Thin Liquid Films and Fluid Interfaces: Models, Experiments and Applications (12w5035)
Robert Behringer (Duke University)
Karen Daniels (North Carolina State University)
Rachel Levy (Harvey Mudd College)
Omar Matar (Imperial College London)
Michael Shearer (North Carolina State University)
Thomas Witelski (Duke University)
The mechanics of thin fluid layers is modeled by the lubrication approximation, which exploits a small aspect ratio to simplify the Navier-Stokes system of partial differential equations of viscous fluid flow. The predictive ability of the model has helped explain novel experimental observations, and has prompted new experimental investigations. For example, since the identification of undercompressive shocks in thin film flow up an incline driven by a thermal gradient against gravity, similar waves have been found in flow driven by surfactants , and in two-phase porous media flow. Experiments with opposing forces provided by thermal gradients, surfactants and spin-coating have uncovered further phenomena that await modeling and analysis .
The workshop will touch on many related aspects of thin films and fluid interfaces. Among these are the dynamics of fluid droplets, contact line dynamics and dewetting, evaporation, complex fluids, thin fluid sheets and threads, instabilities and pattern formation, vibrated and rotated thin films. The breadth of recent activity in this field suggests that a workshop that brings together experts and junior researchers from the many disparate groups will generate a vigorous and timely exchange of ideas.
The study of fluid droplets is a classic test-bed for the use of mathematical analysis and modeling to further the understanding of intricate and complicated fluid dynamics observed in experiments. Droplets at rest or spreading on a flat solid substrate represent a fundamental natural state of a finite-mass body of fluid with a free surface. They are ubiquitous in technological processes and nature, from micro-samples in labs-on-chips, to molten metals in manufacturing, condensed dew on plants, and depositions of bio-films in blood vessels. Droplets also have formed the basis for the thorough mathematical analysis of many fluid mechanics problems, from the classical descriptions of sessile drops in terms of axisymmetric surfaces of constant mean curvature to current studies of contact line dynamics on nano-structured hydrophobic substrates. Recent mathematical and experimental studies make use of fluid droplets to study transport mechanisms, intrinsic instabilities, and dynamic responses to external forcing. The proposed workshop will include several of these topics:
1. Spreading dynamics and contact instabilities due to the presence of soluble or insoluble surfactants or other additives such as nano-particles;
2. Convective instabilities and contact line effects in fluid mixtures subject to evaporation;
3. The influence of substrate properties (heterogeneous patterning, models of dewetting potentials and disjoining pressure, hydrophobicity, and slip-lengths); properties of complex fluids (mixtures, suspensions, non-Newtonian constitutive relations); droplets and contact line motion;
4. External forcing imposed by temperature or chemical gradients (Marangoni effects), electric fields, or motion of the substrate, typically with lateral or vertical vibration.
External forcing is a hot experimental research topic in micro- and nano-fluidics, in which the motion of droplets is controlled in very small confining geometries. This research is driven partly by the application to small-scale chemistry using lab-on-a-chip, which is leading to spectacular advances in the analysis of biochemicals, cell culture and health-care testing.
The study of systems with surface-active chemicals at interfaces provides an extra layer of complexity; these so-called surfactants may be present in the form of contaminants or may be added as part of a manufacturing process. Gradients of surfactant concentration give rise to surface tension variations that induce interfacial flows from regions of high concentration (low surface tension) to regions of low concentration. Study of such Marangoni-driven flows is of central importance to numerous industrial, biomedical and daily life settings; these include coating flow technology, microfluidics, surfactant replacement therapy for neonatal infants, film drainage in emulsions and foams and drying of semi-conductor wafers in microelectronics.
Surfactant-driven flows are also often accompanied by complex dynamics which include rupture, dewetting, and fingering; examples of the latter phenomena may be observed upon deposition of a surfactant solution droplet on the surface of a very thin fluid film. Recent modeling work has incorporated aspects of micelle-formation into the governing equations and resulted in trends that are qualitatively consistent with experimental observations. However, a number of open problems remain. These include isolating the mechanism underlying the super-spreading of droplets on hydrophobic substrates driven by certain types of surfactants and explaining recent experimental observations that surfactant solutions spreading on gels generate cracking and starburst pattern formations.
