The Long and Winding Path to Statistical Models for Large Ensembles of Sliding Drops: Berkeley Fluids Seminar

Seminar | April 15 | 12-1 p.m. | 3110 Etcheverry Hall

 Professor Uwe Thiele, Institute of Theoretical Physics, University of Münster

 Department of Mechanical Engineering (ME)

Abstract: After a brief review of a number of experiments on dewetting/spreading/sliding thin films/drops of simple liquids we introduce the concept of a gradient dynamics (hydrodynamic long-wave) model for the evolution of interface-dominated films and drops on solid substrates.

Next, we employ classical density functional theory (DFT) [1] to determine wetting potentials and Derjaguin (disjoining) pressures that encode the adsorption and wetting behaviour of liquids at solid substrates [2]. Entering them into the dynamical model we consider the spreading of individual (terraced) drops on either an adsorption layer or a completely dry substrate. To achieve this, the hydrodynamic model is modified such that for very thin layers a diffusion equation is recovered [3].

Next, we focus on the dynamics of individual sliding drops on an incline [4]. In particular, we discuss their bifurcation diagram and the occurring transformations in dependence of the driving force. We show that a number of shape transitions occur at saddle-node bifurcations. Further there is a global bifurcation that results in dynamic states where a main sliding droplet emits small satellite droplets at its rear (pearling instability) that subsequently coalesce with the next droplet. These pearling states show the period-doubling route to chaos [5].

The single-drop results are then related to direct numerical simulations on a large domain that examine the interaction of many sliding drops. The ongoing coalescence and pearling behavior results in a stationary distribution of drop sizes, whose shape depends on the substrate inclination and the overall liquid volume. We illustrate that aspects of the steady long-time drop size distribution may be deduced from the single-drop bifurcation diagrams. In the final coarse-graining step we use the obtained single-drop information to construct a statistical model for the time-evolution of the drop size distribution and show that it captures the main features of full-scale simulations [6].

[1] A. P. Hughes, U. Thiele, and A. J. Archer, Am. J. Phys. 82, 1119-1129 (2014).
[2] A. P. Hughes, U. Thiele and A. J. Archer, J. Chem. Phys. 142, 074702 (2015) and J. Chem. Phys. 146, 064705 (2017).
[3] H. Yin, D. N. Sibley, U. Thiele and A. J. Archer, Phys. Rev. E 95, 023104 (2017).
[4] T. Podgorski, J.-M. Flesselles and L. Limat, Phys. Rev. Lett. 87, 036102 (2001).
[5] S. Engelnkemper, M. Wilczek, S. V. Gurevich and U. Thiele, Phys. Rev. Fluids 1, 073901 (2016).
[6] M. Wilczek, W. Tewes, S. Engelnkemper, S. V. Gurevich and U. Thiele, Phys. Rev. Lett. 119, 204501 (2017).

Biography: Uwe Thiele is a Professor of Theoretical Physics in Münster, Germany. After his PhD (Dresden) he worked as research associate in Madrid, Berkeley, Dresden and Augsburg, before becoming faculty first at Loughborough University and later in Münster. There he is a director of the Institute of Theoretical Physics and also speaker of the Center of Nonlinear Science (CeNoS) of the University of Münster. He is mainly interested in dynamic phenomena related to simple, complex and active fluids and soft matter in systems that involve deformable interfaces between fluid phases. Such flows are inherently nonlinear and therefore subject to instabilities that may trigger transitions to intricate spatio-temporal behaviour. Particular present projects concern, e.g., pattern deposition in dip-coating, the bifurcation structure behind depinning, the dynamics of solidification in colloidal suspensions, gradient dynamics models for film flows of complex liquids and the spreading of biofilms. In all projects approaches from applied mathematics, dynamical systems and bifurcation theory are combined with (non)-equilibrium thermodynamics and statistical physics.

 pmarcus@me.berkeley.edu, 510-642-5942