Small-amplitude oscillations of viscous, capillary bridges are characterized by their frequency and rate of damping. In turn, these depend on the surface tension and viscosity of the liquid, the dimensions of the bridge, the axial and azimuthal wavenumbers of each excited mode and the relative magnitude of gravity. Both analytical and numerical methods have been employed in studying these effects. Increasing the gravitational Bond number decreases the eigenvalues in addition to modifying the well-known Rayleigh stability limit for meniscus breakup. At high Reynolds numbers results from inviscid and boundary-layer theories are recovered. At very low Reynolds numbers oscillations become overdamped. The analysis is applicable in measuring properties of semiconductor and ceramic materials at high temperatures under well-controlled conditions. Such data are quite scarce.

Small-amplitude oscillations of capillary bridges are examined in the limit of large modified Reynolds number. The contact line between the free surface of the bridge and the upper and lower supporting walls is allowed to undergo a restrained motion by taking its velocity to be proportional to the slope of the free surface there. It is found that the oscillation frequency and damping rate depend on the aspect ratio of the bridge, the mode being excited, the motion of the contact line, and the modified Reynolds number. Very good agreement with other studies is obtained for Re>100.

Spin coating of two commercially used polymer solutions is studied both theoretically and experimentally. Physical and rheological characterization of these solutions indicates that under the spinning conditions currently used they behave as nonvolatile, viscoelastic fluids with constant viscosity and elasticity. The corresponding Reynolds (Re) and Deborah (De) numbers are up to order unity. The theoretical analysis demonstrates and explains why, at very short times after the inception of impulsive spinning, the velocity and stress fields in such fluids develop in an oscillatory manner. The amplitude of these oscillations increases with the ratio of the retardation parameter to the Deborah number, whereas their damping rate gets smaller as De increases. Since these oscillations dissipate very rapidly, and before substantial thinning of the film takes place, the thinning rate, velocity, and shear stress components do not deviate eventually from those of a Newtonian fluid. Such a complete explanation of similar experimental findings has not been offered before. The radial normal stress component does increase considerably over its Newtonian value, and this explains certain ‘‘experimental practices.’’ Similar oscillatory development early on occurs even at higher Re, as long as Re∼De, but it is dissipated again, this time because of the abrupt thinning of the film. The theoretical results are in good agreement with experimental measurements of ‘‘dry film’’ thickness and with dynamical measurements of ‘‘wet film’’ thickness during spinning, which are reported herein for the first time. Care must be taken in reporting ‘‘dry film’’ thickness because the commercial solutions under study retain part of the solvent after ‘‘soft baking’’ over a hotplate. Complete solvent removal produces dry films, but requires treatment in a vacuum oven, higher temperatures, and longer heating times.

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Articles you may be interested inSymmetry reductions and some exact solutions for rotating flows of an Oldroyd-B fluid with Hall currents AIP Conf.Flow of a fractional Oldroyd-B fluid over a plane wall that applies a time-dependent shear to the fluid AIP Conf.The transient flow of an Oldroyd-B fluid over an infinite disk set in rotation impulsively is studied under the similarity assumption. The unsteady velocity and stress field is calculated exactly for short times by a power series expansion in time. The order of magnitude of the velocity and stress components is found to depend on the relative magnitude of the Deborah number (De) and the ratio of solvent to polymeric viscosities (JLr)' When either one becomes very small, a solution using singular perturbations and Laplace transforms is developed. It is found that the diffusive mechanism for momentum transfer, which exists for about JLr>O.l (depending on De) dramatically changes and turns into a propagating wave for JLr