Particle collision efficiencies for a sphere

Abstract

Trajectories are calculated for small particles introduced upstream into a fluid flowing past a fixed sphere. Unseparated potential flow is taken as the velocity profile for the fluid, and the effect of gravity is included in the formulation when it acts along the axis of symmetry. Using a numerical procedure, particle trajectories which graze the sphere, and the corresponding collision efficiencies, are calculated for values of the Stokes number σ. When gravity is neglected, an analytic solution is obtained for large values of σ which is in good agreement with the numerical results for σ as low as 5. These results are compared with those of Sell (1931) and Langmuir & Blodgett (1946). When gravity is included, a critical value of the Stokes number σc is calculated for which no collisions occur until σ > σc.

The Inertial Hydrodynamic Interaction of Particles and Rising Bubbles with Mobile Surfaces

“…[1.5] For intermediate particle dimensions under conditions where This was confirmed in papers in which the finite size of the particles was taken into account ( 39,40 ) . With decreasing K É K c , [1.11] particle size and a corresponding decrease in inertial forces and the Stokes number K , the inertial deposition of parti-the role of inertial forces cannot, a priori, be excluded.…”

Dust Deposition in Granular Bed Filters: Theories and Experiments

“…43 were used. The figures contain also results of Herne, 44 Michael and Norey, 45 Langmuir, 10 42 with some experiments of Walton and Woolcock. 47 As seen in the figures, the solutions are in good agreement for the two limiting cases …”

Exact and Approximate Expressions for Bubble–Particle Collision

“…The determination of an expression for R c in [1] is a nontrivial exercise which has occupied the attention of many researchers in collodial hydrodynamics during the past six decades since the original work of Sutherland (2) (which dealt with potential flow around the bubble in the absence of both inertial forces and gravitational effects); principal contributions in this area include the work of Yoon and Luttrell (1, 3), Ahmed and Jameson (4), Schulze (5, 6), Flint and Howarth (7), Nguyen-Van and Kmet (8), Nguyen-Van (9), Weber (10), Weber and Paddock (11), Reay and Ratcliff (12), Dobby and Finch (13), Anfruns and Kitchener (14,15), Spielman (16), and Michael and Norey (17). During the course of this analysis, we will have occasion to refer to specific results in several of the papers referenced above and, in particular, will indicate the manner in which many of those results are either special cases of or approximations to the more exact relations that are derived below.…”

“…In [17] and [18],ṽ ps represents the (terminal) particle settling velocity for Stokesian particles, v ps ϭ ṽ ps is the true particle settling velocity, and G is the dimensionless particle settling velocity. For Stokesian particles, therefore, G ϭṽ ps /v B .…”

“…Using the definitions [17] and [18], in [16], assuming that St Ӎ 0, so that inertial effects are discounted, and noting that Ϫv ps ϭ ͉v ps ͉, ϪG ϭ ͉G͉, we easily find that…”