ICMS

Jul 6, 2009 - Jul 9, 2009

Royal Society of Edinburgh, 22-26 George Street, Edinburgh

Organisers

Name	Institution
Duffy, Brian	University of Strathclyde
Homsy, G.M. "Bud"	University of California at Santa Barbara
Wilson, Stephen	University of Strathclyde

Workshop photographs are available here.

Thin films of fluid are of central importance in numerous industrial, biomedical, geophysical and domestic applications, and display a rich and varied range of behaviours, including pattern formation, dewetting, rupture and finite-time blow up. As well as being of great interest in their own right, thin-film flows provide a “test bed” for research into a huge range of challenging nonlinear problems in physics, chemistry and mathematics. As a consequence research by a wide range of scientists, including physicists, engineers, chemists and mathematicians, using a wide variety of analytical, numerical and experimental techniques on many different aspects of thin-film flow has grown dramatically in recent years as novel applications have continued to appear and increasingly sophisticated theoretical and experimental techniques have been developed.

The aim of this meeting is to bring together leading international experts in thin-film flow from across several different traditional academic disciplines, including mathematics, engineering, physics and chemistry, to report on their latest discoveries and to foster new inter-disciplinary collaborations. Such a genuine mixing of scientists with common interests from different specialities is rare and, we believe, is the most likely way to spark genuinely new and exciting research.

This meeting will be organised by Professor Stephen Wilson and Dr Brian Duffy (University of Strathclyde) together with Professor G. M. “Bud” Homsy (University of California, Santa Barbara). Bud won the American Physical Society Fluid Mechanics Prize in 2006 and has a distinguished track record of research in many areas of fluid mechanics, including thin-film flow.

This meeting builds on the great success of the 1999 ICMS meeting "The Dynamics of Thin Fluid Films" organised by Wilson, Duffy and Michael Grinfeld from the University of Strathclyde.

The workshop will cover the latest developments in thin-film flow including (but not limited to) the rapidly growing fields of foam dynamics, micro-fluidics and nano-technology, as well as the latest experimental and numerical techniques and asymptotic analysis, all of which are able to cast new light on the subtle interplay between competing physical effects in thin-film flows.

Specific topics we hope to cover include (but are not limited to) the following:

• the analysis of evaporating layers and droplets,
• the complex structure and dynamics of surfactant-laden flows, the coarsening dynamics of droplets, thin-film flow of visco-plastic and visco-elastic fluids (including exciting developments on cooling lava flows), the propagation of thin fluid-filled cracks,
• thin-film modelling of the Arctic ice sheet and shelf (including its breakup), and numerous new and exciting biological and medical applications (including wound healing, biofilm formation and growth,
• the dynamics of fluid linings, and several aspects of cell motion.

As well as an invitation list of distinguished international experts, we also intend to include a number of postgraduate and early-career researchers with an interest in thin-film flow.

This workshop will also incorporate a Knowledge Transfer seminar. There are two main objectives for the seminar:

• to raise awareness within industry of how ICMS can help companies access and commercially exploit academic research and expertise in mathematics and computing
• to understand how companies working in the area of thin films use mathematics and computing in their businesses and to identify potential areas of collaboration on new and industrially motivated problems.

During the seminar some examples will be discussed in which mathematical ideas and techniques have been successfully applied to the solution of problems motivated by thin film applications. Representatives from industry are also invited to give a short company presentation highlighting any areas in which a mathematical approach to a problem could be of benefit.

Workshop funded by:
EPSRC
SFC
LMS
EUROMECH
EMS
GMJT

Arrangements

Participation
Participation is by invitation only. The workshop will begin on Monday 6 July and finish on Thursday 9 July 2009.

UK Visas
If you are travelling from overseas you may require an entry visa. A European visa does not guarantee entry to the UK. Please use this link to the UK Visas site to find out if you need a visa and if so how to apply for one. If you do require a visa, ICMS can provide a signed invitation letter.

Venue
The meeting will be held at the Royal Society of Edinburgh, 22-26 George Street, Edinburgh, EH2 2PQ. The Conference Room is equipped with an OHP, data projector and flipchart.

The ICMS travel pages contain advice on how to travel to Edinburgh and useful maps of the city centre.

Accommodation
ICMS has arranged single en-suite rooms in local guest houses for those who require it. Accommodation is typically about 15 to 30 minutes walk from the Royal Society of Edinburgh. Participants are also free to make their own arrangements and may claim back the cost, with receipts, up to a maximum of £65.00 a night for up to 4 nights. A list of Edinburgh accommodation of various sorts and prices is available here . Sections 1-3 are particularly relevant.

Meals and Refreshments
There will be a combined Registration and informal wine reception on Sunday evening 5 July 2009, at ICMS, 14 India Street.

Morning and afternoon refreshments will be provided on each day of the workshop.

Light buffet lunches will be provided on only Monday 6 July and Thursday 9 July at the Royal Society of Edinburgh at no cost to participants. For the remainder of the days, participants are free to explore the many cafés, sandwich shops, restaurants and bars nearby. On arrival we will provide you with a ‘welcome’ pack which will contain information about eating places nearby.

On Tuesday 7 July a mezze style informal evening meal will be provided in Nargile Turkish Restaurant, 73 Hanover Street, at 19.00. The Workshop Dinner will take place on the evening of Wednesday 8 July at 19.00 at The Magnum Restaurant, 1 Albany Street. The workshop grant will cover the cost of these meals.

Registration
There will be a combined Registration and informal wine reception from 18.00 to 19.30 on Sunday evening 5 July 2009, at ICMS, 14 India Street.

Wine and snacks will be available throughout that period and you may register at any time between 18.00 and 19.30.

