Instability Of Free Surface Research Articles

Free surface instability of a rotating liquid film of a second-order fluid

The free surface instability of a liquid film of an incompressible second-order fluid attached to a rotating circular cylinder is studied with respect to rotationally symmetric infinitesimal disturbances. The surface mode is examined in detail; the shear wave mode is qualitatively discussed. The results show that for any Reynolds numberR and any surface tensionT, there is always a range of wave numberm for which the flow is unstable. The dependence of the growth rate as well as the critical wave numberm, on the normal stress coefficients of the fluid is studied quantitatively for small as well as for finiteR. It is found that while the first normal stress coefficient has no effect on the stability of the flow, the presence of the second normal stress coefficient always tend to make the flow less stable (i.e., larger growth rate). The critical wave length (which corresponds to the mode of maximum instability and thereby determines the wave length of the breaking apart of the rings formed on the cylinder) is longer for a second-order fluid than for a Newtonian one. These effects (larger growth rate and longer critical wave length) are more pronounced asR increases and/orb (the thickness parameter) increases for a fixed surface tension parameterS. Surface tension is always stabilizing. Decreasing surface tension increases the growth rate, more so for larger magnitude of the second normal stress coefficient.

Free surface instability of a layer of visco-elastic liquid flowing down an inclined plane

The present investigation is concerned with the free-surface instability of an incompressible third-order fluid film flowing down an inclined plane under the action of gravity. Applying linear hydrodynamic stability theory, the eigenvalue problems governing the stability of the flow are derived for the general case where the disturbances propagate along an arbitrary direction oblique to the main flow. Long wave solution has been obtained by the method of asymptotic expansion. SmallReynolds number solutions are obtained only for two-dimensional disturbances. Direct numerical method is used to compute the neutral stability curves, damping and amplification curves for various parametric values for the case of second-order fluid with two-dimensional disturbances when wave numbers are not small. The investigation is limited to the study of the free-surface modes.

Free surface instability in electrohydrodynamics

The study of electrostatic effects on the motion of fluids goes back to the work of Rayleigh (l) who discussed the effect of surface charges on the vibration of spherical drops, and Bassett (2) who studied the effect of a radial electric field on the stability of a jet. The subject has recently been taken up again by Melcher (3) and Crowley (4), and the author became interested in the subject through the monograph of the former author in which a wide variety of wave problems are described.

Critical Analysis of Open-Channel Resistance

Despite continued progress in the analysis of closed-conduit and boundary-layer resistance, many of the results have been slow to find their way into the hydraulics of open channels. In this paper an effort is made to take greater advantage of existing knowledge in related fields, largely through findings from a continuing program of research in which the writer has been engaged for several decades. The general resistance function is examined under the following interdependent categories: Effects of viscosity, roughness, and shape of cross section; effects of boundary nonuniformity; and effects of unsteadiness, particularly free-surface instability. Special attention is given to such matters as integration of the logarithmic velocity law, variation of roughness form and concentration, channel choking in the critical region, and resistance augmentation by both standing and traveling waves.

Stability of a Non-Newtonian Liquid Film Flowing Down an Inclined Plane

A layer of a non-Newtonian liquid, of which the constitutive equation is triply nonlinear, flows down an inclined plane under the action of gravity. The stability of the flow against wave formation is investigated. With M denoting a parameter involving the first and the second viscosities, the critical Reynolds number is given as a function of M and the slope of the plane, for small values of M. The theory presented here shows how free-surface instability of non-Newtonian fluids can be attacked, and provides a basis for stability experiments with non-Newtonian fluids.