On the Filamentation of Liquid by Means of Rotating Discs : 3rd Report, Theory of Filament Formation of Liquid

Abstract

Continued from the previous reports, the nature of filaments produced from the periphery of a rotating disc is examined comparing with the dripping of water drops from a tube. When a very small amount of water is fed to a capillary tube, the water dripps from the lower end of the tube. But when the amount of feed of water is increased beyond a certain value, the water flows down in a smooth laminar flow. At first sight, the filament produced from a rotating disc corresponds to this smooth laminar flow, but the close observation reveals that the liquid film produced from a rotating disccorrespond to this smooth laminar flow, and the filament correspond to the unstable chained beads which appear at the transition from the dropwise dripping to the smooth laminar flow. The stretching action of the tangential momentum of the flying mass of liquid left from the Rotating disc will be transmitted to the liquid column on account of viscosity, enabling the unstable chained beads to become a kind of very stable viscous flow. It is this stable viscous flow that makes the generation of the filaments possible. These facts will clearly be seen from the photographs of the unstable water columns sprung out of the periphery of rotating disc shown in the second report. Applying both theoretical and dimensional consideration to the results given in the second report, the following semi-empirical formulae to the critical flow rates are derived. The critical maximum flow rate for the dropwise atomization [numerical formula] The critical flow rate for the minimum pitch of filament [numerical formula] The critical minimum flow rate for the film formation for viscous liquid of Dρ/μ<30cm/s [numerical formula] And the critical minimum flow rate for film formation for non-viscous liquid of Dρ/μ>30cm/s [numerical formula] In the above formulae q1, q2, q3cm3/s : critical flow rates, D cm : diameter of disc, n rpm : rotational speed of disc, ρ g/cm3 : density of liquid, σ dyn/cm : surface tension of liquid, μ dyn·s/cm2 : viscosity of liquid. The reason why the from of {1+10(μ/√(ρσD))1/3} is adopted instead of ((μ/√(ρσD))1/3 lies in the fact that the critical flow rates q1 and q2 are still existing for the non-viscous liquid of μ&cong;0.