Those who cannot register on Sunday evening may do so at the Royal Society of Edinburgh, 22-26 George Street from 09.00 to 09.50 before the talks start on Monday morning. PLEASE NOTE THAT THE WORKSHOP WILL NOT TAKE PLACE AT ICMS, 14 INDIA STREET.

Financial Arrangements
Unless otherwise specified in your invitation letter, the workshop grant will cover the cost of your bed and breakfast accommodation, tea/coffee throughout the workshop, lunch on Monday and Thursday only, the wine reception, the informal supper on Tuesday and the Workshop Dinner on Wednesday evening.

If we have agreed to pay some of your travel costs, you will be informed by email. Reimbursement will take place after the workshop and will involve payment directly into your bank account. At Registration you will be given an expenses claim form and this should be submitted to ICMS, with original receipts. It would be helpful if you could bring your bank details to the workshop. In addition to the bank account number, participants from the USA and Canada will require their bank’s routing number, those from the UK will be asked for the bank sort code, and those from Europe and the rest of the world, their IBAN and SWIFT/BIC code. We cannot reimburse any item without a signed claim form and original receipts.

Unless otherwise stated in your invitation or further correspondence, all participants will be asked to pay a modest registration fee of 60.00 GBP to help cover local costs. Please note members of EUROMECH are offered a reduced rate of 30.00 GBP. This can be paid at Registration in cash, by sterling cheque or by providing credit/debit card details. Please note we do not accept American Express or Discover Card.

If you wish to pay this fee in advance please use this credit or debit card payment form. The form should be printed out, completed and faxed back (as email is not a secure way of sending credit card information). The fax number is on the form.

Programme

EACH TALK IS 20 MINUTES FOLLOWED BY 10 MINUTES FOR DISCUSSION/CHANGEOVER APART FROM THOSE MARKED WITH *

Sunday 5 July

18.00 - 19.30

Registration and informal wine reception, ICMS, 14 India Street

 

Monday 6 July

9.00 - 09.50	Registration and Coffee
	Droplets and spreading
09.50 – 10.30 *	David Quere (ESPCI and École polytechnique) Drops in asymmetric landscapes
10.30 – 11.00	John Lister (University of Cambridge) The dynamics of pendent drops on a thin film coating
11.00 – 11.30	Tea/Coffee
11.30 – 12.00	Serafim Kalliadasis (Imperial College London) Influence of spatial heterogeneities on contact line dynamics PDF of Presentation
12.00 – 12.30	Patrick Tabeling (ESPCI) Droplets and microfluidics
12.30 -14.00	Lunch provided in the Wellcome Room East, RSE
	Non-isothermal flows
14.00 – 14.30	Tatiana Gambaryan-Roisman (Technische Universität Darmstadt) Marangoni convection and nano-particles deposition in evaporating liquid films on substrates with non-uniform thermal conductivity
14.30 - 15.00	Brian Duffy (University of Strathclyde) Non-isothermal flow of a thin film on a stationary or rotating cylinder
15.00 – 15.30	Uwe Thiele (Loughborough University) Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions
15.30 – 16.00	Tea/Coffee
16.00 – 16.30	Vladimir Ajaev (Southern Methodist University) The effect of evaporation on fingering instabilities
16.30 – 17.00	Mark Kelmanson (University of Leeds) Multiple-timescale asymptotics for coating flows PDF of Presentation

 

Tuesday 7 July

	Spreading
9.00 - 09.40 *	Jens Eggers (University of Bristol) Hydrodynamic theory of coating
09.40- 10.10	Natalia Ivanova (Loughborough University) Kinetics of spreading of aqueous trisiloxane solutions over hydrophobic surfaces
10.10 – 10.40	Laurent Limat (CNRS and Université Paris Diderot) Structure formation observed for two kinds of dewetting fronts
10.40 – 11.10	Luc Lebon (CNRS and Université Paris Diderot) Liquid/liquid spreading without and with flow
11.10 – 11.40	Tea/Coffee
11.40 – 12.10	Jacco Snoeijer (University of Twente) Maximum size of drops levitated by an air cushion THIS TALK WILL BE PRESENTED BY Jens Eggers (University of Bristol)
12.10 – 12.40	Ulysse Delabre (Laboratoire de Physique Statistique) Coalescence driven by line tension
12.40 -14.00	Lunch break (no lunch provided). Poster session in the Wellcome Room East, RSE
	Flow over topography
14.00 – 14.30	Nuri Aksel (University of Bayreuth) Linear and nonlinear resonance in viscous film flow over topography PDF of Presentation
14.30 - 15.00	Philip Gaskell (University of Leeds) Competing geometric and inertial effects on local flow structure in film flow over corrugated substrates
15.00 – 15.30	Stephen Wilson (University of Strathclyde) Sheets, rivulets and droplets subject to an external air flow
15.30 – 16.00	Tea/Coffee
16.00 – 16.30	Henry Power (University of Nottingham) Integral equation simulation of three-dimensional thin film flow over and around obstacles
16.30 – 17.00	Harvey Thompson (University of Leeds) Inertial thin film free-surface flow over planar substrates with topography
19.00 -	Informal evening meal at Nargile Turkish Restaurant, 73 Hanover Street

 

