When Sessile Drops Are No Longer Small: Transitions from Spherical to Fully Flattened
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1 purify When Sessile Drops Are No Longer Small: Transitions from Spherical to Fully Flattened protect transport Chuck Extrand & Sung In Moon October 00
2 Outline Introduction Objectives Materials Method Analysis Results and Discussion Conclusions Page
3 Introduction Page
4 Introduction Page 4
5 Introduction Page 5
6 Introduction θ Page 6
7 Introduction Often done with an automated goniometer Page 7
8 Introduction Height-diameter method h " =! arctan h a a Page 8
9 Introduction Height-volume method V / &, V ) h!! # 0 =. arc cot$ * - ' $ % + / h ( " Page 9
10 Page 0 Introduction Diameter-volume method ( ) ( ) ( ) ( )!!!! "!!! # $!!!! %!!! & ' ( ( ( ) * + + +, -.. / 0.. / ( ( ( ) * + + +, -.. / 0.. / = / / / / / / arctan a V a V a V a V V a
11 Introduction Direct method Tangent Indirect methods Height-diameter Height-volume Diameter-volume Page
12 Introduction Why use indirect methods? In some cases, it s easier to measure dimensions than construct tangent Rough solid Geometry or curvature Page
13 Introduction Why use indirect methods? Size or geometry precludes use of goniometer Whole part testing Non-destructive Quality assurance Failure analysis Page
14 Introduction Limitations of indirect methods? Equations listed earlier assume spherically proportioned drops No easy way to estimate transition points Larger drops require sophisticated iterative numerical methods Page 4
15 Objectives Understand the transition points where gravity causes distortion: Deviation from spherical proportions Fully flattened Use this knowledge to specify liquids and volumes for use with indirect methods Page 5
16 Materials Solid surfaces PFA PC Si wafers Si : used as received, moderately hydrophilic Si : cleaned and aged, more hydrophilic Liquids Water Ethylene glycol (EG) Diiodomethane (MI) Page 6
17 Materials Liquid properties Liquid Water ρ (kg/m ) 998 γ (mn/m) 7 Ethylene glycol 0 48 Diiodomethane 0 5 Page 7
18 Materials Contact angles measured by tangent method independent of volume Liquid Solid θ (o ) Water Ethylene glycol Diiodomethane PFA PC Si Si PFA PFA Page 8
19 Method Deposit sessile drops of progressively larger volumes (V) Measure: Height (h) Contact diameter (a) Contact angle (θ) Analyze: Examine dimensional changes Determine transitions Page 9
20 Analysis Small drops spherically proportioned! h s a h s = a " tan! Page 0 Mack 96, Bartell & Zuidema 96
21 Analysis Intermediate-sized drops - meniscus height around circular rods " h z r # L! R / ' ) $ ' ) h m = % ( )(! cos* )" % + ( ) & ( g # & ( g / a $ " #! / Page Extrand and Moon 009
22 Analysis Large drops fully flattened! h l a h l & $ * # = ( )( ' cos( )! % ) g " / Page Poisson 8, Quincke 868
23 Results and Discussion Water on PFA V = µl a =. mm h = 0.8 mm Page
24 Results and Discussion Water on PFA V = 50 µl a = 4.8 mm h =.7 mm Page 4
25 Results and Discussion Water on PFA V =,000 µl a = 5 mm h = 4.6 mm Page 5
26 Results and Discussion 5 4! = 08 o (mm) h 0 experimental values Water on PFA a (mm) Page 6
27 Results and Discussion (mm) h 5 4 0! = 08 o Water on PFA a (mm) experimental values h s Page 7
28 Results and Discussion (mm) h 5 4 0! = 08 o Water on PFA a (mm) experimental values h s h m Page 8
29 Results and Discussion (mm) h 5 4 0! = 08 o Water on PFA a (mm) experimental values h s h m h l Page 9
30 Results and Discussion! = 90 o (mm) h a (mm) experimental values h s h m h l Ethylene glycol on PFA Page 0
31 Results and Discussion.0.5! = 85 o.0 experimental values h s (mm) h 0.5 h m h l 0.0 Diiodomethane on PFA a (mm) Page
32 Results and Discussion Transition from spherical to distorted h s = h m (mm) h 5 4 0! = 08 o Water on PFA a (mm) experimental values h s h m Page
33 Page Results and Discussion Transition from spherical to distorted height (h xc ) and volume (V xc )!! " # $ $ % & ' ( ( ) * + +, - ' + ( ) * +, - = cos sin 8 tan / /... / 0 g h xc / / cos sin 8 tan tan 48!! " # $ $ % & ' ( ( ) * + +, - ' + ( ) * +, - + ( ) * +, - =.... / 0 g V xc
34 Results and Discussion Determine experimental values of h xc and V xc (mm) h 5 4 0! = 08 o Water on PFA a (mm) experimental values h s Page 4
35 Results and Discussion 5 4 PFA PC Si Si Water xc (mm) h ! ( o ) Page 5
36 Results and Discussion xc l)µ ( V Water PFA PC Si Si ! ( o ) Page 6
37 Conclusions Three distinct shape domains were observed: Small and spherical Medium and distorted Larger and fully flattened Various models for height gave reasonable predictions Contact angles carefully measured by the tangent method were independent of drop size Page 7
38 Conclusions The distortion transition depended on surface tension, density and somewhat unexpectedly, also wettability Predicted values of the height and volume for the onset of distortion agreed fairly well with the measured values At the extremes, it is anticipated that very small volumes are required to produce drops with spherical proportions Page 8
39 Questions? Page 9
40
41 Analysis A number of investigators have examined drop shape by numerical methods: Bashforth & Adams (88) Ferguson (9) Ellefson & Taylor (98) Blaisedell (940) Staicopolus (96) Butler & Bloom (966) Maze & Burnet (969) Huh & Scriven (969) Padday (969) Page 4
42 Results and Discussion Water on PFA Page 4
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