Paradoxes in Capillary Flows James Sprittles Yulii Shikhmurzaev No Solution! Infinite Stresses!
McDaniel, Misty, Operations Manger has reference to this Academic Journal, PHwiki organized this Journal Paradoxes in Capillary Flows James Sprittles Yulii Shikhmurzaev What Is A Capillary Flow! One in which surface tension is of importance An effect caused by asymmetry of intermolecular as long as ces. Acts as a stretched elastic membrane at a surface. Gradients in surface tension drive bulk motion (Marangoni effects). Present at both liquid-gas in addition to liquid-solid boundaries. Introduction With: A Big Computer A Good Textbook An Endless Supply of (Good) Coffee A Lack of Social Life Can we describe all capillary flows
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1. A Classical Approach The Classical Recipe In The Bulk: (Incompressible) NavierStokes At Fluid Boundaries: Balance of Stress With Capillary Forces. Particles On a Free Surface, f(x,y,z,t)=0, Move With It (Kinematic Condition) At Solid Boundaries: No Slip Ink Jet Printing: Breakup of Liquid Threads A drop of ink is pushed from the nozzle.
Breakup of Liquid Threads Predictions of Classical Model: Infinite Axial Velocity at Breakup. Infinite Pressure at Breakup. Rate of Fresh Free Surface Area Creation Becomes Infinite Main Problem: Solution Required After Breakup. Ink Jet Printing: Spreading of Liquids Ink drops l in addition to in addition to then spread on solid. Drop In Equilibrium No Solution! Drop Out of Equilibrium Coalescence Of Liquid Volumes Ink drops coalesce with adjacent ones on the paper. Infinite Stresses!
Ink Jet Printing: Impact On Chemically Patterned Surfaces Pattern a surface to correct deposition Flow Over Chemically Patterned Surfaces Solid 1 Solid 2 Predictions of The Classical Recipe Molecular Dynamics Simulations of Flow Over Chemically Patterned Surfaces Courtesy of Professor N.V. Priezjev More wettable Compressed Less wettable Rarefied No Slip = No Effect!
Also – Flow Generated By Rotating Cylinders Formation of a Cusp/Corner The Free Surface Is a Streamline. Summary No Solution Flow of Liquids Over Solids Singular Solution Coalescence of Drops Cusps Breakup Of Liquids Wrong Solution Flow Over Chemically Patterned Surfaces A Big Computer Cant H in addition to le These. 2. A St in addition to ard Approach
Flow Of Liquids Over Solids Two Issues: Allow For A Solution Describe The Angle Between The Free Surface in addition to the Solid (The Contact Angle). St in addition to ard Solution: Allow Slip Between Solid in addition to Liquid Let Does The St in addition to ard Model Work Impact of a Microdrop Radius = 25 mm, Impact Speed = 12.2 m/s Re=345, We=51, = 100, . Experiments of Dong 06. My Simulation Q) Does The St in addition to ard Model Work My Simulation Experiment: Renardy et al
A) Yes in addition to No! Experimentally Prediction of St in addition to ard Model St in addition to ard Models Problems: Incorrect Kinematics Pressure Singularity at Contact Line Contact Angle Depends on Flow U, m/s U, m/s U 3. A New (ish) Approach Breakup Of Liquid Threads New free surface is created. New free surface particles are initially out of equilibrium.
Spreading of Liquids on Solids Solid Gas Liquid In Frame Moving With Drop Interfaces are shown with finite thickness as long as representation only. Coalescence Of Liquid Volumes Particles on the surface become trapped in the bulk. Coalescence Of Liquid Volumes
Near Cusp/Corner Gas Liquid Corner/Cusp Interfaces are shown with finite thickness as long as representation only. Surface Tension Relaxation Summary All are associated with transition from one surface tension to another Relaxation of surface tension takes finite time/distance Mass, momentum in addition to energy exchange between surface in addition to bulk Gradients in surface tension (Marangoni effect)
Simplest Model of Interface Formation Generalisation of st in addition to ard/classical model In the bulk: On liquid-solid interfaces: On free surfaces: At contact lines: Predictions/Propag in addition to a Generalises st in addition to ard/classical recipe. Removes singularities inherent in both classical in addition to st in addition to ard approaches. Predicts contact angle depends on flow field. Ensures one can (numerically) apply a unified approach to all these problems (=easier!). Agrees with experiment. Conclusion/Sales Pitch With: A Big Computer An Endless Supply of (Good) Coffee A Lack of Social Life The RIGHT Textbook We can describe capillary flows!
Chemically Patterned Surface Surfaces With Wettability Gradients
McDaniel, Misty Operations Manger
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