Wednesday 8 July

	Coating and films
9.00 - 09.30	Eugene Benilov (University of Limerick) On the stability of shallow rivulets
09.30- 10.00	Rouslan Krechetnikov (University of California at Santa Barbara) Controversies of the Landau–Levich problem
10.00 – 10.30	Alex Oron (Technion-Israel Institute of Technology) Stability of temporally forced liquid films
10.30 – 11.00	Jacy Bird (Harvard University) Dynamics of thin curved films
11.00 – 11.30	Tea/Coffee
11.30 – 12.00	Benoit Scheid (Universite Libre de Bruxelles) Non-monotonic behaviours of the draw resonance instability in stretching viscous sheets
12.00 – 12.20 *	John Billingham (University of Nottingham) Thin, three dimensional climbing drops
12.30 -14.00	Lunch break
	Bubbles
14.00 – 14.30	Andrew Hazel (The University of Manchester) Steady propagation of air fingers in rectangular tubes
14.30 - 15.00	Anne Juel (The University of Manchester) Partially-occluded tubes can force switch-like transitions in the behaviour of propagating bubbles
15.00 – 15.30	Wendy Zhang (University of Chicago) Memory as vibration in a disconnecting air bubble
15.30 – 16.00	Tea/Coffee
	Stability and rupture
16.00 – 16.30	Dirk Peschka (Weierstrass Institute for Applied Analysis and Stochastics) Self-similar rupture for thin films with slip PDF of Presentation
16.30 – 17.00	Ranganathan Usha (Indian Institute of Technology) Thin film flow down a porous incline: dynamics and stability
19.00 -	Workshop Dinner at The Magnum Restaurant, 1 Albany Street, Edinburgh (dress informal)

 

Thursday 9 July

	Novel applications
9.00 - 09.30	Peter Evans (Humboldt-Universität zu Berlin) Thin film models for quantum dot structures in solid films
09.30- 10.00	Günther Grün (University of Erlangen-Nürnberg) On phase-field models for dynamic electrowetting
10.00 – 10.30	Andrew Hogg (University of Bristol) The flow and arrest of viscoplastic fluids
10.30 – 11.00	John King (University of Nottingham) Thin film modelling of growing populations of cells
11.00 – 11.30	Tea/Coffee
11.30 – 12.00	Lennon O'Naraigh (Imperial College London) Instability in two-phase turbulent stratified flow
12.00 – 12.30	Rosemary Dyson (University of Nottingham) A fibre-reinforced fluid model of anisotropic root cell growth
	Knowledge transfer afternoon
12.30 -13.30	Networking lunch provided in the Wellcome Room East, RSE
14.00 – 14.30	David Gelder (Mathematics for Manufacturers) The interaction between surface diffusion and very low Reynolds number flow
14.30-15.00	Michele Taroni (University of Oxford) Mathematical modelling of the screen-printing process
15.00-15.30	Dilwyn Jones (Emral Ltd) Institute of Physics Printing and Graphics Science Group. Air lubrication effects in handling and winding of thin web materials. PDF of Presentation
15.30-16.00	Tea/Coffee

 

Presentations:

