Dynamics of liquid drops in precision deposition on solid surfaces J.E Sprittles Y.D. Shikhmurzaev Particulate Engineering Seminar May 2009

Overview Drop Impact and SpreadingDrop Impact and Spreading – –Experiments – –Conventional Modelling and its Flaws – –The Interface Formation Model – –Numerical Simulations Flow Over Chemically Patterned SurfacesFlow Over Chemically Patterned Surfaces Propagation of Wetting Fronts Through Porous MediaPropagation of Wetting Fronts Through Porous Media

Worthington 1876 – First Experiments

Worthington’s Sketches Millimetre sized drops of milk on glass.

Millimetre Drop Impact, Spreading and Rebound Courtesy of Romain Rioboo

50 Micron Drop of Water Impacting at 12 m/s Dong 06

Theoretical Modelling of Dynamic Wetting Flows.

The Classical Fluid Mechanics ApproachBulk Incompressible Navier Stokes Solid – Liquid Boundary No-Slip Liquid – Gas (Free) Boundary Balance of stresses + Kinematic Condition No Solution! (Huh & Scriven 1970)

The Usual Remedy (A Quick Fix)Bulk Incompressible Navier Stokes Solid – Liquid Boundary No-Slip Liquid – Gas (Free) Boundary Balance of stresses + Kinematic Condition Slip Solution exists (Dussan & Davis 74)

) The Contact Angle: Static Case. R σ 1e σ 3e - σ 2e θsθs Hydrophobic – Non wettable Hydrophilic – Wettable Young Equation Contact Line

) The Contact Angle: Dynamic Case. R σ1σ1 σ 3 - σ 2 θsθs Young Equation ? Dynamic Contact Angle Formula U Assumption: A unique angle for each speed

Summary of Conventional Model Two Issues: 1) Allow For A Solution 2) Determine the Dynamic Contact Angle. U Conventional Modelling: 1)Allow Slip Between Solid and Liquid 2) Prescribe angle:

Is the angle actually a function of the speed? U, m/s Experiments answer, NO! “There is no universal expression to relate contact angle with contact line speed”. (Bayer and Megaridis 06) U

As In Curtain Coating Standard model predicts: Fixed Substrate Speed Unique Contact Angle (Marston et al 06) U

Hydrodynamic Assist to Wetting Dynamic contact angle as a function of coating speed for different flow rates. (Blake & Shikhmurzaev 02). U, cm/s Standard model predicts: Fixed Substrate Speed Unique Contact Angle Controlled Flow Rate U

The Interface Formation Model (Shikhmurzaev 93)

Dynamic wetting is the process of making an initially dry solid wet. In other words, it is a process of creating a new/fresh liquid-solid interface. Thus, it is a particular case from a general class of flows with formation/disappearance of interfaces. Forming interface Formed interface Physics of Dynamic WettingLiquid-solidinterface Solid

R σ 1e σ 3e - σ 2e Dynamic contact angle results from dynamic surface tensions. The angle is now determined by the flow field. Slip created by surface tension gradients (Marangoni effect) θsθs θdθd Static situationDynamic wetting σ1σ1 σ 3 - σ 2 R

Liquid Drops Spreading on Solids: Process of Interface Formation Solid Gas Liquid In Frame Moving With Drop Interfaces are shown with finite thickness for representation only.

The Simplest Model of Interface Formation. In the bulk: On liquid-solid interfaces: At contact lines: On free surfaces: Interface Formation Model θdθd e2e2 e1e1 n n f (r, t )=0

Comparison With Experiments Perfect wetting (Hoffman 1975; Ström et al. 1990; Fermigier & Jenffer 1991) Partial wetting (□: Hoffman 1975;  : Burley & Kennedy 1976; ,,  : Ström et al. 1990) The theory is in good agreement with all experimental data published in the literature.

A Few Other Processes With Forming Interfaces

Development of a Numerical Platform

Finite Element Modelling: The Spine Method (Scriven and co-workers) The Spine Nodes fixed on solid. Nodes define free surface.

Simulation of Microdrop Impact and Spreading Experiment Dong 06. Simulation Sprittles. Ink-jet printer range. Radius = 25  m, Impact Speed = 12.2m/s

Drop Impact on a Hydrophobic (non-wettable) Substrate Rebound on a Hydrophobic Substrate Radius = 25  m, Impact Speed = 5m/s

Pyramidal Drops (mm size drop) Experiment Renardy et al. Simulation Sprittles.

Current Research: Flow Over Chemically Patterned Surfaces.

Flow Over a Chemically Patterned Surface ) What happens in this region? Molecular Dynamics Simulations Predict Flow Disturbance No Slip => No effect

Agreement Between Molecular Dynamics and our Numerical Platform Solid 2 less wettable Qualitative agreement Sprittles & Shikhmurzaev, Phys. Rev. E 76, (2007. Sprittles & Shikhmurzaev, EPJ (2009)

Drop Impact onto a Chemically Patterned Surface Pattern a surface to ‘correct’ deposition.Pattern a surface to ‘correct’ deposition. Courtesy of Professor Roisman (Darmstadt)

Future Research: The Propagation of Wetting Fronts Through Porous Media

The ProblemMacroscale bulk equations: Oil displaced by water. Van Meurs et al 57 Microscale Macroscale ? Wetting front evolution: Darcy Mass Continuity

Application to Powders ) Porous Media

) The Bundle of Tubes Model (Washburn 1921) x Pore Size fails to scale according to pore size in the Lucas–Washburn equation “The absorption rate depends on the square root of time but fails to scale according to pore size in the Lucas–Washburn equation even though the constants of surface energy, contact angle and fluid viscosity have been maintained.” (Schoelkopf et al 02)