Showing papers by "Robert Pfeffer published in 1976"

A study of unsteady forces at low Reynolds number: a strong interaction theory for the coaxial settling of three or more spheres

Abstract: Unsteady multiparticle creeping motions are complicated by the appearance of Basset, virtual mass and acceleration forces and by the difficulty of calculating fluid-particle interactions for three or more closely spaced particles. The present theoretical and experimental investigation explores the importance of each of these complicating features by examining in detail the gravitational-hydrodynamical interaction between three or more spheres falling along a common axis. The strong interaction theory developed to describe this motion accurately satisfies the viscous boundary conditions along the surface of each sphere and includes all the unsteady force terms in the equations of motion for the spheres. The experimental measurements for the three-sphere chain are in excellent agreement with theoretical predictions provided the Basset force is retained in the dynamic force balance. These results indicate, in general, that the Basset force is the most important unsteady force in gravitational flows at low Reynolds numbers in which the flow configuration is slowly changing due to fluid-particle interactions. The unsteady theory for small but finite Reynolds numbers shows that the departures in particle spacings, due to the integrated effect of the Basset force, from those predicted by quasi-steady zero Reynolds number theory grow as $ for large times and are of the order of the particle dimensions if the duration of the interaction is of 0(Re«1a/C/t). Here Rero is based on the terminal settling velocity U t and radius a of the sphere. This condition is satisfied in most sedimentation problems of interest. Virtual mass and particle acceleration forces on the other hand, are of negligible importance except during a short-lived initial transient period. An intriguing new feature of the three-sphere motion for large times was discovered. One finds that there is a critical initial spacing criterion which determines whether the two leading spheres in the chain will asymptotically approach a zero or a finite fluid gap as time goes to infinity. Numerical solutions for longer chains show that there is a tendency for the leading third of the chain to break up into doublets and triplets whereas the spheres in the latter third of the chain tend to space out separately.

Reoperation for amputation neuroma of the cystic duct.

Abstract: Two cases of amputation neuroma of the cystic duct are reported. In both instances, significant symptoms were totally relieved by excision of the neuroma. Review of the literature reveals at least twenty similar cases with the same results. Emphasis is placed on the importance of considering this diagnosis in postcholecystectomy patients after all the usual causes of right upper quadrant symptoms have been ruled out.

An approximate theory for incompressible viscous flow past two-dimensional bluff bodies in the intermediate Reynolds number regime O(1) < Re < O(102)

Abstract: A new approximate theory is proposed for treating the flow past smoothly contoured two-dimensional bluff bodies in the intermediate Reynolds number range O(1) < Re < 0(102), where the displacement effect of the thick viscous layer near the surface of the body is large and a steady laminar wake is present. The theory is based on a new pressure hypothesis which enables one to take account of the displacement interaction and centrifugal effects in thick viscous layers using conventional first-order boundary-layer equations. The basic question asked is how the wall pressure gradient in ordinary boundary -layer theory must be modified if the pressure gradient along the displacement surface using the Prandtl pressure hypothesis is to be equal to the pressure gradient along this surface using a higher-order approximation to the Navier-Stokes equation in which centrifugal forces are considered. The inclusion of the normal pressure field with displacement interaction is shown to be equivalent to stretching the streamwise body co-ordinate in first-order boundary-layer theory such that the streamwise pressure gradient as a function of distance along the original and displacement body surfaces are equal.While the new theory is of a non-rigorous nature, it yields results for the location of separation and detailed surface pressure and vorticity distribution which are in remarkably good agreement with the large body of available numerical Navier-Stokes solutions. A novel feature of the new boundary-value problem is the development of a simple but accurate approximate method for determining the inviscid flow past an arbitrary two-dimensional displacement body with its wake.