Presentation Details
Ajaev, Vladimir
The effect of evaporation on fingering instabilities
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We investigate the flow of evaporating thin films of viscous liquid on inclined solid substrates under the influence of gravity. A lubrication-type approach is used to develop a three-dimensional model of the flow and study the effect of evaporation on the fingering instability that develops along the contact line in the transverse direction of the flow is studied. It is found that evaporation acts to suppress the instability if the evaporation number, a nondimensional measure of the mass flow rate across the interface, is above a critical value. The critical value decreases as the inclination angle is decreased. For the values of evaporation number below the critical one, the fingers grow initially, but then saturate at a length which depends on the evaporation conditions. It is also shown that thermocapillarity acts to enhance the instability. (Joint work with J.Klentzman)
Aksel, Nuri
Linear and nonlinear resonance in viscous film flow over topography
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We study the gravity-driven flow of a viscous liquid over a periodically undulating inclined substrate numerically and analytically. Numerical solutions of the full, steady Navier-Stokes equation are computed to study the influence of the film thickness, inertia and capillarity on the free surface. We observe that the first few harmonics of the free surface exhibit local maxima by varying the Reynolds number. This resonance effect is amplified with increasing bottom steepness. Furthermore, the interface position shows bistable resonance, when the bottom undulations are steep enough. Motivated by the numerical findings, we approximate the Navier-Stokes equation for rather weak bottom undulations and arbitrary film thickness by deriving an Orr-Sommerfeld equation. The analytical and numerical results predict very well the linear behaviour of the full numerical solution. Furthermore, it can be concluded, that the resonance is associated with an interaction of the undulated film with capillary-gravity waves traveling against the mean flow direction. The linear analysis of the Orr-Sommerfeld equation only captures the leading harmonic of the free surface. We therefore derive an integral boundary-layer equation for thin films and solve it analytically and numerically. The resonance of leading and higher harmonics of the free surface can be predicted by an analytic resonance condition. It can be shown that higher harmonics of the free surface are generated by a nonlinear coupling of the wall with lower-order harmonics of the free surface. Finally the integral boundary-layer approach reproduces the bistability of the Navier-Stokes equation. Joint work with C Heining (University of Bayreuth), V Bontozoglou (University of Thessaly) and A Wierschem (Management Center Innsbruck).
Benilov, Eugene
On the stability of shallow rivulets
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We examine the linear stability of a capillary rivulet under the assumption that it is shallow enough to be described by the lubrication approximation. It is shown that rivulets on a sloping plate are stable regardless of their parameters, whereas rivulets on the underside of a plate can be either stable or unstable, depending on their widths and the plate's slope. For the case of a horizontal plate, sufficiently narrow rivulets are shown to be stable and sufficiently wide ones unstable, with the threshold width being pi/2 (sigma/g rho)^1/2 (rho and sigma are the liquid's density and surface tension, g is the acceleration due to gravity). It is also shown that, even though the plate's slope induces in a rivulet a sheared flow (which would normally be viewed as a source of instability) -- in the present problem, it is a stabilising factor. The corresponding stability criterion involving the rivulet's width and the plate's slope is computed, and it is demonstrated that, if the latter is sufficiently strong, all rivulets are stable regardless of their widths.
Billingham, John
Thin, three dimensional climbing drops
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In this talk I will discuss how the thin droplet approximation, recently used by Benilov to study two dimensional droplets shaken up an inclined plane, can be extended to three dimensions. I will show how to solve the resulting free boundary problem numerically, and present some preliminary results. (Joint work with Eugene Benilov)
Bird, Jacy
Dynamics of thin curved films
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We study the dynamics of a thin curved film that is subject to capillary, inertial, and applied forces.
Delabre, Ulysse
Coalescence driven by line tension
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We will present an experimental study about the coalescence driven by line tension. We can observe such a situation in thin nematic films on water where nematic pancakes coexist with a trilayer of molecules. We have measured how the line tension depends on the thickness of the film. This enables us to rescale the dynamics of the coalescence with the size and shape of the domains. We compare the dynamics with previous models. Finally we show that when two domains of different thicknesses coalesce, a fingering phenomenon occurs in the transition region.
Duffy, Brian
Non-isothermal flow of a thin film on a stationary or rotating cylinder
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Using the lubrication approximation we investigate two-dimensional steady flow of a thin film of fluid with temperature-dependent viscosity on a uniformly heated or cooled horizontal cylinder, which may be stationary or rotating about its axis. Using a combination of analytical and numerical methods we analyse the problem in general and in a number of physically relevant asymptotic limits (including weak and strong heating and large and small heat transfer) and thus elucidate the role of non-isothermal effects.
Dyson, Rosemary
A fibre-reinforced fluid model of anisotropic root cell growth
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We consider the primary root elongation zone of the model plant Arabidopsis thaliana, in which cells undergo rapid anisotropic growth: the radius remains approximately constant whilst the length increases 30 fold or more. Plant cells differ from animal cells by the presence of a tough cell wall, containing oriented cellulose microfibrils, which maintains a high turgor pressure within the cell. Growth has been traditionally modelled using the “Lockhart equation” which relates the growth rate of the cell length to the internal pressure but takes no account of the mechanical anisotropy caused by the microfibrils; growth is assumed to only occur axially. We employ a fibre-reinforced fluid model for a pressurised hollow viscous cylinder, exploiting the small aspect ratio of the walls, to represent a growing cell. By taking an appropriate limit of the various viscosity functions we give a solution in which the microfibrils maintain the cell radius whilst allowing growth axially. We find an expression for the growth rate of the cell length, which reduces to the “Lockhart equation” upon appropriate simplification.
Eggers, Jens
Hydrodynamic theory of coating
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A prototypical problem in the study of coating is that of a solid plunging into or being withdrawn from a liquid bath. If the fluid does not wet the solid, the solid remains dry unless it is withdrawn at sufficiently high speed so that fluid is entrained by viscous drag. We show that there exists a critical speed above which a three-phase contact line is no longer sustainable, and the solid is being coated with a liquid film. We explain the nature of this transition by matching the highly curved contact line region to the static profile far away from it. Next we consider the properties of the resulting film covering the substrate. If the fluid wets the solid, the film thickness scales according to the classical theory of Landau, Derjaguin, and Levich. If the film results from a dynamic wetting transition, the entrained film is much thicker. All our theoretical predictions are compared in detail to experiment.
Evans, Peter
Thin film models for quantum dot structures in solid films
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The modelling of nanostructures arising in epitaxially grown thin films is important for the study of self-organised quantum dots. Typical PDE models for evolution by "surface diffusion" include contributions to the chemical potential from misfit strain and free surface energy. The former arises from a lattice mismatch with the substrate (driven by the Asaro-Tiller-Grinfeld instability and giving rise to Stranski-Krastanow islands); the latter includes "wetting" effects. We present models for film evolution which include anisotropy of the free surface energy. We examine the stationary states resulting from the model, and show results from 2D and 3D numerical simulations displaying facetted shapes which exhibit coarsening behaviour.
Gambaryan-Roisman, Tatiana
Marangoni convection and nano-particles deposition in evaporating liquid films on substrates with non-uniform thermal conductivity
