By Victor Ya. Shkadov, Gregory M. Sisoev (auth.), H.-C. Chang (eds.)
The lively box of multi-phase movement has gone through basic alterations within the final decade. Many salient advanced interfacial dynamics of such flows at the moment are understood at a simple point with specific mathematical and quantitative characterization. this can be rather a departure from the normal empirical technique. At an IUTAM Symposium at Notre Dame, in 1999, many of the top researchers within the box amassed to study the growth to this point and to think about destiny instructions. Their stories are summarized during this complaints. issues coated comprise solitary wave dynamics on viscous movie flows, sheet formation and drop entrainment in stratified move, wetting and dewetting dynamics, self-similar drop formation dynamics, waves in bubbly and suspension circulation, and bubble dynamics. it's a targeted and crucial reference for utilized mathematicians, physicists, examine engineers, and graduate scholars to maintain abreast of the most recent theoretical and numerical advancements that promise to rework multi-phase move research.
Read or Download IUTAM Symposium on Nonlinear Waves in Multi-Phase Flow: Proceedings of the IUTAM Symposium held in Notre Dame, U.S.A., 7–9 July 1999 PDF
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Additional resources for IUTAM Symposium on Nonlinear Waves in Multi-Phase Flow: Proceedings of the IUTAM Symposium held in Notre Dame, U.S.A., 7–9 July 1999
Example text
Therefore, Q*(t*) = (wVr/2)sinwt•. For large enough Womersley number {3 (w/va) 112 b, where va is the air viscosity, the core axial velocity field is assumed to take the following form: = u • = { U*(t*) U"1t") (b- r•) 0:::; r• :::; b- 6 b- 6::::; r• ::::; b (4) where 6 = (va/w) 112 is a Stokes boundary layer thickness, and U*(t*) is determined from Q*(t*): wVr . • U *( *) (5) t = 27rb2(1- a) smwt where a= 6/b « 1. 1 = (p,aw}/(t 3 a) is a dimensionless frequency 'Y 36 D. B. GROTBERG representing the ratio of the capillary time scale to the time scale due the oscillatory core flow.
Introducing the traveling wave transformation into Eqs. , h.. 2(1- Ce + Ce h1 ) 2 ) hi{h 1Ce-(1-Ce+Ce h1 ))}/{-We h{ }. The asymptotic form of the wavy film can be obtained by integrating directly the above set of ODEs. The numerical procedure requires only an initial condition, which can be taken as a small perturbation from the smooth film solution. A complete comparison of numerical computation and experimental data is presented in [8]. e. near zero), we can perform a weakly nonlinear analysis to explore the flow dynamics near criticality.
If we kept all terms up to order &2, the coefficient in Eq. 132: (12b) Eq. (12b) agrees well with experimental data. Although Eqs. (12) were derived for flows near criticality only, Fig. 6 shows convincing evidences that such correlation is also useful in predicting the maximum film thickness for low to intermediate Reynolds number and especially for low Kapitza fluids. The analytical result, Eq. (12a), may be used to determine the critical flow rate at occlusion for a vertically falling film between two parallel plates.
