Some Aspects of Drops Impacting on Solid Surfaces

1. Some Aspects of Drops Impacting on Solid Surfaces J.E Sprittles Y.D. Shikhmurzaev EFMC7 Manchester 2008

2. Motivation • Drop impact and spreading occurs in many industrial processes. • 100 million inkjet printers sold yearly. • Recent experiments show standard models of drop impact and spreading will be inadequate for microdrops. Photos courtesy of Romain Rioboo

3. The Moving Contact Line Problem U The classical recipe of: Bulk Incompressible Navier Stokes Solid No-Slip Free Surface Stress balance with capillary pressure. Fails to provide a solution for a drop spreading steadily over a solid substrate.

4. Flow Of Liquids Over Solids Two Issues: • Allow For A Solution • Describe The Angle Between The Free Surface and the Solid (The Contact Angle). Standard Solution: • Allow Slip Between Solid and Liquid • Let U

5. Standard Modelling of Axisymmetric Drop Impact and Spreading • Bulk: Incompressible Navier-Stokes • Boundary: Classical conditions apart from no-slip being replaced by Navier Slip: • Contact Angle Related to contact line speed using empirical relation (Jiang et al 79)

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

7. Does The Standard Model Work?Pyramidal Drops (Millimetre Size) Experiment Renardy et al. Simulation Sprittles.

8. Qualitatively OKQuantitatively Not Standard Recipe’s Problems: • Incorrect Kinematics • Logarithmic Pressure Singularity at the Contact Line. • But perhaps worst of all…. Prediction of Standard Model Experimentally U U, m/s

9. Experiments answer, NO! “There 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) 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) U, m/s

10. As in Curtain Coating (Used To Industrially Coat Materials) U U, cm/s Standard models: Fixed Substrate Speed => Unique Contact Angle Dynamic contact angle as a function of coating speed for different flow rates (Blake & Shikhmurzaev 02).

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

12. The Interface Formation Model’s Predictions Unlike conventional models: • The contact angle is determined by the flow field. • No stagnation region at the contact line. • No infinite pressure at the contact line => Numerics easier

13. Simplest Model of Interface Formation f (r, t )=0 e1 n n θd e2 • Generalisation of standard/classical model In the bulk: On free surfaces: On liquid-solid interfaces: At contact lines:

14. Qualitative Results:IFM In Frame Moving With Contact Line Liquid Gas Solid Speed U

15. Increasing impact speed Changes flow field Qualitative Results:IFM In Frame Moving With Contact Line Liquid Gas Solid Solid Speed U

16. Mock 05 et al - Drop Impact onto Chemically Patterned Surfaces • Pattern a surface to ‘correct’ deposition. Courtesy of Professor Roisman

17. Flow over a transition between solids of differing wettabilities. Standard model predicts no effect. Chemically Patterned Surfaces What happens in this region? Shear flow in the far field Solid 2 Solid 1

18. Molecular Dynamics Simulations More wettable Compressed Less wettable Rarefied Courtesy of Professor N.V. Priezjev

19. Results - Streamlines Solid 2 less wettable Qualitative agreement Sprittles & Shikhmurzaev, Phys. Rev. E 76, 021602 (2007). Sprittles & Shikhmurzaev, EPJ (2008), In Print

20. Thanks

21. Drop Impact on a Hydrophobic (non-wettable) Substrate • Does The Standard Model Work? Rebound on a Hydrophobic Substrate Re=100, We=10, β = 100, .

22. Does The Standard Model Work? Impact of a Microdrop Radius = 25 mm, Impact Speed = 12.2 m/s Re=345, We=51, β = 100, . Experiment Dong 06. Simulation Sprittles.

23. Shikhmurzaev Model • Solid-liquid and liquid-gas interfaces have an asymmetry of forces acting on them. • In the continuum approximation the dynamics of the interfacial layer should be applied at a surface. • Surface properties survive even when the interface's thickness is considered negligible. Surface tension Surface density Surface velocity

24. Shikhmurzaev ModelWhat is it? • Generalisation of the classical boundary conditions. • Considers the interface as a thermodynamic system with mass, momentum and energy exchange with the bulk. • Used to relieve paradoxes in modelling of capillary flow.