Does a droplet roll or slide ?

Seminar Week talk at The Institute of Mathematical Sciences

Transcript

1. Does a droplet roll or slide on an inclined surface ? Ronojoy Adhikari The Institute of Mathematical Sciences Sumesh Thampi and Rama Govindarajan Jawaharlal Nehru Center for Advanced Scientific Research
2. An ancient observation ...
3. An ancient observation ... http:/www./religiousleftlaw.com/2012/02/the-three-yogas-of-the-bhagavad-gītā-an-introduction.html
4. An ancient observation ... brahmany adhaya karmani sangam tyaktva karoti yah lipyate na sa papena padma-patram ivambhasa ---Bhagavadgita ~ 200BCE http:/www./religiousleftlaw.com/2012/02/the-three-yogas-of-the-bhagavad-gītā-an-introduction.html
5. An ancient observation ... brahmany adhaya karmani sangam tyaktva karoti yah lipyate na sa papena padma-patram ivambhasa ---Bhagavadgita ~ 200BCE http:/www./religiousleftlaw.com/2012/02/the-three-yogas-of-the-bhagavad-gītā-an-introduction.html One who performs his duty without attachment, surrendering the results unto the Supreme God, Is not affected by sinful action, as the lotus leaf is untouched by water.
6. An ancient observation ... brahmany adhaya karmani sangam tyaktva karoti yah lipyate na sa papena padma-patram ivambhasa ---Bhagavadgita ~ 200BCE http:/www./religiousleftlaw.com/2012/02/the-three-yogas-of-the-bhagavad-gītā-an-introduction.html One who performs his duty without attachment, surrendering the results unto the Supreme God, Is not affected by sinful action, as the lotus leaf is untouched by water. प"प#िमवा(भसा
7. प"प#िमवा(भसा
8. An ancient observation ... brahmany adhaya karmani sangam tyaktva karoti yah lipyate na sa papena padma-patram ivambhasa ---Bhagavadgita ~ 200BCE http:/www./religiousleftlaw.com/2012/02/the-three-yogas-of-the-bhagavad-gītā-an-introduction.html One who performs his duty without attachment, surrendering the results unto the Supreme God, Is not affected by sinful action, as the lotus leaf is untouched by water. प"प#िमवा(भसा
9. ...and a modern question. ? rolling sliding
10. Why is this important ?
11. Why is this important ? self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
12. Why is this important ? self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
13. Why is this important ? self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
14. Why is this important ? adhering surfaces want minimum amount of pesticide avoid contamination of soil and water self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
15. Why is this important ? adhering surfaces want minimum amount of pesticide avoid contamination of soil and water self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
16. Why is this important ? adhering surfaces want minimum amount of pesticide avoid contamination of soil and water self-cleaning surfaces want minimum amount of maintenance avoid economic costs of cleaning
17. The physics of drops and surfaces sessile droplet solid liquid vapour pendant droplet s o l i d liquid vapour
18. Statics and energy minimization
19. Statics and energy minimization lv sv ls ✓ Alv Als liquid-vapour interface area liquid-solid interface area surface tension
20. Statics and energy minimization lv sv ls ✓ Alv Als liquid-vapour interface area liquid-solid interface area surface tension E = lv Alv ( sv sl)Asl “Hamiltonian’’ equilibrium : minimize surface area at constant volume
21. Statics and energy minimization lv sv ls ✓ Alv Als liquid-vapour interface area liquid-solid interface area surface tension E = lv Alv ( sv sl)Asl “Hamiltonian’’ equilibrium : minimize surface area at constant volume E = 0 with V constant gives drop shape and contact angle ✓ “constrained variational problem’’
22. The variational solution lv sv ls ✓ Alv Als liquid-vapour interface area liquid-solid interface area surface tension cos ✓ = sv sl lv hemispherical cap Young-Laplace Law + +
23. Wetting water droplet in oil on brass water droplet in oil on glass good wetting poor wetting images from wikipedia
24. Where is gravity ?
25. Where is gravity ? E = lv Alv ( sv sl)Asl + Z V ⇥gz dV
26. Where is gravity ? E = lv Alv ( sv sl)Asl + Z V ⇥gz dV gravity surface tension = R ⇥gz dV lv Alv
27. Where is gravity ? E = lv Alv ( sv sl)Asl + Z V ⇥gz dV gravity surface tension = R ⇥gz dV lv Alv Bo = ⇥gL2 lv Bond Number
28. Where is gravity ? E = lv Alv ( sv sl)Asl + Z V ⇥gz dV gravity surface tension = R ⇥gz dV lv Alv Bo = ⇥gL2 lv Bond Number small Bond number - gravity not important - small droplets large Bond number - gravity important - large droplets
29. Where is gravity ? E = lv Alv ( sv sl)Asl + Z V ⇥gz dV gravity surface tension = R ⇥gz dV lv Alv Bo = ⇥gL2 lv Bond Number small Bond number - gravity not important - small droplets large Bond number - gravity important - large droplets Too much of Bond - cannot solve constrained variational problem analytically, need numerical solutions for shape and contact angle.
30. Shape and contact angle changes with Bo movie from mit opencourseware project
31. Shape and contact angle changes with Bo movie from mit opencourseware project
32. Drop dynamics
33. Drop dynamics cartoon
34. Drop dynamics cartoon reality leading contact angle trailing contact angle
35. Drop dynamics cartoon reality leading contact angle trailing contact angle contact angles and shape no longer determined by energy minimization.
36. Drop dynamics cartoon reality leading contact angle trailing contact angle contact angles and shape no longer determined by energy minimization. now, a full fluid dynamical problem has to be solved.
37. Drop dynamics cartoon reality leading contact angle trailing contact angle contact angles and shape no longer determined by energy minimization. now, a full fluid dynamical problem has to be solved. this is a “free boundary problem”, where the surface where boundary conditions are imposed is part of the problem!
38. Drop dynamics cartoon reality leading contact angle trailing contact angle contact angles and shape no longer determined by energy minimization. now, a full fluid dynamical problem has to be solved. this is a “free boundary problem”, where the surface where boundary conditions are imposed is part of the problem! hard! hard! hard!
39. Landau-Ginzburg theory = ⇢l ⇢v ⇢l + ⇢v F = Z A 2 2 + B 4 4 + K 2 (r )2 mathematical interface physical interface = 2 3 p 2KA3/B2 = p 2K/A } “phi4 soliton”
40. Dynamics with Landau-Ginzburg theory @t + · j = 0 @t(⇢v) + · = 0 j = ⇥v + Mr F ⇥ = ⇤vv + rp + ⇥rv + r F ⌅ conservation laws constitutive equations
41. What’s new ? previous work our work approximate solutions exact numerical solution small Bond number arbitrary Bond number small OR large contact angle arbitrary contact angle
42. Droplet motion under gravity
43. Droplet motion under gravity
44. What is rolling for a drop ?
45. A scalar from shape q = 4 area (perimeter)2
46. A rolling law for drops
47. प"प#िमवा(भसा
48. Thank you for your attention!