Contact Line Dynamics on Heterogeneous Substrates
by Daniel Herde
Date of Examination:2014-01-21
Date of issue:2014-04-14
Advisor:Dr. Martin Brinkmann
Referee:Prof. Dr. Marcus Müller
Referee:Prof. Dr. Stephan Herminghaus
Persistent Address:
http://dx.doi.org/10.53846/goediss-4449
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Abstract
English
Fluid interfaces in contact with solid substrates play an important role in fields ranging from microfluidics, over oil recovery and inkjet printing to coating processes. Effective models for the static wetting of structured substrates exist, as models for the dynamics of a fluid interface moving over a molecularly uniform and flat substrate. In the present work, the effect of a periodically varying wetting energy on the dynamics of contact lines is studied. To study the static configurations, a minimisation approach for the free energy and continuation methods are employed. The dynamics of the free interface flow are modeled in the Stokes limit using boundary element methods. This is complemented by simulations of a simplified system in the form of the thin film model. First, the effect of surface heterogeneities on a contact line driven with a constant velocity is addressed. A connection between the motion of the contact line over the substrate and the macroscopic contact angle is observed. To get a better understanding of the response of the fluid interface to the variation of the contact angle, a time periodic variation of the contact angle is introduced. This allows to characterise the displacement of the contact line depending on the driving frequency and slip in the system. Based on the observed response of the fluid interface, a mode expansion model is proposed to give a simplified description for the motion of the contact line. The basic assumption is that there is no distinction between the response of the interface to a non-sinusoidal variation of the contact angle with time and the response to the contact angle determined by the current position of the contact line. This is followed by a study on the motion of a droplet driven over a heterogeneous substrate with a constant body force. There, the effect of the amplitude and characteristic length scale of the heterogeneity on the possible droplet configurations is studied. It continues with a study of the depinning process and dynamics of the depinned droplets. In the limit of high slip lengths, a coexistence of pinned and depinned droplets was observed. To understand the mechanism underlying this transition, a simplified model based on the translation and deformation mode of the droplet is considered. The model shows how the varying mobility ratio of these two modes allows for a change in the observed bifurcation scenario.
Keywords: free interface flows; contact line dynamics; boundary element methods