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Evaporation of liquid layers is encountered in many technical applications, including self-assembly of nano-particles, ink-jet printing, cooling and distillation. Marangoni convection plays an important role in hydrodynamics of nonisothermal liquid films. We develop a model describing Marangoni convection, interface dynamics and evaporation in liquid films on composite substrates or substrates of functionally graded materials. Non-uniform thermal conductivity of the substrate causes non-uniformity of temperature distribution at the liquid-gas interface which leads to appearance of Marangoni stresses, convective vortices and film deformation. The computed velocity field is used for simulation of nano-particles motion and deposition at the solid wall. We show that the substrate thermal conductivity non-uniformity has a pronounced effect on transport processes in the liquid film. Theoretical and numerical simulations are accompanied by experiments.
Gaskell, Philip
Competing geometric and inertial effects on local flow structure in film flow over corrugated substrates
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Liquid film flow over rigid substrates containing well-defined topographical features are ubiquitous throughout engineering, science and the precision manufacturing industries. Although the focus to date, both experimental and theoretical, has been on ‘thin’ films and the associated film thickness distribution, the internal flow structure can also be crucial in determining the functional performance of the films and their propensity for defects. This paper describes recent studies into the subtle interplay between inertia and topographic geometry on the flow structure, in the form of kinematically and inertially-induced eddies, in film flow over corrugated substrates. In the case of shear-driven flow between rigid substrates, the impact of local laminar thermal mixing on global heat transfer is also described.
Gelder, David
The interaction between surface diffusion and very low Reynolds number flow
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Glass is widely used as a substrate for thin films, but requires targetted attention to the nature of the glass surface This may involve careful control of either intrinsic or specially applied surface films. A short summary of some related modelling issues is offered. The work described in detail concerns glazes, when glass is the film - normally on a ceramic - and fired at a temperature below the melting temperature of its constituents, to give a high viscosity liquid before quenching. Surface diffusion (most simply the tendency for bulk material to move along the surface away from more convex areas) is generally deemed insignificant in fluid mechanics. However there are grounds for thinking it may be important in this situation. Glazes (not the more desirable ones) can spread or retract significantly during firing, and the surface diffusion mechanism provides a simple model for the triple point movement at constant contact angle. Since glaze profiles can potentially be measured to very high accuracy after quenching, in principle they can distinguish the physics, and potentially whether in this case surface diffusion is the key mechanism rather than the generally preferred but inherently more complex slip model.
Grün, Günther
On phase-field models for dynamic electrowetting
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By energy considerations and Onsager's variational principle, we derive phase-field models for phenomena where the shape and the wetting behaviour of liquid droplets are influenced by applied electric fields. We are interested both in conductive liquids and in electrolytes. Our models couple the Navier-Stokes-system of fluid flow, Cahn-Hilliard-type equations for the phase-field and transport equations for charge/ion densities with the potential equation of electrostatics. Special emphasis is put on the evolution of the contact angle. Both theoretical arguments and selected numerical simulations (in 2D and in 3D) show that in contrast to the classical Lippmann formula the microscopic contact angle coincides with the Young angle when equilibrium states are reached. Moreover, we present numerical simulations on field induced droplet motion.
Hazel, Andrew
Steady propagation of air fingers in rectangular tubes
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We consider the influence of aspect ratio on the steady propagation of an air finger into a uniform rectangular tube, initially filled by an incompressible Newtonian fluid. Results from experimental studies and finite-element simulations will be presented for aspect ratios in the range one to fifteen. The agreement between the measured and simulated finger widths and wet fractions (relative volume of fluid remaining in the tube after passage of the air finger) is within the 1% experimental error. We present empirical evidence for the existence of approximate scalings that relate the wet fractions in rectangular tubes to those in a square tube. Our results also indicate that the system is approximately quasi-two-dimensional for aspect ratios greater than or equal to eight, when we obtain quantitative agreement with the two-dimensional model of McLean & Saffman (1981) for the relative finger width. To the best of our knowledge, this is the first quantitative agreement between two- and three-dimensional models of Saffman--Taylor fingering.
Hogg, Andrew
The flow and arrest of viscoplastic fluids
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Thin film of viscoplastic fluids may be arrested on sloping substrates when the downslope component of their weight combined with the hydrostatic pressure gradient is less than the yield stress. The principle is used in rheological devices such as the Bostwick consistometer to determine the magnitude of the yield stress and the consistency of the material. In this study we examine the approach to the arrested state to investigate how long flows from particular initial conditions will propagate until they are arrested. To this end we adopt a Herschel-Bulkley model of the rheology of the fluid and we examine both the arrested state and the temporal approach towards it. We show that the arrested state is only attained asymptotically with the perturbations to it decaying as 1/t^n, where n is the index of the Herschel-Bulkley rheology. This result is established for both flows over horizontal surfaces and along inclined planes and we discuss the implications for interpreting the results from the rheological measurement devices.
Ivanova, Natalia
Kinetics of spreading of aqueous trisiloxane solutions over hydrophobic surfaces
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The spreading of solutions of trisiloxane with different (from 4 to 9) ethoxy units over highly hydrophobic and smooth Teflon AF coated silicon wafers was investigated. It was found, that trisiloxane solutions show just insignificant spreading. At concentration below critical aggregation concentration (CAC) a time lag of spreading was detected. Three regimes of spreading were identified: at C < CAC nonwetting both at the beginning and the end of the spreading; at concentrations around CAC a transition from initial nonwetting to partial wetting at the end of the spreading; and partial wetting occurs at higher concentrations. The experimental results were analyzed in the framework of a theoretical model [1] of autophilic phenomenon [2]. It was shown that at C<CAC the spreading of surfactants solutions follows a theoretically predicted law [1]. At C>CAC the spreading proceeds in two stages: the short first stage, which is followed by a much slower second stage. The second stage develops according to the model [1]; however the first stage is assumed to be related to the disintegration of surfactant aggregates in the vicinity of the moving contact line [3]. The authors would like to acknowledge the support from EPSRC, UK. References 1. Starov, V., S. Kosvintsev, Velarde M. J. Colloid Interface Sci., 227, (2000). 2. Kumar N., Varanasi K., Tilton R., Garoff S. Langmuir, 19, (2003). 3. Ivanova N., Starov V., Johnson D., Hilal N., and Rubio R. Langmuir, 25(6), (2009).
Jones, Dilwyn
Institute of Physics Printing and Graphics Science Group. Air lubrication effects in handling and winding of thin web materials.
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The first part of the presentation will describe the activities of the Printing and Graphics Science Group, one of the Subject Groups of the Institute of Physics, the UK and Eire based organisation for physicists. The Group’s objectives are to promote the application of physics in graphics arts technology, printing, packaging and papermaking and the development of innovative printing in new markets such as displays, lighting and printed electronics. Forthcoming events include a sequel to the sold-out 2008 meeting on “Dynamics of Printed Drops” on November 2nd, and the annual Student Conference on December 1st. The second part will cover some applications of thin film flow to processes where web materials are transported and wound into rolls at speeds up to 40 m/s. The entrainment of air by surfaces converging at high velocity causes a fall in the apparent coefficient of friction between them. Simple models have been developed and are in use in industry. However, there is scope for better physics-based models to bring in surface contact, deformation of the substrate and elastomeric roller coverings, air escape from wound rolls and fluid inertia effects at very high speed.
Juel, Anne
Partially-occluded tubes can force switch-like transitions in the behaviour of propagating bubbles
