Journal of Fluid Mechanics



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Domain relaxation in Langmuir films


JAMES C. ALEXANDER a1, ANDREW J. BERNOFF a2, ELIZABETH K. MANN a3, J. ADIN MANN Jr a4, JACOB R. WINTERSMITH a5 and LU ZOU a3
a1 Department of Mathematics, Case Western Reserve University, Cleveland, OH 44106, USA
a2 Department of Mathematics, Harvey Mudd College, Claremont, CA 91711, USA
a3 Department of Physics, Kent State University, Kent, OH 44242, USA
a4 Department of Chemical Engineering, Case Western Reserve University, Cleveland, OH 44106, USA
a5 Department of Physics, Harvey Mudd College, Claremont, CA 91711, USA

Article author query
alexander jc   [Google Scholar] 
bernoff aj   [Google Scholar] 
mann ek   [Google Scholar] 
mann ja   [Google Scholar] 
wintersmith jr   [Google Scholar] 
zou l   [Google Scholar] 
 

Abstract

We report on theoretical studies of molecularly thin Langmuir films on the surface of a quiescent subfluid and qualitatively compare the results to both new and previous experiments. The film covers the entire fluid surface, but domains of different phases are observed. In the absence of external forcing, the compact domains tend to relax to circles, driven by a line tension at the phase boundaries. When stretched (by a transient applied stagnation-point flow or by stirring), a compact domain elongates, creating a bola consisting of two roughly circular reservoirs connected by a thin tether. This shape will then relax slowly to the minimum-energy configuration of a circular domain. The tether is never observed to rupture, even when it is more than a hundred times as long as it is wide. We model these experiments by taking previous descriptions of the full hydrodynamics, identifying the dominant effects via dimensional analysis, and reducing the system to a more tractable form. The result is a free boundary problem for an inviscid Langmuir film whose motion is driven by the line tension of the domain and damped by the viscosity of the subfluid. Using this model we derive relaxation rates for perturbations of a uniform strip and a circular patch. We also derive a boundary integral formulation which allows an efficient numerical solution of the problem. Numerically this model replicates the formation of a bola and the subsequent relaxation observed in the experiments. Finally, we suggest physical properties of the system (such as line tension) that can be deduced by comparison of the theory and numerical simulations to the experiment. Two movies are available with the online version of the paper.

(Received November 1 2005)
(Revised June 25 2006)


Key Words: Complex fluids; Interfacial flows.


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