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Material from Talks

John R. Andrews (Ink Jet Business Unit, Xerox Corporation) JAndrews@crt.xerox.com

Micro-boiling and Pico-jetting

Thermal ink jet is a marking technology that uses explosive boiling within fluidic structures with dimensions of a few tens of microns to project droplets of water-based marking fluids having volumes of a few tens of picoliters at a substrate such as paper. In this presentation, we will provide a description of thermal ink jet and highlight some of the physical phenomena that are critical to a quantitative understanding of how thermal ink jet works. The descriptions will be highlighted by experimental data in both explosive boiling and jetting. Finally, some of the challenges in developing a quantitative understanding of thermal ink jet will be discussed.

Jacqueline Ashmore (GSAS, Harvard University)

Non-Newtonian Coating   pdf    postscript

Osman A. Basaran (School of Chemical Engineering, Purdue University)  obasaran@ecn.purdue.edu

Drop Formation: From Dripping to Drop-on-demand Drop Production and Analysis through Computation and Ultra High-speed Visualization

Drop formation plays a central role in applications as diverse as ink-jet printing, biochip arrayers for genomic analysis, spray coating, and separations. One objective of our research is to provide a fundamental understanding of drop production by so-called drop-on-demand (DOD) drop generators commonly found in ink-jet printers. In analyzing the complex problem of drop formation by a DOD device, we found it useful to first study the classical problem of continuous dripping from a capillary. We have tackled dripping through a dual-pronged approach relying on computation and high-speed visualization. In the computations, either the two-dimensional (2-d) Navier-Stokes system or else a one-dimensional (1-d) counterpart of it based on the slender-jet approximation is solved using the finite element method (FEM). Two versions of the 2-d FEM algorithm have been developed: one relies on algebraic and the other on elliptic mesh generation. Both are shown to predict the entire formation dynamics, including breakup, with 1% accuracy compared to experiments. When appropriate, the 1-d algorithm is used to study the formation of hundreds of drops in a sequence. This analysis makes it possible to develop an operability or a bifurcation diagram which at last provides the theory for the long-standing problem of a dripping faucet much fancied in the physics community. Since control of satellite droplets is a major issue in operation of printers as well as DNA arrayers, the 2-d algorithm is also used to study the fate of contracting slender filaments, which are precursors of satellites. Certain unexpected yet fascinating dynamical responses exhibited by satellites are confirmed by means of an ultra high-speed digital imaging system that is capable of recording multiple frames at an astounding frame rate down to 10 nanoseconds. The accuracy of our new 2-d algorithms will be highlighted by demonstrating that they can predict scaling laws, and transitions from one scaling law to another, determined from local analyses of the governing equations as breakup is approached. The talk will conclude by highlighting recent computational and experimental work underway in our group on DOD drop formation.

Andrew Belmonte (Pritchard Lab, Dept of Mathematics, Penn State)

Viscoelastic Filament Dynamics: Exact Solutions and Instabilities

I will present some recent results for the dynamics of the filament formed during the drop pinch-off process: 1) a new family of exact solutions to the Upper Convected Maxwell model for a purely extensional cylindrical filament, and 2) observations of the unusual pinch-off dynamics of a wormlike micellar solution, in which the filament instability is highly localized.

John W. M. Bush (Department of Mathematics, Massachusetts Institute of Technology) bush@math.mit.edu    http://www-math.mit.edu/~bush/

Fluid Pipes

We present the results of a combined theoretical and experimental investigation of laminar vertical water jets impinging on a water reservoir. We consider the parameter regime where, in a pure system, the jet is characterized by a stationary field of capillary waves at its base. When surfactant is added to the reservoir, the reservoir-to-jet surface tension gradient transports the surfactant a finite distance up the jet surface until a balance is achieved between viscous and Marangoni stresses. The length of jet surface covered by surfactant is cylindrical and quiescent: water enters the reservoir as if through a rigid pipe. A theoretical description of the resulting fluid pipe is deduced by matching extensional flow upstream of the pipe onto entry pipe flow within it. Theoretical predictions for the pipe height are validated by an accompanying experimental study.

Anne-Marie Cazabat (Laboratoire de Physique de la Matiere, College de France)

Spreading of Surfactant Solutions

Joint work with M.Cachile and M.Schneemilch.

