Nonlinear oscillations of pendant drops

Journal Article · Thu Sep 01 04:00:00 EDT 1994 · Physics of Fluids; (United States)

DOI:https://doi.org/10.1063/1.868120· OSTI ID:7143128

Basaran, O A; DePaoli, D W ^[1]

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1. Chemical Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6224 (United States)

Whereas oscillations of [ital free] drops have been scrutinized for over a century, oscillations of [ital supported] ([ital pendant] or [ital sessile]) drops have only received limited attention to date. Here, the focus is on the axisymmetric, free oscillations of arbitrary amplitude of a viscous liquid drop of fixed volume [ital V] that is pendant from a solid rod of radius [ital R] and is surrounded by a dynamically inactive ambient gas. This nonlinear free boundary problem is solved by a method of lines using Galerkin/finite element analysis for discretization in space and an implicit, adaptive finite difference technique for discretization in time. The dynamics of such nonlinear oscillations are governed by four dimensionless groups: (1) a Reynolds number Re, (2) a gravitational Bond number [ital G], (3) dimensionless drop volume [ital V]/[ital R][sup 3] or some other measure of drop size, and (4) a measure of initial drop deformation [ital a]/[ital b]. The change in frequency [Delta][omega] of pendant drops with increasing initial deformation is drop size dependent. As the average linear size of pendant drops characterized by [ital V][sup 1/3] becomes large compared to the rod radius, [ital V][sup 1/3]/[ital R][much gt]1, [Delta][omega] falls as [ital a]/[ital b] rises, in accordance with results for free drops. The dynamics of very small drops, i.e., ones for which [ital V][sup 1/3]/[ital R][much lt]1, however, are profoundly affected by the presence of the solid rod. For such small drops, [Delta][omega] rises as [ital a]/[ital b] rises, a remarkable fact. The results show that for drops of a given size, the frequency is insignificantly affected by viscosity over a wide of range of Reynolds numbers. However, when Re falls below a critical value, the nature of drop motion changes from underdamped oscillations to an aperiodic return to the rest state (Abstract Truncated)

• DOE Contract Number: AC05-84OR21400
• OSTI ID: 7143128
• Journal Information: Physics of Fluids; (United States), Journal Name: Physics of Fluids; (United States) Vol. 6:9; ISSN 1070-6631; ISSN PHFLE6
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
CALCULATION METHODS
DROPLETS
FINITE ELEMENT METHOD
FLUIDS
GALERKIN-PETROV METHOD
ITERATIVE METHODS
LIQUIDS
NUMERICAL SOLUTION
OSCILLATIONS
PARTICLES
REYNOLDS NUMBER
SURFACE PROPERTIES
SURFACE TENSION
TRANSIENTS