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Wetting as a Macroscopic and Microscropic Process. J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) Seminar at KAUST, February 2012. ‘Impact’ . A few years after completing my PhD. Wetting: Statics. Wettable (Hydrophilic).
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Wetting as a Macroscopic and Microscropic Process J.E. Sprittles (University of Birmingham / Oxford, U.K.) Y.D. Shikhmurzaev (University of Birmingham, U.K.) Seminar at KAUST, February 2012
‘Impact’ A few years after completing my PhD.....
Wetting: Statics Wettable (Hydrophilic) Non-Wettable (Hydrophobic)
Capillary Rise 27mm Radius Tube Stangeet al 03 50nm x 900nm Channels Han et al 06 1 Million Orders of Magnitude!!
Inkjet Printing of P-OLED Displays Microdrop Impact & Spreading
Modelling: Why Bother? • - Recover Hidden Information • - Map Regimes of Spreading 3 – Experiment Millimetres in Milliseconds - Riobooet al (2002) Flow Inside Solids – Marston et al 2010 Microns in Microseconds - Dong et al (2002)
Dynamic Contact Angle • Required as a boundary condition for the free surface shape. r r t Pasandideh-Fard et al 1996
) U Speed-Angle Formulae Dynamic Contact Angle Formula Young Equation σ1 σ3 - σ2 Assumption: A unique angle for each speed R
) Drop Impact Experiments Bayer & Megaridis 06
Capillary Rise Experiments Sobolevet al 01
Physics of Dynamic Wetting Liquid-solid interface Solid Forming interface Formed interface • Make a dry solid wet. • Create a new/fresh liquid-solid interface. • Class of flows with forming interfaces.
Relevance of the Young Equation Static situation Dynamic wetting σ1e σ1 θe θd σ3 - σ2 σ3e - σ2e R R Dynamic contact angle results from dynamic surface tensions. Theangle is now determined by the flow field. Slip created by surface tension gradients (Marangoni effect)
f (r, t )=0 e1 n n θd e2 Interface Formation Modelling In the bulk: Interface Formation Model On free surfaces: On liquid-solid interfaces: At contact lines:
A Finite Element Based Computational Framework JES &YDS 2011, Viscous Flows in Domains with Corners, CMAME JES & YDS 2012, Finite Element Framework for Simulating Dynamic Wetting Flows, Int. J. Num. Meth Fluids. JES & YDS, 2012, Finite Element Simulation of Dynamic Wetting Flows as an Interface Formation Process, to JCP. JES & YDS, 2012, The Dynamics of Liquid Drops and their Interaction with Surfaces of Varying Wettabilities, to PoF.
Impact at Different Scales Millimetre Drop Microdrop Nanodrop
Pyramidal (mm-sized) Drops Experiment of Renardyet al, 03.
Microdrop Impact 25 micron water drop impacting at 5m/s on left: wettable substrate right: nonwettable substrate
Microdrop Impact Pressure Scale Velocity Scale
Flow Control on Patterned Surfaces JES & YDS 2012, to PoF
‘Hydrodynamic Resist’ Smaller Capillaries
Summary: Dynamic Wetting Models Meniscus shape unchanged by dynamic wetting Meniscus shape dependent on speed of propagation. Hydrodynamic Resist: Meniscus shape influenced by geometry Dynamic Dynamic Dynamic Equilibrium Equilibrium Equilibrium Meniscus Washburn Model Basic Dynamic Wetting Models Interface Formation Model and Experiments
Capillary Rise: Models vs Experiments • Compare to experiments of Jooset al 90 and conventional Lucas-Washburn theory • Lucas-Washburn assumes: • Poiseuille Flow Throughout • Spherical Cap Meniscus • Fixed (Equilibrium) Contact Angle
Lucas-Washburn vs Full Simulation R = 0.074cm; every 50secs R = 0.036cm; every 100secs
Comparison to Experiment Washburn Washburn Full Simulation Full Simulation JES & YDS 2012, to JCP
Problems and Issues • Micro: Pore scale dynamics of: • Menisci in wetting front • Ganglia • Macro (Darcy-scale) dynamics of: • Entire wetting front • Ganglia in multiphase system • Multi-scale porosity: • Motion on a microporous substrate
Continuum Model • Simplest Case First: Full Displacement (no ganglia formation) Kinematic boundary condition Dynamic boundary condition ?
Wetting Front: Modes of Motion Threshold mode Wetting mode
Some Unexplained Effects ) 1). T. Delker, D. B. Pengra & P.-z. Wong, Phys. Rev. Lett.76, 2902 (1996). g z 2). M. Lago & M. Araujo, J. Colloid & Interf. Sci.234, 35 (2001).
Suggested Description ) Non-Washburnian ) z ) g 2/3 of height in 2 mins 1/3 of height in many hours Washburnian
Developed Theory ) z g Random Fluctuations ‘Break’ Threshold Mode YDS & JES 2012, JFM; YDS & JES 2012, to PRE
Wetting: Micro-Macro Coupling Spreading on a Porous Medium
Current State of Modelling • 1) Contact Line Pinned • 2) Shape Fixed as Spherical Cap
The Reality Equilibrium shape is history-dependent.
Spreading on a Porous Substrate θD θw U θd