The aggregation of nanoparticles at interfaces and their influence on the flow has also received recent interest; these effects become accentuated in the presence of evaporation. In this case the particles may or may not be surface active. Particles have been observed to give rise to an acceleration of contact line motion as well as terrace-formation at the contact line (due to the structural intermolecular forces associated with their confinement between the fluid-liquid and liquid-solid interfaces); intricate patterns have also been observed in the wake of a dewetting, evaporating nanoparticle-laden film. In the case of surface-active nanoparticles, Marangoni effects can induce droplet motion and the recoiling and oscillation of fluid lenses. Systems involving thin films and droplets with nanoparticles are still relatively poorly understood and represent an opportunity for productive discussion and collaboration at the workshop.
A central component of the workshop will be the inclusion of experimental studies. The list of invited participants includes experts on experiments with thin flows, wetting, contact line deposits, vibrated drops and films, interfacial phenomena (including compliant and patterned substrates), viscoelasticity, locomotion, surfactant dynamics, multiphase flows, foams, bubbles, and droplets. In this field, new experimental phenomena and measurement techniques frequently arise in labs, opening up new challenges for theory and modeling.
The proposed workshop is related to two previous BIRS workshops, held in December 2003 and February 2010, but will provide a different focus. The 2003 meeting emphasized new developments in the theory of thin films, and helped identify new areas for experiment and theory. The recent 2010 workshop leaned heavily towards practical implementation, especially the role of thin films research in the design of microfluidic devices. The proposed 2012 workshop will emphasize the interplay between experiments, modeling, mathematical analysis and simulation. The distinguishing feature will be the role of experiments, in connection with both fundamental issues and applications. The workshop program will be designed to give ample time for presentations and discussion. The organizers (with the exception of Matar) are investigators in a focused research group (FRG) in thin liquid films, supported by the U.S. National Science Foundation (FRG: Collaborative Research: Dynamics of Thin Liquid Films: Mathematics and Experiments). The NSF grant has a workshop budget that will pay travel expenses for young researchers to participate in the workshop.
Each day will contain three sessions of three or four 20-minute talks, with a small number of longer overview talks at the beginning of the workshop. The three sessions will be in the morning, afternoon, and/or evening, allowing for an informal discussion session each afternoon for several hours. Additionally, there will be ample time for small group discussions. This format
works well with the BIRS facilities to promote interaction between junior and senior participants and to encourage the development of new collaborations and joint research projects across disciplinary boundaries. Depending on the level of interest, we will organize a poster session for the evening of day two; this is a good way for students and postdocs to publicize their research.
Each topical session will be followed by a guided discussion on the themes of that session, led by one of the organizers or a senior participant. These guided discussions, which the organizers have used or experienced at other workshops, provide a forum for comparing and contrasting approaches and for highlighting open questions. The discussion points will be prepared using drafts of the session talks. The discussions will be summarized along with the individual talks in the final BIRS report.
Day one: Overview and challenges: surface tension driven flow.
The first session will contain one or two talks outlining recent progress and areas of current interest in flows driven by surface tension gradients. The remainder of the day will be devoted to lectures on current research on experiments and theory of such flows, and applications.
Day two: Flows with additives.
The focus of day two will be the role of additives in modifying flow. Examples of additives include surfactants and nanometer-scale particles. Applications to biology and medicine.
Day three: Droplets and applications.
The general area of droplets, and associated issues of contact line dynamics and dewetting/film rupture will form the theme for day three. Modeling of evaporation has exciting possibilities, informed by quantitative experimental observations.
Day four: External forcing and interaction with solid boundaries, including patterned and compliant surfaces.
Day five: Future directions: participants volunteer for 5-minute presentation to begin discussion of a topic. (Morning only)
1. R. V. Craster and O. K. Matar. Dynamics and stability of thin liquid films. Reviews of
Modern Physics, 81(3):1131, 2009.
2. S.J. Weinstein and K.J. Ruschak. Coating flows. Ann. Rev. Fluid Mech. 36 (1), 29-53. 2004.
3. D. Bonn, J. Eggers, J. Meunier, and E. Rolley. Wetting and spreading. Rev. Mod. Phys. 81, 739-805, 2009.
4. R. Levy, M. Shearer, and T. P. Witelski. Gravity-driven thin liquid films with insoluble surfactant: Smooth traveling waves. European J. Appl. Math., 18, 679-708, 2007.
5. D. W. Fallest, A. M. Lichtenberger, C. J. Fox and K. E. Daniels. Fluorescent visualization of a spreading surfactant. New J. Phys. 12, 073029, 2010.