The spontaneous spreading of solutions of nonionic CnEm surfactants in ethylene and diethylene glycol on hydrophilic surfaces is controlled by the relative humidity RH of the gas phase, and the relative surfactant concentration c* = c / cmc. In the (c*,RH) plane, fast dendritic spreading is observed inside a well defined domain, while normal spreading is observed outside. Also the characteristics of the dendritic pattern depend on the position in the plane. The relative humidity controls the thickness of the preexisting water film on these hydrophilic substrates. It is also possible to spin coat an ethylene or diethylene glycol film on the substrate. Depending on the film thickness, the dendritic pattern may be strongly modified. The experimental data are analyzed in reference to the models by Troian et al.

Itai Cohen (Nagel Group, James Franck Institute, University of Chicago)  icohen@midway.uchicago.edu

Snakes Eating Elephants: Using Selective Withdrawal to Coat Micro Particles

Joint work with Sidney Nagel, Hui Li, James Hougland and Milan Mrksich.

In the Selective withdrawal experiment a suspended tube, whose orifice rests slightly above a water-oil interface, is used to withdraw the fluids. By changing the rate of flow, we control a transition between a state where only oil is withdrawn through the tube and one where water is entrained in a thin spout along with the oil. Understanding the physics of this transition is vital for various engineering applications including the manufacture of coatings for micron-sized particles. Coating is achieved by replacing the water with a pre-polymer solution containing the particles to be coated. These particles are also entrained with the solution and, as they rise, they eventually become larger than the spout width. At this point the spout breaks up and the particles are left with a thin coat of pre-polymer. Depending on the pre-polymer, we harden the coat using chemicals, light, or temperature. We find that the thickness of the coat can be controled by varying the flow rate and controlling the hysteretic effects involved in the transition.

Morton M. Denn (The Benjamin Levich Institute for Physico-Chemical Hydrodynamics, City College of CUNY)

Droplet Size Effects for Liquid Crystalline Polymers in a Flexible Polymer Matrix

Droplets of a liquid crystalline polymer in a matrix of a flexible polymer exhibit unusual dynamical behavior when the droplet size becomes comparable to the correlation length for nematic order. I will describe some rheological and droplet relaxation experiments that illustrate unusual scaling and an apparent droplet-size dependence of the interfacial tension. I will then describe the results of a molecular simulation exploring the effect of far-field nematic order on the structure of the ``interphase' and the equilibrium interfacial tension between the two phases.

Paul Duineveld (Philips Research (WB31))   paul.duineveld@philips.com

Ink-jet Printing of Materials for Light-emitting Displays; the Stability of Printed Liquid Lines

Philips is investigating displays of light-emitting polymers. One of the advanta ges of polymers is that they can be applied from a solution which enables wet chemical processes as spin coating. This technique is suitable for making monochrome displays. However, for full colour displays this is not useful because these pol ymers can not withstand ething solutions. Therefore selective patterning techniques ha ve to be applied. Ink-jet printing is an interesting technique because it can generate high resolution patterns and is suitable for mass production. First a brief overview is given of the display principles, the drop formation (e specially the high molecular weight polymer solutions give special drop formation) and som e examples of ink-jet printed displays. The main part of the talk will be devoted to an instability of a printed line. I t is well known from the literature that a liquid ridge is unstable. Two boundary conditio ns for instabilities have been studied recently. These are: constant contact angle and constant contact line, e.g. when printing a hot wax on a cold substrate. The printed polymers have interesting properties. Depending on the conditions o f the substrate the wetting of the polymer solutions can be changed. This includes bot h the advancing and the receding contact angles. Under several conditions the receding contct angle is zero. This can result in a peculiar instability of a printed li ne, that depends on several variables. In this presentation experiments and a first theor etical model to describe this instability will be presented.

Jens Eggers (Fachbereich Physik Universität Gesamthochschule Essen) eggers@lux1.theo-phys.uni-essen.de

Air Entrainment Through Free-Surface Cusps

In many industrial processes, such as pouring a liquid or coating a rotating cylinder, air bubbles are entrapped inside the liquid. We propose a novel mechanism for this phenomenon, based on the instability of cusp singularities that generically form on free surfaces. The air being drawn into the narrow channel of a cusp destroys its stationary shape when the walls of the channel come too close. Instead, a sheet emanates from the cusp's tip, through which air is entrained. Our analytical theory of this instability is confirmed by experimental observation and quantitative comparison with numerical simulations of the flow equations.

