title: Obtaining self-similar scalings in focusing flows.
abstract: The surface structure of converging thin fluid films displays self-similar behavior, as was shown in the work by Diez et al. [Q. Appl. Math. 210, 155 (1990)]. Extracting the related similarity scaling exponents from either numerical or experimental data is nontrivial. Here we provide two such methods. We apply them to experimental and numerical data on converging fluid films driven by both surface tension and gravitational forcing. In the limit of pure gravitational driving, we recover Diez' semianalytic result, but our methods also allow us to explore the entire regime of mixed capillary and gravitational driving, up to entirely surface-tension-driven flows. We find scaling forms of smoothly varying exponents up to surprisingly small Bond numbers. Our experimental results are in reasonable agreement with our numerical simulations, which confirm theoretically obtained relations between the scaling exponents.
authors.affiliation: Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA.|Physical Chemistry and Soft Matter, Wageningen University, Wageningen, The Netherlands.
authors.forename: Joshua A
authors.initials: JA
authors.lastname: Dijksman
authors.affiliation: Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA.|Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06511, USA.
authors.forename: Shomeek
authors.initials: S
authors.lastname: Mukhopadhyay
authors.affiliation: Harvey Mudd College, Department of Mathematics, 301 Platt Boulevard, Claremont, California 91711, USA.
authors.forename: Cameron
authors.initials: C
authors.lastname: Gaebler
authors.affiliation: Department of Mathematics, Duke University, Box 90320, Durham, North Carolina 27708-0320, USA.
authors.forename: Thomas P
authors.initials: TP
authors.lastname: Witelski
authors.affiliation: Department of Physics & Center for Nonlinear and Complex Systems, Duke University, Box 90305, Durham, North Carolina 27708-0305, USA.
authors.forename: Robert P
authors.initials: RP
authors.lastname: Behringer