Analytical solutions for the profile of two-dimensional droplets with finite-length precursor films

Carlos Alberto Perazzo, J. R. Mac Intyre, and J. M. Gomba
Phys. Rev. E 96, 063109 – Published 13 December 2017

Abstract

By means of the lubrication approximation we obtain the full family of static bidimensional profiles of a liquid resting on a substrate under partial-wetting conditions imposed by a disjoining-conjoining pressure. We show that for a set of quite general disjoining-conjoining pressure potentials, the free surface can adopt only five nontrivial static patterns; in particular, we find solutions when the height goes to zero which describe satisfactorily the complete free surface for a finite amount of fluid deposited on a substrate. To test the extension of the applicability of our solutions, we compare them with those obtained when the lubrication approximations are not employed and under conditions where the lubrication hypothesis are not strictly valid, and also with axisymmetric solutions. For a given disjoining-conjoining potential, we report a new analytical solution that accounts for all the five possible solutions.

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  • Received 8 September 2016
  • Revised 31 October 2017

DOI:https://doi.org/10.1103/PhysRevE.96.063109

©2017 American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Carlos Alberto Perazzo1,2,*, J. R. Mac Intyre3,†, and J. M. Gomba3,‡

  • 1IMeTTyB, Universidad Favaloro-CONICET, Solís 453, C1078AAI Buenos Aires, Argentina
  • 2Departamento de Física y Química, FICEN, Universidad Favaloro, Sarmiento 1853, C1044AAA Buenos Aires, Argentina
  • 3Instituto de Física Arroyo Seco IFAS (UNCPBA) and CIFICEN (UNCPBA-CICPBA-CONICET), Pinto 399, 7000, Tandil, Argentina

  • *perazzo@favaloro.edu.ar
  • jmintyre@exa.unicen.edu.ar
  • jgomba@exa.unicen.edu.ar

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Issue

Vol. 96, Iss. 6 — December 2017

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