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Microscale process engineering and many lab-on-a-chip applications require the precise control of bubbles and droplets. We investigate geometry-induced control and find that partial occlusion of rectangular tubes can lead to new families of steadily-propagating bubbles, which localize in the least-constricted regions of the cross-section. By tuning the occlusion geometry, a switch-like transition is achieved from centered to localized bubbles at a critical value of the flow rate. This subcritical bifurcation can be used to manipulate and direct suspended bubbles or droplets within microfluidic devices by variation of flow rate alone. Moreover, the three-fold discrepancies in liquid recovery efficiencies arising in partially-occluded tubes could be significant in many practical two-phase flows such as oil recovery applications.
Kalliadasis, Serafim
Influence of spatial heterogeneities on contact line dynamics
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We consider contact line motion over spatially heterogeneous substrates by using a two-dimensional droplet of a partially wetting fluid spreading over such substrates as a model system. The spreading dynamics is modelled under the assumption of small contact angles where the long-wave expansion in the Stokes-flow regime can be employed to derive a single equation for the evolution of the droplet thickness. Through a singular perturbation approach, the flow in the vicinity of the contact line is matched asymptotically with the flow in the bulk of the droplet to yield a set of two coupled differential equations for the spreading rates of the two droplet fronts. Analysis of these equations for deterministic substrates reveals a number of intriguing features that are not present when the substrate is flat. Our formalism is then used to investigate droplet equilibria and dynamics in the presence of small-scale, random substrate variations. Using an appropriate stochastic representation for such substrates, we provide a rational definition of "substrate roughness" and we assess the statistics of droplet equilibria and dynamics via a perturbation approach.
Kelmanson, Mark
Multiple-timescale asymptotics for coating flows
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A summary will be presented of recent multiple-timescale analyses of the rich and varied dynamics of a thin viscous film coating the surface of a horizontal rotating cylinder. The competing influences of rotational, capillary, gravitational and inertial effects will be discussed, with particular interest focussed on the role of scaling, and how this can lead to apparent contradictions regarding stability. A newly discovered explicit functional form of transient decay rate of leading-order free-surface disturbances will be presented, and all theoretical results will be validated against spectrally accurate numerics.
King, John
Thin film modelling of growing populations of cells
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Some applications from mathematical biology will be described, including to tissue growth.
Krechetnikov, Rouslan
Controversies of the Landau-Levich problem
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I this talk I will discuss a number of physical effects - due to surfactants, substrate roughness, and substrate-liquid interaction potentials - in the classical problem of dip-coating. Recent developments pose new questions and revive interest in the old ones such as on the origin of film thickening phenomena.
Lebon, Luc
Liquid/liquid spreading without and with flow
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We investigated some fundamental aspects of a liquid spreading on a liquid film flowing or not. Such configuration is of practical importance in environnement or processes for example.
Limat, Laurent
Structure formation observed for two kinds of dewetting fronts
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I will discuss shortly two kinds of situation in which a receding contact line leads to complex structure formation. (1) with A. Daerr, I. Peters and J. Snoeijer: a drop sliding down an incline under partial wetting conditions forms a conical tail, whose structure has been modeled rather successfully by us with J. Eggers and H.A. Stone. Recently we have investigated the mechanism that limits the curvature at the tip of the cone, both with experiments and models. We found that the curvature is regularized at a mesoscopic scale but depends on the microscopic scale in a way that allows us to extract its approximate, nanometric, value from measurements at the micron scale. In some sense, the point singularity of the cone is in fact a strongly bent line singularity, which introduces specific dependances in the problem, different from what is usually expected for other singularities. (2) with G. Berteloot, C.-T. Pham, A. Daerr, F. Lequeux, A. Hohang, P. Kavehpour and M. Receveur: we have investigated the deposition of colloids behind a contact line that recedes because of both hydrodynamical and evaporation effects, in two geometries (sessile drops and dip coating). In the first case, experiments and a balistic model show that the deposit growth follows a t^(2/3) law until complex instabilities occur with buckling and fracture formation, evidenced by microscopy. In the second case, different regimes are observed, one involving stick-slip. We propose also a simple lubrication model of the dynamics that leads to the prediction of a minimal thickness of this deposit that we checked sucessfully in dip coating experiment.
Lister, John
The dynamics of pendent drops on a thin film coating
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As sometimes observed on a kitchen or bathroom ceiling, a layer of liquid coating the underside of a rigid horizontal boundary is unstable and accumulates into an array of pendent drops. If the initial layer is sufficiently thin then these drops do not drip off, but are held on the ceiling in a near-equilibrium between surface tension and gravity. We examine the nonlinear dynamics that govern the slow evolution and motion of such pendent drops, as they continue to accumulate fluid from the surrounding remnant thin film of liquid. On small domains the drops are pinned by the boundary conditions and drain the surrounding film. On large domains, a single drop is capable of steady translation over an otherwise uniform horizontal film, and a colliding pair of translating drops may coalesce or may `bounce' off each other. The nonlinear dynamics with two horizontal dimensions is significantly different from that with one horizontal dimension.
O'Naraigh, Lennon
Instability in two-phase turbulent stratified flow
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We study the instability of a thin liquid layer sheared by a turbulent gas flow. We characterize the type of instability observed by introducing a convenient definition of `slow' and `fast' waves. We estimate the character of the unstable waves based on the liquid film thickness and the Reynolds number of the gas flow.
Oron, Alex
Stability of temporally forced liquid films
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The talk will be focused on investigation of stability of falling liquid films on a tangentially oscillating substrate. The issues of linear and nonlinear stability will be discussed. Film stabilization will be shown to be possibly achieved by its boundary forcing. Some relevant experimental observations will be also discussed. Nonlinear dynamics of forced films is shown to display time-periodic, quasiperiodic and genuinely nonstationary flows. The research is supported by the European Union via the FP7 Marie Curie scheme [PITN-GA-2008-214919 (MULTIFLOW.]
Peschka, Dirk
Self-similar rupture for thin films with slip
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In this talk a model for thin film rupture will be presented. Numerical simulations indicate that near the rupture point viscosity and van-der-Waals forces are dominant and that there exist self-similar solutions of the second kind. For a corresponding simplified model the self-similar large-time behavior will be analyzed. There exists a one-parameter family of self-similar solutions and we establish necessary and sufficient conditions for convergence to any self-similar solution in a certain parameter regime.
Power, Henry
Integral equation simulation of three-dimensional thin film flow over and around obstacles
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Gravity driven Stokes flow down an inclined plane over and around multiple obstacles is considered. The flow problem is formulated in terms of a boundary integral equation, and solved using the boundary element method. A Hermitian radial basis function is used for the interpolation of the free surface, generation of the unit normal and curvature, and to prescribe the far field conditions and contact angle condition on the obstacle/free surface intersection. Explicit profiles are produced for flow over and around two obstacles placed in various locations relative to one another. Interaction due to two obstacles is given by comparisons made with the profiles for flow over and around individual obstacles. In general, when the obstacles are separated by a sufficiently large distance the flow profiles are identical to a single obstacle analysis. For flow over and around two obstacles inline with the incident flow, effects of the governing parameters are examined, with variations in plane inclination angle, Bond number, obstacle size, and in the case of obstacles intersecting the free surface, static contact angle considered. Finally, solutions are obtained where steady flow profiles can be over and around the obstacles raising the awareness of possible multiple solutions.