Daniel D. Joseph (Department of Aerospace Engineering and Mechanics, University of Minnesota)   joseph@aem.umn.edu

Capillary Collapse and Rupture

Joint work with Tom Lundgren.

The breakup of a liquid capillary filament is analyzed as an aviscous potential flow near a stagnation point on the centerline of the filament towards which the surface collapses under the action of surface tension forces. We find that the neck is of parabolic shape and its radius collapses to zero in a finite time. During the collapse the tensile stress due to viscosity increases in value until at a certain finite radius (which is about 1.5 microns for water in air) the stress in the throat passes into tension presumably inducing cavitation there.

Damir Juric (Mechanical Engineering Georgia Institute of Technology) damir.juric@me.gatech.edu

3D Numerical Simulation of Phase Change

A new three dimensional phase change/front tracking technique is described which combines the accuracy of an explicit Lagrangian front tracking of the phase interface with the ease of implementation of a simple level set/distance function technique. It fully models the important features of phase change dynamics: complex interface dynamics, fluid flow, heat and solute transport coupled with local interfacial physics involving surface tension, latent heat, interphase mass transfer and jumps in material properties. Three dimensional numerical investigations include the affect of fluid motion on solidifying dendrites and heat transfer during film and nucleate boiling.

Dimos Poulikakos (Laboratory of Thermodynamics in Emerging Technologies (LTNT), Institute of Energy Technology, Department of Mechanical and Process Engineering, ETH Zurich)  poulikakos@iet.mavt.ethz.ch   http://www.ltnt.ethz.ch

On the Deposition of Monodispersed Molten Microdroplets in Industrial Jetting Processes

The reliable and repeatable microdroplet generation and deposition of non-traditional liquids is of paramount importance to a plethora of emerging technologies. In this lecture the deposition of picoliter size droplets of molten materials will be discussed with emphasis on three dimensional phenomena and substrate melting phenomena. The three dimensinality of the phenomenon is induced by non axisymmetric impact or by the motion of the substrate upon which the microdroplet is deposited. The substrate melting is a result of the energy input from the impacting molten material. The novel solder jetting process for the manufacturing of microelectronics is used to underpin the industrial importance and relevance of the phenomena investigated. The numerical modelling is based on the Lagrangian Finite-Element formulation of the Navier-Stokes, energy and material transport equations. The model accounts for a host of complex thermofluidic phenomena, exemplified by surface tension effects and heat transfer with solidification in a severely deforming domain. The dependence of the molten volume on time is determined and discussed. The influence of the thermal and hydrodynamic initial conditions on the amount of remelting is discussed for a range of superheat, Biot and Reynolds numbers. Multidimensional and convective heat transfer effects, as well as material mixing between the droplet and the substrate are found and quantified and the underlying physics is discussed. . Good agreement in the main features of the maximum melting depth boundary between the present numerical results and published experiments of other investigators for larger (mm-size) droplets is obtained, and a complex mechanism was identified, showing the influence of the droplet fluid dynamics on the substrate melting and resolidification.

Elbridge Gerry Puckett (Department of Mathematics, University of California, Davis)

The Formation of Droplets in Microscale Jetting Devices

Micro-scale jetting devices are used in a variety of applications, from ink jet printers to microelectronics manufacturing, biomedical procedures and equipment (e.g., dye-assisted laser surgery), medical diagnostics manufacturing, micro-optics manufacturing, IC thermal management and dispensing small amounts of chemicals in Neuroscience research. In this talk I will describe recent research directed at developing a numerical method for modeling these devices. I will begin with a discussion of the physical processes which characterize micro-scale jetting, and which make them difficult to model; follow with a general description of a numerical method I have developed - in collaboration with others - with which one can modeling the entire jetting process; from the application of a time dependent pressure or velocity pulse at the inflow boundary of the nozzle, through the formation of the lead and satellite droplets, to the eventual coalescence of some or all of the satellite droplets; and end with an overview of some of the open research problems which remain to be addressed in this area, such as the development of models for piezo electrically and thermally induced jetting.

