Fluid Dynamics of Floatig Particles
Tuesday, November 4, 4:15pm, Room A260 - FAMU-FSU College of Engineering, 2525 Pottsdamer Street.

Abstract: We have developed a numerical package to simulate particle motions in fluid interfaces. The particles are moved in a direct simulation respecting the fundamental equations of motion of fluids and solid particles without the use of models. The fluid-particle motion is resolved by the method of distributed Lagrange multipliers and the interface is moved by the method of level sets. The present work fills a gap since there are no other theoretical methods available to describe the nonlinear fluid dynamics of capillary attraction. Two different cases of constrained motions of floating particles are studied here. In the first case, we study motions of floating spheres under the constraint that the contact angle is fixed by the Young-Dupré law; the contact line must move when the contact angle is fixed. In the second case, we study motion of disks (short cylinders) with flat ends in which the contact line is pinned at the sharp edge of the disk; the contact angle must change when the disks move and this angle can change within the limits specified by Gibbs extension to the Young-Dupré law. The fact that sharp edged particles cling to interfaces independent of particle wettability is under appreciated and needs study. The numerical scheme presented here is at present the only one which can move floating particles in direct simulation. We simulate the evolution of single heavier-than-liquid spheres and disks to their equilibrium depth and the evolution to clusters of two and fours spheres and two disks under lateral forces collectively called capillary attraction. New experiments by Wang, Bai and Joseph (WBJ 2003) on the equilibrium depth of floating disks pinned at the edge are presented and compared with analysis and simulations.

Potential Flows of Viscous and Viscoelastic Fluids
Friday, November 7, 3:30pm, Mathematics Colloquium, 101 Love Building.

Abstract: Potential flows are solutions of the Navier-Stokes equations. They are needed to satisfy the boundary conditions like the no-slip condition on a rigid body. The role of the potential flows in Navier-Stokes theory can be formulated in terms of the Helmholtz decomposition. Boundary conditions cannot be satisfied by irrotational flows alone or by rotational flows alone; both are required and they are tightly coupled at the boundary. The boundary conditions in the exact theory are different than the no penetration condition for purely irrotational flows; Robin conditions in which a linear sum of Neumann and Dirichlet conditions should be considered. Purely irrotational theories of the flow of viscous fluids give excellent approximations to flows with small vorticity and large viscosity. The pressure is not continuous at a free surface as has been assumed in hundreds of papers since Euler. The normal stress is continuous and it contains an irrotational viscous contribution. All the solutions of free surface problems for inviscid fluids can be improved by including the viscous term in the normal stress balance. Another irrotational approximation to the flow of a viscous fluid is based on the dissipation method introduced by Stokes. In the case of capillary-gravity waves, the assumption that the potential energy is equal to the kinetic energy and the wave speed is independent of viscosity, which is true for inviscid fluids, can be relaxed and the dependence of the wave speeds on the viscosity of viscous fluids in irrotational flows determined.. All of the studies of potential flows with free surfaces in the celebrated book of Lamb and the corpus of papers by G.I. Taylor are flawed in one way or another. Especially interesting results arise from the analysis of particle motions in potential flows of viscoelastic fluids. The peculiar facts about micro structural arrangements of particles, which are the opposite of the arrangements in Newtonian fluids, can be explained by change in the sign of the normal stress from compression to tension.