Quere, David
Drops in asymmetric landscapes
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We present a few examples of drops which self-propel, due to some asymmetry. We focus on three situations: 1) Drops in cones, where the asymmetry is geometric. 2) Leidenfrost drops on a ratchet, where gas flows generate a directed motion . 3) Confined drops in presence of surfactants, where the motion betrays the efficiency of detergency. The main contributors to this work are (in alphabetic order) John Bush, Christophe Clanet, Guillaume Lagubeau, Marie Le Merrer, Keyvan Piroird, Manu Prakash and Pierre Renvoisé.
Scheid, Benoit
Non-monotonic behaviours of the draw resonance instability in stretching viscous sheets
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Stretching viscous sheets are encountered in the polymer film industry, e.g. the film casting process, as well as in the glass sheet industry. Classically this problem has an instability called draw resonance, when the draw ratio — corresponding to the ratio of the outlet velocity relative to the inlet velocity — is beyond a critical value. This instability is characterized by symmetric oscillations of both the film thickness and the width of the sheet. In this work we present results on how the critical draw ratio is modified individually by strong cooling and lateral stretching in non-monotonic ways. Under cooling, we found a window with respect to heat transfer properties corresponding to a strong stabilization of the system, along which an original physical mechanism that explains this stabilization based on the relative amplitude and phase of axial-averaged quantities. Under lateral stretching, we found that the draw resonance can either be promoted or hindered depending on the relative importance of normal and tangential components of the stress specified at the lateral edges. Additionally,our theory is shown to rationalize stability properties of practical forcing such as prescribed transverse velocity at the edges.
Snoeijer, Jacco
Maximum size of drops levitated by an air cushion. THIS TALK WILL BE PRESENTED BY Jens Eggers.
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Liquid drops can be kept from touching a plane solid surface by a gas stream entering from underneath. The most famous example are the so-called Leidenfrost drops that float above a hot plate, levitated by a stream of water vapor. In this talk we discuss two instabilities of such levitated drops, one of which we resolve theoretically. Above a critical drop radius no stationary drops can exist, below the critical radius two solutions coexist. However, only the solution with the smaller gap width is stable, the other is unstable. We compare our results to experimental data and use boundary integral simulations to show that unstable drops develop a gas “chimney” which breaks the drop in its middle.
Tabeling, Patrick
Droplets and microfluidics
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The talk will present work currently done in the microfluidic group at ESPCI regarding droplets and microfluidic technology. Depending on the available time, I will talk about droplet breakup, colloidal droplets, droplet and unique cell, droplets and complex fluids.
Taroni, Michele
Mathematical modelling of the screen-printing process
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Screen printing is the most widely used and convenient method of producing electronic circuits found in a range of devices, from flat-screen monitors to solar cells. The desired circuit pattern is printed onto the substrate by pushing a paste through a screen, which has a stencil attached to it. The pastes are concentrated particle dispersions whose rheological behaviour is highly non-Newtonian. In this talk, we treat the pastes as power-law fluids and present a lubrication-theory based model for the process, which can be analysed using matched asymptotic expansions. In particular, we highlight the aspects of particular interest to industrial manufacturers Dupont, and describe the interaction between academia and industry from a student's perspective.
Thiele, Uwe
Modelling approaches to the dewetting of evaporating thin films of nanoparticle suspensions
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We review recent experiments on dewetting thin films of evaporating colloidal nanoparticle suspensions and discuss several theoretical approaches to describe the ongoing processes. These approaches range from microscopic discrete stochastic theories to mesoscopic continuous deterministic descriptions. In particular, we focus on (i) a microscopic kinetic Monte Carlo model, (ii) a dynamical density functional theory and (iii) a hydrodynamic thin film model. Models (i) and (ii) are employed to discuss the formation of polygonal networks, spinodal and branched structures resulting from the dewetting of an ultrathin `postcursor film' that remains behind a mesoscopic dewetting front. We highlight, in particular, the presence of a transverse instability in the evaporative dewetting front which results in highly branched fingering structures. The subtle interplay of decomposition in the film and contact line motion is discussed. Finally, we discuss a simple thin film model (iii) of the hydrodynamics on the mesoscale. We employ coupled evolution equations for the film thickness profile and mean particle concentration. The model is used to discuss the self-pinning and de-pinning of a contact line related to the `coffee-stain' effect. In the course of the talk we discuss the advantages and limitations of the different theories, as well as possible future developments and extensions.
Thompson, Harvey
Inertial thin film free-surface flow over planar substrates with topography
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Thin liquid free surface films flowing over substrates containing topography/patterning arise in many areas of science and engineering and are an important component of several high-tech manufacturing processes, where the goal is to minimise the free-surface disturbances induced by the topography in order to provide the desired functional properties. This presentation will use a new, accurate method for solving three-dimensional, inertial, free-surface film flows over topography to investigate the role of inertia in amplifying free surface disturbances and to study the combined influences of inertial and other important physical effects, such as electric field and evaporative effects, on the magnitude and extent of these disturbances.
Usha, Ranganathan
Thin film flow down a porous incline: dynamics and stability
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A two-dimensional laminar flow a thin Newtonian liquid film on a porous substrate is examined. The porous medium is modeled as a Darcy layer and appropriate slip boundary conditions proposed by Beavers and Joseph and Jones and Beavers at the liquid layer-porous substrate interface are employed.An evolution equation is derived using a long-wave analysis. A linear stability analysis of the base flow is performed and the critical condition for the onset of instability is obtained. A weakly nonlinear stability analysis is performed using method of multiple scales and a numerical solution of the nonlinear evolution equation is obtained.The results show that the presence of a porous substrate promotes instability . Further, stationary solutions are obtained and surface structures are examined. The conditions under which the porous substrate can be replaced by an effective slip condition is derived and the corresponding slip-length is obtained in terms of the thickness of the film, porosity and Darcy number and differences in different models are presented.
Wilson, Stephen
Sheets, rivulets and droplets subject to an external air flow
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Sheet, rivulet and droplet of fluid subject to an external air flow arise in many everyday and industrial situations, ranging from rain on the windscreen of a moving car to industrial coating processes. In this talk we will discuss a number of specific problems of this general kind and describe some of the insights that a combination of analytical and numerical methods can bring to them.
Zhang, Wendy
Memory as vibration in a disconnecting air bubble
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The disconnection of an underwater bubble provides a simple example of this competition between asymmetry and focusing.Focusing a finite amount of energy dynamically into a vanishingly small amount of material requires that the initial condition be perfectly symmetric. In reality, imperfections are always present and cut-off the approach towards the focusing singularity. We use a combination of theory, simulation and experiments to show that the dynamics near disconnection contradicts the prevailing view that the disconnection dynamics converges towards a universal, cylindrically-symmetric singularity. Instead an initial asymmetry in the shape of the bubble neck excites vibrations that persist until disconnection. We argue that such memory-encoding vibrations may arise whenever the formation of the singularity involves a focusing of materials.

