Drop Impact and Spreading on Surfaces of Variable Wettability.ppt

1、Drop Impact and Spreading on Surfaces of Variable Wettability,J.E Sprittles Y.D. Shikhmurzaev,Bonn 2007,Swansea 2007,Motivation,Drop impact and spreading occurs in many industrial processes. 100 million inkjet printers sold yearly. NEW: Inkjet printing of electronic circuits. Why study the old probl

2、em of drops spreading on surfaces?,Swansea 2007,Worthington 1876 First Experiments,Swansea 2007,Worthingtons Sketches,Millimetre sized drops of milk on smoked glass.,Swansea 2007,Modern Day Experiments (mm drops of water),Courtesy of Romain Rioboo,Swansea 2007,Xu et al 03 Drops dont splash at the to

3、p of Everest!,Swansea 2007,Renardy 03 et al - Pyramidal Drops,Impact of oscillating water drops on super hydrophobic substrates,1,2,3,4,Swansea 2007,The Simplest Problem,How does a drops behaviour depend on: fluid properties, drop speed, drop size,. etc?,Spread Factor,Apex Height,Contact Angle,a,Swa

4、nsea 2007,The Contact Angle,In equilibrium the angle defines the wettability of a solid-liquid combination. How should we describe it in a dynamic situation?,More Wettable (Hydrophilic),Less Wettable (Hydrophobic),Solid 1,Solid 2,Swansea 2007,Modelling of Drop Impact and Spreading Phenomena,The Movi

5、ng Contact Line Problem Conventional Approaches and their Drawbacks The Shikhmurzaev Model,Swansea 2007,The Moving Contact Line Problem,Liquid,Inviscid Gas,Contact line,Contact angle,Solid,Swansea 2007,The Moving Contact Line Problem,No-Slip Impermeability,Kinematic condition Dynamic condition,Navie

6、r-Stokes Continuity,Contact angle prescribed,No solution!,Swansea 2007,The Conventional Approach,These are treated separately by: 1)Modifying the no-slip condition near the Contact Line (CL) to allow slip, e.g. 2)Prescribing the Contact Angle as a function of various parameters, e.g.,One must: 1)All

7、ow a solution to be obtained. 2)Describe the macroscopic contact angle.,Swansea 2007,Experiments Show This Is Wrong,Can one describe the contact angle as a function of the parameters? “There is no universal expression to relate contact angle with contact line speed”. (Bayer and Megaridis 06) “There

8、is no general correlation of the dynamic contact angle as a function of surface characteristics, droplet fluid and diameter and impact velocity.” (Sikalo et al 02),Swansea 2007,As in Curtain Coating,Used to industrially coat materials. Conventional models: Fixed substrate speed = Unique contact angl

9、e,Swansea 2007,Hydrodynamic Assist of Dynamic Wetting,The contact angle depends on the flow field.,See: Blake et al 1994, Blake et al 1999, Clarke et al 2006,Swansea 2007,Angle Also Dependent On The Geometry: Flow Through a Channel,The contact angle is dependent on d and U. (Ngan surface velocity, a

10、nd surface density, .,Equation of State,Input of Wettability,Swansea 2007,The Shikhmurzaev Model:Constant Wettability,Bulk,Interfacial Layer: For Visualisation Only. In the continuum limit.,If then we have Navier Slip,Swansea 2007,Solid-Liquid Boundary Conditions Shikhmurzaev Equations,Bulk,Tangenti

11、al velocity,Surface velocity,Solid facing side of interface: No-slip,Layer is for VISUALISATION only. In the continuum limit,Swansea 2007,Solid-Liquid Boundary Conditions Shikhmurzaev Equations,Bulk,Continuity of surface mass,Normal velocity,Solid facing side of interface: Impermeability,Layer is fo

12、r VISUALISATION only. In the continuum limit,Swansea 2007,Problem Formulation,2D, steady flow of an incompressible, viscous, Newtonian fluid over a stationary flat solid surface (y=0), driven by a shear in the far field. Bulk Navier Stokes equations:,Boundary Conditions Shear flow in the far field,

13、which, using gives:,Swansea 2007,Results - Streamlines,Consider solid 1 (x0). Coupled, nonlinear PDEs were solved using the finite element method.,Swansea 2007,Results Different Solid Combinations,Consider different solid combinations.,Swansea 2007,Results Size of The Effect,Consider the normal flux

14、 out of the interface, per unit time, J. We find:,The constant of proportionality is dependent on the fluid and the magnitude of the shear applied.,Swansea 2007,Results - The Generators of Slip,Variations in slip are mainly caused by variations in surface tension.,1) Deviation of shear stress on the

15、 interface from equilibrium. 2) Surface tension gradients.,Swansea 2007,Periodically Patterned Surface,Consider Solid 1 More Wettable. Consider a=1 - Strips Have Equal Width.,Swansea 2007,Results - Streamlines,Solid 2 less wettable,Qualitative agreement,Swansea 2007,Results Velocity Profiles,Tangent

16、ial (slip) velocity varies around its equilibrium value of u=9.8.,Fluxes are both in and out of the interfacial layer. Overall mass is conserved.,Swansea 2007,Further Work,Compare results with molecular dynamics simulations. Devise experiments to test predictions. Fully investigate periodic case. Si

17、ngle transition investigation is in: Sprittles Strm et al. 1990; Fermigier : Burley , , : Strm et al. 1990),It has been shown that the theory is in good agreement with all experimental data published in the literature.,Swansea 2007,Mechanism of Relaxation,Comparison of the theory with experiments on fluids with different vi