Extension of Rayleigh-Taylor Instability Theory with Applications

Author: Whipple, Christopher George

Year: 1974

Degree: Dissertation (Ph.D.)

Advisor: Plesset, Milton S.

Committee Member: Unknown, Unknown

Option: Engineering

DOI: 10.7907/5bc3-w217

Abstract

A theoretical derivation is presented for interfacial waves, both stable and unstable, which includes viscosity and surface tension. This result is extended to the case where one fluid has a finite thickness and is bounded by a rigid boundary or a free surface. As these solutions present formidable algebraic difficulties, approximate forms of solutions, which are motivated by physical arguments, are also given, and, through the use of a computer, the full theoretical result is shown to be fairly accurately reproduced by these approximations. The theory is used to give an explanation of the bioconvection patterns which have been observed with cultures of microorganisms which have negative geotaxis. Since such organisms tend to collect at the surface of a culture and since they are heavier than the culture medium the conditions for Rayleigh-Taylor instability are met. It is shown that the observed patterns are quite accurately explained by the theory. Similar observations with a viscous liquid loaded with small glass spheres are described. A behavior similar to the bioconvective patterns with microorganisms is found and the results are also explained quantitatively by Rayleigh-Taylor instability theory with viscosity. Further physical considerations of the bioconvection demonstrate the validity of the Rayleigh-Taylor instability model, and describe the steady state circulation of microorganisms. An approximate solution to a viscous fluid of finite depth with an exponential density gradient is developed, and the applicability of this result to certain bioconvective situations is discussed.

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