Some unsteady parallel flows of particulate suspensions

Peddieson, John

doi:10.1007/bf00411778

Cited by 9 publications

(1 citation statement)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…That is, the region where or is of order unit$ Generalization of these ideas to apply away from the small-particle mass-fraction limit does not present any conceptual difficulty. However, the fully coupled equations for the two phases, including their mutual interaction, are so complicated that even when diffusion is neglected, in the isothermal case with an incompressible host fluid, they have been solved only for simple homogeneous unidimensional or parallel flows (Michael 1963;Nag, Jana & Datta 1979;Peddieson 1976;Singleton 1965), and the exceptional case of the motion of a dusty gas induced by the uniform rotation of an infinite disk (Zung 1969). Other valuable solutions have been confined either to this limit of very small particle loading, or the limit of very small particle relaxation time 7 (compared with macroscopic times), which is unfortunately incapable of predicting some of the interesting inertial effects that concern us here.…”

Section: Introductionmentioning

confidence: 99%

Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Mora

Rosner

1982

J. Fluid Mech.

View full text Add to dashboard Cite

A formalism that accounts for inertial and diffusive effects in the dynamics of a dilute gas-particle suspension is introduced. The treatment is purely deterministic away from a very thin Brownian diffusion sublayer, while, within the sublayer, inertial effects are small, permitting a near-equilibrium expansion in powers of the Stokes number (particle relaxation time divided by flow characteristic residence time). This expansion provides phenomenological expressions for the particle velocity including two terms : the standard Brownian diffusion, and an additional inertial drift velocity which is closely related to the pressure diffusion term of the Chapman-Enskog expansion. As an example, the general formalism is applied in detail to the case of Stokes flow about a sphere, and sketched for the similar case of a cylinder. Two competing mechanisms are seen to affect the total rate of particle capture by the sphere : (if the stagnation-point region is considerably enriched in particles owing to the high compressibility of the particle phase, which leads to locally enhanced deposition; (ii) centrifugal forces tend to deplete the Brownian diffusion sublayer of particles, reducing diffusion rates away from the stagnation point to the surface. The first effect is seen to dominate over the second except in a very narrow zone of small Stokes numbers. Our method bridges the gap between Levich's solution for the ‘pure-diffusion’ limit and Michael's treatment in the ‘pure-inertia’ limit.

show abstract

Section: Introductionmentioning

confidence: 99%

Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Mora

Rosner

1982

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

Unsteady Flow of Suspension through a Rectangular Pipe

1982

View full text Add to dashboard Cite

Unsteady Flow of a Binary Mixture of Fluids Between Annular Space of Two Circular Cylinders

Srivastava

Singh

1982

Z Angew Math Mech

View full text Add to dashboard Cite

IntroductionFluid dynamics of a continiiiinl theory of mixture ha,s, from historic times, been object of mient.ific and engineering rewarah. Historical discussion on the development of the subject is sufficiently available in the literature. A more fundamental and rigorous theoretical approach of the modern phase of the continiium theory of mixture can be found in the treatises of TRUES- DELL [l] and TRUESDELL and TOUPIN [2] and in papers by NRINQEN and INGRAM [3], GREEN and NEGHDI [4] and MILL^ [5,6]. AT~IN and CRAINE [7] reoently derived the fundamental equations of continuum theory of mixture and have given the historical development of the subject. In a subsequent paper [8], they applied the basic theory for different types of a binary, chemically reacting and non-reacting mixture of fluids. WIL-HELM and VAN DEB WEBFF [9] studied binary mixture of NEWmman fluids in a pipe, In addition, a number of authors have worked on multiphase or two-phase flows from a different view point, much of the work being concerned with the suspension of solid particles in fluids. An extensive review of the theory of solid-fluid mixture has been given by MARBLE [lo, 111 and So0 [12]. These studies include the work of DAVIDSON and HAR- RISON [13], MUBEY [14], BBENNEB [El, DIGIOVANNI and LEE [la], DREW [17,18] and PEDDIESON [19].

show abstract

Some unsteady parallel flows of particulate suspensions

Cited by 9 publications

References 8 publications

Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Effects of inertia on the diffusional deposition of small particles to spheres and cylinders at low Reynolds numbers

Unsteady Flow of Suspension through a Rectangular Pipe

Unsteady Flow of a Binary Mixture of Fluids Between Annular Space of Two Circular Cylinders

Contact Info

Product

Resources

About