J.E. Sprittles (University of Ox as long as d, U.K.) Y.D. Shikhmurzaev (University of Bir

J.E. Sprittles (University of Ox as long as d, U.K.) Y.D. Shikhmurzaev (University of Bir www.phwiki.com

J.E. Sprittles (University of Ox as long as d, U.K.) Y.D. Shikhmurzaev (University of Bir

Ankarlo, Darrell, Morning Host has reference to this Academic Journal, PHwiki organized this Journal J.E. Sprittles (University of Ox as long as d, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) Workshop on the Micromechanics of Wetting & Coalescence Microfluidic Technologies Often the key elements are the interaction of: Drops with a solid – Dynamic Wetting Drops with other drops – Coalescence Dynamic Wetting Phenomena 50nm Channels 27mm Radius Tube 1 Million Orders of Magnitude! Millimetre scale Microfluidics Nanofluidics Emerging technologies Routine experimental measurement

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Microdrop Impact Simulations 25mm water drop impacting at 5m/s. Experiments: Dong et al 06 Coalescence of Liquid Drops Hemispheres easier to control experimentally Thoroddsen et al 2005 Ultra high-speed imaging Paulsen et al 2011 Sub-optical electrical (allowing microfluidic measurements) Thoroddsen et al 2005 A Typical Experiment 230cP water-glycerol mixture: Length scale is chosen to be the radius of drop Time scale is set from so that Electrical: Paulsen et al, 2011. Optical:Thoroddsen et al, 2005.

Coalescence Frenkel 45 Solution as long as 2D viscous drops using con as long as mal mapping Hopper 84,90,93 & Richardson 92 Scaling laws as long as viscous-dominated flow Eggers et al 99 (shows equivalence of 2D in addition to 3D) Scaling laws as long as inertia-dominated flow Duchemin et al 03 (toroidal bubbles, Oguz & Prosperetti 89) Problem Formulation Two identical drops coalesce in a dynamically passive inviscid gas in zero-gravity. Conventional model has: A smooth free surface An impermeable zero tangential-stress plane of symmetry Analogous to wetting a geometric surface with: The equilibrium angle is ninety degrees Infinite ‘slip length’.

Problem Formulation Bulk Free Surface Liquid-Solid Interface Plane of Symmetry Bridge radius: Undisturbed free surface: Longitudinal radius of curvature: Conventional Model’s Characteristics Initial cusp is instantaneously smoothed Surface tension driving as long as ce when resisted by viscous as long as ces gives (Eggers et al 99): Conventional Model’s Characteristics

Assumed valid while after which (Eggers et al 99): Test scaling laws by fitting to experiments No guarantee this is the solution to the conventional model Traditional Use of Scaling Laws Computational Works Problem dem in addition to s resolution over at least 9 orders of magnitude. The result been the study of simplified problems: The local problem – often using the boundary integral method as long as Stokes flow (e.g. Eggers et al 99) or inviscid flow. The global problem – bypassing the details of the initial stages Our aim is to resolve all scales so that we can: Directly compare models’ predictions to experiments Validate proposed scaling laws

JES & YDS 2011, Viscous Flows in Domains with Corners, CMAME JES & YDS 2012, Finite Element Framework as long as Simulating Dynamic Wetting Flows, Int. J. Num. Meth Fluids. JES & YDS, 2012, The Dynamics of Liquid Drops in addition to their Interaction with Surfaces of Varying Wettabilities, Phy. Fluids. JES & YDS, 2013, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, J. Comp. Phy. Resolving Multiscale Phenomena Arbitrary Lagrangian Eulerian Mesh Based on the ‘spine method’ of Scriven in addition to co-workers Coalescence simulation as long as 230cP liquid at t=0.01, 0.1, 1. Microdrop impact in addition to spreading simulation.

Benchmark Simulations ‘Benchmark’ code against simulations in Paulsen et al 12 as long as identical spheres coalescing in zero-gravity with Radius Density Surface tension Viscosities Giving two limits of Re to investigate: Hence establish validity of scaling laws as long as the conventional model High Viscosity Drops ( ) High Viscosity Drops: Benchmarking Influence of minimum radius lasts as long as time Paulsen et al 12

High Viscosity Drops: Scaling Laws Eggers et al 99 r=3.5t Not linear growth Low Viscosity Drops ( ) Low Viscosity Drops: Toroidal Bubbles Toroidal bubble As predicted in Oguz & Prosperetti 89 in addition to Duchemin et al 03 Increasing time

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Low Viscosity Drops: Benchmarking Paulsen et al 12 Eggers et al 99 Duchemin et al 03 Low Viscosity Drops: Benchmarking Crossover at Actually nearer Hemispheres of water-glycerol mixture with:

Qualitative Comparison to Experiment Coalescence of 2mm radius water drops. Simulation assumes symmetry about z=0 Experimental images courtesy of Dr J.D. Paulsen Quantitative Comparison to Experiment 3.3mPas 48mPas 230mPas Conventional Modelling: Key Points Accuracy of simulations is confirmed Scaling laws approximate conventional model well Conventional model doesn’t describe experiments

Microdrop Impact 25 micron water drop impacting at 5m/s on left: wettable substrate right: nonwettable substrate Microdrop Impact Velocity Scale Pressure Scale 25mm water drop impacting at 5m/s.

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