2004/08/16 by G. Ka"lbermann, Ka"lbermann, G.
Physics and Astronomy · #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Soft Condensed Matter (cond-mat.soft) #cond-mat.other #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.cond-mat/0408353
19 pages 1 figure
arxiv created 2004/08/16 · arxiv updated 2009/12/01
We develop a stream function approach for the horizontal Hele-Shaw, Saffman-Taylor finger. The model yields a nonlinear time-dependent differential equation. The finger widths derived from the equation are 1>λ>(1)/(√(5)), in units of half the width of the Hele-Shaw cell, in accordance with observation. The equation contains the correct dispersion relation for the creation of the finger instability. In an accompanying paper the stationary solutions of the equation are found numerically.