Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Results of experiments with thermocapillary flow in shallow liquid layers heated from the side are presented. The fluid has Prandtl number 17 and the main configuration investigated is an annular gap to avoid side‐wall effects. The liquid depth d was d≤3.00 mm to have negligible buoyancy effects. Various instabilities have been observed. At a Marangoni number M≂6⋅102, a transition to steady multicellular flow occurred. The convection cells are longitudinal rolls embedded in the main flow all rotating in the same direction. At M≂3⋅103, a transition of the steady multicellular flow to time‐dependent flow states (t) was observed. Two different t‐flow states have been identified by thermocouple measurements and by visualization of the dynamic‐free surface deformations of oscillatory flow. Both t states can be described by disturbances in the form of traveling waves. A short‐wavelength t state with small surface deformations and with waves traveling in azimuthal direction is the preferred mode for d≤1.4 mm. A long‐wavelength t state with larger surface deformations and with waves traveling in radial and in azimuthal directions is preferred for d≥1.4 mm. The stability diagram, wavelength, frequency, and phase speed of both t states are presented and the findings in comparison to an already existing theory by Smith and Davis [J. Fluid Mech. 132, 119, 145 (1983)] are discussed.

Instabilities of shallow dynamic thermocapillary liquid layers

The problem of steady, laminar, thermosolutal Marangoni convection flow of an electrically-conducting fluid along a vertical permeable surface in the presence of a magnetic field, heat generation or absorption and a first-order chemical reaction effects is studied numerically. The general governing partial differential equations are converted into a set of self-similar equations using unique similarity transformations. Numerical solution of the similarity equations is performed using an implicit, iterative, tri-diagonal finite-difference method. Comparisons with previously published work is performed and the results are found to be in excellent agreement. Approximate analytical results for the temperature and concentration profiles as well as the local Nusselt and sherwood numbers are obtained for the conditions of small and large Prandtl and Schmidt numbers are obtained and favorably compared with the numerical solutions. The effects of Hartmann number, heat generation or absorption coefficient, the suction or injection parameter, the thermo-solutal surface tension ratio and the chemical reaction coefficient on the velocity, temperature and concentration profiles as well as quantitites related to the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are presented in graphical and tabular form and discussed. It is found that a first-order chemical reaction increases all of the wall velocity, Nusselt and Sherwood numbers while it decreases the mass flow rate in the boundary layer. Also, as the thermo-solutal surface tension ratio is increased, all of the wall velocity, boundary-layer mass flow rate and the Nusselt and Sherwood numbers are predicted to increase. However, the exact opposite behavior is predicted as the magnetic field strength is increased.

J. Metzger

Papers

Coupling and separation of buoyant and thermocapillary convection