David Quere (Laboratoire de Physique de la Matiere Condensee, College de France) quere@ext.jussieu.fr

Unconventional Impacts (Bouncing Drops and Capture by a Small Fiber)

We present recent experiments on drop impacts in unusual conditions. First, impacts on superhydrophobic surfaces which repel the drops (full rebound). We are mainly interested in the shape of the drop during the contact together with the contact time which caracterizes the rebound. Second, we discuss the possible capture of a liquid drop by a solid much smaller than it (impact on a small fiber).

Michael Renardy (Department of Mathematics, Virginia Polytechnic Institute)

Breakup of Newtonian and Viscoelastic Jets

The talk will review recent results on capillary breakup or its absence in liqui d jets. The model considered is a one-dimensional approximation based on cross-section a veraging, and inertia are neglected. Results on finite time breakup or its absence and sim ilarity solutions for the asymptotics of breakup are discussed for several constitutive models.

Michael Siegel (Department of Mathematical Sciences, New Jersey Institute of Technology) misieg@impulse.njit.edu

Tip Streaming Instabilities for Slender Axisymmetric Bubbles with Surfactant: an Asymptotic Approach

Tipstreaming refers to the process by which a bubble in an extensional flow develops cusp-like ends, which subsequently emit slender filaments or bubbles into the exterior fluid. G. I. Taylor first identified this process in a seminal paper describing experiments performed in a four- roller mill. More recent experiments have shown that the presence of surfactant is critical for the onset of tipstreaming.

In this talk slender body theory is applied to investigate the deformation of an inviscid bubble in the presence of an insoluble surfactant. Of particular interest are the conditions for the breakup of a single drop in uniaxial zero Reynolds number extensional flow. We first discuss the steady state solutions; these include a class for which ``stagnant caps'' of surfactant partially coat the bubble surface. Although it is well known that steady slender drops exist for all capillary number Q in the absence of surfactant, our results show that steady drops with surfactant can only exist if Q is below a critical value, which is determined in the analysis. The breakup of inviscid bubbles in the presence of surfactant is therefore identified with the lack of a steady solution, rather than the instability of an existing solution at a critical Q. This behavior is analogous to that for drops of low viscosity, for which steady shapes do not exist above a critical capillary number. However, it is suggested that surfactant effects provide the dominant mechanism for breakup in very low viscosity drops. Time dependent studies employing the slender drop approximation show that, above the critical capillary number, the drop breaks by a rapid growth at its end. A possible connection between the observed behavior and the phenomenon of tip-streaming is discussed.

Pushpendra Singh (Department of Mechanical Engineering, New Jersey Institute of Technology) singhp@njit.edu

Numerical Simulation and Modeling of Non-Newtonian Multiphase Liquids

The capability of numerically simulating flows of non-Newtonian multiphase liquids, e.g., Newtonian and viscoelastic liquids containing solid particles or gas bubbles, is useful both for simulating flows in industrial applications and for modeling physics. For simulating the motion of rigid particles suspended in the Newtonian and viscoelastic fluids we have developed a distributed Lagrange multiplier/fictitious domain method (DLM). In this method the governing fluids equations are solved everywhere in the domain, including inside the particles. The flow inside the particles is forced to be a rigid body motion using a distributed Lagrange method. The level set method is used for tracking the motion of bubbles. A finite element code based on these two methods is developed for simulating the motion non-Newtonian multiphase flows in two and three-dimensions.

David B. Wallace (Vice President, Technology Development, MicroFab Technologies, Inc.)   dwallace@microfab.com

Ink-Jet Applications, Physics, and Modelling - an Industrial/Applied Research View

Ink jet printing technology has been used for a wide range of applications other than ink on paper, including the manufacturing of gene chips, displays, micro-optic elements, and electronic assemblies. These applications will be discussed, along with important aspects of the physics of the process will be discussed. The modelling of these processes will be discussed, both from a philosophical and practical example viewpoint.

Material from talks

IMA "HOT TOPICS" Workshop: Analysis and Modeling of Industrial Jetting Processes

"Hot Topics" Workshops

2000-2001 Program: Mathematics in Multimedia

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