Stability of liquid zones

The criterion for the stability of a liquid zone of volume V and length L between two parallel circular coaxial plates of radius R and Ru is formulated via the calculus of variations. The liquid in the zone is static or uniformly rotating with angular velocity Ω and is subject to a gravitational acceleration g along the axis of the plates. For Ω = 0, V = πR2L, R = Ru, numerical computations give the maximum stable value of LR as a function of the Bond number e ≡ ρgR 2γ, where ρ is the density difference between the liquid and the surrounding fluid and γ is the liquid-fluid surface tension. Experimental measurements of the stability of water zones are in good agreement with the numerical results. Experimental and theoretical results for horizontal liquid zones (gravitational field perpendicular to the axis of the plates) show that for e < 0.5 horizontal zones are more stable than vertical zones.

[1]  Oskar Bolza,et al.  Lectures on the calculus of variations , 1905 .

[2]  G. Forsythe,et al.  Computer solution of linear algebraic systems , 1969 .

[3]  L. E. Scriven,et al.  Shapes of axisymmetric fluid interfaces of unbounded extent , 1969 .

[4]  G. Mason.  An experimental determination of the stable length of cylindrical liquid bubbles , 1970 .

[5]  J. F. Padday,et al.  The stability of axisymmetric menisci , 1973, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[6]  E. Pitts.  The stability of pendent liquid drops. Part 2. Axial symmetry , 1974, Journal of Fluid Mechanics.

[7]  M. C. Wilkinson,et al.  The static profiles of several solid/oil/water/vapor configurations , 1976 .

[8]  J. Carruthers,et al.  Studies of Floating Liquid Zones in Simulated Zero Gravity , 1972 .

[9]  K. Mika,et al.  Shape and stability of Menisci in czochralski growth and comparison with analytical approximations , 1975 .

[10]  L. E. Scriven,et al.  Pendular rings between solids: meniscus properties and capillary force , 1975, Journal of Fluid Mechanics.

[11]  C. W. Gear,et al.  Numerical initial value problem~ in ordinary differential eqttations , 1971 .

[12]  L. M. Hocking.  The stability of a rigidly rotating column of liquid , 1960 .

[13]  D. Dyson,et al.  Stability of fluid interfaces of revolution between equal solid circular plates , 1971 .

[14]  J. Carruthers,et al.  The stabilities of floating liquid zones in simulated zero gravity , 1972 .

[15]  J. M. Haynes.  Stability of a fluid cylinder , 1970 .

[16]  L. Rayleigh,et al.  XVI. On the instability of a cylinder of viscous liquid under capillary force , 1892 .

[17]  J. F. Padday.  The profiles of axially symmetric menisci , 1971, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.