Vol. 88, No. 2, 1980

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The stability of the axially symmetric pendent drop

Henry Wente

Vol. 88 (1980), No. 2, 421–470

This paper analyzes the stability of the axially symmetric pendent drop for three different physical arrangements; problem A, constant pressure, fixed circular opening; Problem B, constant volume, prescribed angle of contact with a horizontal plate; Problem C, constant volume and fixed circular opening. As examples, the following results are established. Relative to Problem B we prove that for any angle of contact, α (0 < α < π), as the volume increases an inflection point will appear on the profile curve before instability occurs. For Problem C we show that if the opening is narrow enough to support a stable drop with a bulge then as the volume is increased drops with both a neck and a bulge will appear before instability occurs.

Mathematical Subject Classification 2000
Primary: 49H05, 49H05
Secondary: 53A10
Received: 9 August 1979
Published: 1 June 1980
Henry Wente
Department of Mathematics
University of Toledo
Toledo OH 43605-3390
United States