The surface profile of a rotating liquid

Perturbation Solution of the Steady Newtonian Flow in the Cone and Plate and Parallel Plate Systems

“…In this region a new stretched variable, say (r -1)/ X(Re,e), is defined, in which X(Re,e) is chosen in such a way that the stresses at the interface are balanced, at least to first order. The interfacial stress balance is established by requiring the surface tension force to equal the net force associated with the stress distributions on both sides of the interface [see, for example, Wasserman and Slattery (1964)]. This will include the mean curvature of the interface, which is, in the present case, a nonlinear function in F"(£), F'(£), and F(£); F(£) is the value of r at the interface, namely, the unknown shape of the interface.…”

Form of spinning liquids in diverse geometries

“…A video of the process for the initial depth of h ¼ 3 cm is available online as the supplementary material. 16 V. DISCUSSION AND CONCLUSIONS While the existing literature on steady state rotation of liquids is largely limited to cylindrical containers and subcritical angular speeds, [2][3][4][5][6][7][8][9][10][11][12][13][14] the experiments described here explore, in four different geometries, how a dry region near the container's lowest point opens up above the critical angular speed.…”

“…[2][3][4][5][6][7] The accuracy of these methods does not typically permit discerning capillary effects near the vessel's walls. The effect of the surface tension has been analyzed in a number of papers [8][9][10] showing that the free surface is flatter near the rim than for a paraboloid. The evolution of the profile of the interface between two immiscible liquids, oil and water, during a spin-up in a rotating cylinder has been studied theoretically and experimentally by Yan et al 11 Because of their parabolic profiles, spinning liquid mirrors held inside cylindrical containers are important in astronomy and for optical devices.…”

Shape of a meniscus in a rotating vertical tube

“…This accounts for the dearth of investigations dealing with this system. The only studies we are aware of are those of Turkington and Osborne,16 Wasserman and Slattery,l7. all of which deal with limiting or approximate solutions, or cover a very restricted range of the variables involved. It is the purpose of this study to investigate this system in more depth, to generate solutions for a wide range of practical conditions, and to evaluate the potential advantages and drawbacks of using rotating menisci for the determination of surface and interfacial tensions.…”