Participants

Name	Institution
Ajaev, Vladimir	Southern Methodist University
Aksel, Nuri	University of Bayreuth
Benilov, Eugene	University of Limerick
Billingham, John	University of Nottingham
Bird, Jacy	Harvard University
Blowey, James	Durham University
Bouchain, David	Ulm University
Daerr, Adrian	Université Paris Diderot
Delabre, Ulysse	Laboratoire de Physique Statistique, ENS
Duffy, Brian	University of Strathclyde
Dyson, Rosemary	University of Nottingham
Eggers, Jens	University of Bristol
Evans, Peter	Humboldt-Universität zu Berlin
Gambaryan-Roisman, Tatiana	Technische Universität Darmstadt
Gaskell, Philip	University of Leeds
Gelder, David	Mathematics for Manufacturers
Grün, Günther	University of Erlangen-Nürnberg
Hazel, Andrew	University of Manchester
Hogg, Andrew	University of Bristol
Ivanova, Natalia	Loughborough University
Jones, Dilwyn	Emral Ltd
Juel, Anne	University of Manchester
Kalliadasis, Serafim	Imperial College London
Kelmanson, Mark	University of Leeds
King, John	University of Nottingham
Krechetnikov, Rouslan	University of California at Santa Barbara
Lebon, Luc	CNRS and Université Paris Diderot
Leslie, Adam	University of Strathclyde
Limat, Laurent	CNRS and Université Paris Diderot
Lister, John	University of Cambridge
Mohd Yatim, Yazariah	University of Strathclyde
O'Naraigh, Lennon	Imperial College London
Oron, Alex	Technion - Israel Institute of Technology
Peschka, Dirk	Weierstrass Institute for Applied Analysis and Stochastics
Power, Henry	University of Nottingham
Quere, David	ESPCI and École Polytechnique
Richard, Céline	Laboratoire de Physique Statistique, ENS
Scheid, Benoit	Universite Libre de Bruxelles
Sileri, Daniele	Imperial College London
Snoeijer, Jacco	University of Twente
Tabeling, Patrick	ESPCI
Taroni, Michele	University of Oxford
Thiele, Uwe	Loughborough University
Thompson, Harvey	University of Leeds
Usha, Ranganathan	Indian Institute of Technology
van den Ende, Dirk	University of Twente
Wilson, Stephen	University of Strathclyde
Zhang, Wendy	University of Chicago
Zubkov, Vladimir	University of Oxford