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The uniform film model for the gravitional approach of fluid drops to plane and deformable interfaces
Author(s) -
Hartland S.,
Robinson J. D.
Publication year - 1973
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450510605
Subject(s) - spheres , surface tension , materials science , planar , rotational symmetry , coalescence (physics) , mechanics , drop (telecommunication) , plane (geometry) , viscosity , compressibility , composite material , physics , geometry , thermodynamics , computer science , mathematics , telecommunications , computer graphics (images) , astronomy , astrobiology
Axisymmetric drainage within thin planar or spherical films of viscosity μ, area A and uniform thickness δ at time t is governed by the equation\documentclass{article}\pagestyle{empty}\begin{document}$$ t = \frac{{3n^2 }}{{16\pi }}\mu \frac{{A^2 }}{F} \cdot \frac{1}{{\delta ^2 }} $$\end{document}where F is the force pressing on the film and n the number of immobile interfaces. Assuming that the film ruptures at a critical thickness which is independent of the physical properties and applied force, expressions of the form\documentclass{article}\pagestyle{empty}\begin{document}$$ \tau \propto n^2 \mu \,\Delta p^a v^b /\sigma ^c $$\end{document}may be obtained for drops approaching rigid and deformable interfaces and rigid spheres approaching deformable interfaces. The values of the exponents a, b and c suggest that an increase in drop volume, V, and density difference, δρ, and a decrease in interfacial tension, σ, should increase the coalescence time, τ, in liquid‐liquid systems. However in gas‐liquid systems an increase in δρ should decrease the coalescence time. The variation of δ with time was obtained experimentally from capacitance measurements. For drops approaching a deformable interface, the corresponding values of n are always close to 1 and in the region between 0 and 2. The values increase when the interfaces are made less mobile by adding surface active agents; they are also larger for drops approaching a rigid interface and for rigid spheres approaching a deformable interface. Consequently the uniform film model adequately describes the approach of drops to rigid and deformable interfaces.