NASA/TMm1999-209636

A New Approach to Measure Contact Angle

and Evaporation Rate With Flow

Visualization in a Sessile Drop

Nengli Zhang

Ohio Aerospace Institute, Brook Park, Ohio

David E Chao

Glenn Research Center, Cleveland, Ohio

Prepared for the

Interfaces for the Twenty-First Century: New Research Directions in Fluid

Mechanics and Materials Science

sponsored by the NASA OLMSA Microgravity Research Division, NSF

Monterey, California, August 16-18, 1999

National Aeronautics and

Space Administration

Glenn Research Center

December 1999

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A NEW APPROACH TO MEASURE CONTACT ANGLE AND EVAPORATION RATE

WITH FLOW VISUALIZATION IN A SESSILE DROP

Nengli Zhang and David F. Chao

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

The contact angle and the spreading process of sessile droplet are very crucial in many

technological processes, such as painting and coating, material processing, film-cooling

applications, lubrication, and boiling. Additionally, as it is well known that the surface free

energy of polymers cannot be directly measured for their elastic and viscous restraints. The

measurements of liquid contact angle on the polymer surfaces become extremely important to

evaluate the surface free energy of polymers through indirect methods linked with the contact

angle data.

Due to the occurrence of liquid evaporation is inevitable, the effects of evaporation on the

contact angle and the spreading become very important for more complete understanding of

these processes. Based on the laser shadowgraphic system used by the present author [1, 2], a

very simple optical procedure has been developed to measure the contact angle, the spreading

speed, the evaporation rate, and to visualize inside convection of a sessile drop simultaneously.

It is of interest to note that evaporation can induce Marangoni-Bdnard convection in sessile

drops [3]. However, the impacts of the inside convection on the wetting and spreading processes

are not clear. The experimental methods used by previous investigators cannot simultaneously

measure the spreading process and visualize the convection inside. The present work provides

the solution for the first time.

The inside convection and the drop profile data can be synchronously recorded through the

CCD camera I and II. CCD camera I would also precisely record the real-time diameter of the

sessile drop which is essential for determination of both spreading speed and evaporation rate.

As it is well known that a sessile drop takes the shape of a spherical cap provided its mass is

sufficiently small, for example, less than 1 mg [4-6]. The sessile drop on the glass slide can be

taken as a thin piano-convex lens with a focal length, f, which can be expressed as

R

f - (1)

1l -- 1

where R is the curvature radius of the spherical cap, n is the refractive index of the liquid. By a

simple geometric relationship as shown in Fig. 1,

d(s + p)

f - (2)

d+D

NASA/TM-- 1999-209636 1
where d is the base diameter of the sessile drop, s is the distance from the center of the drop base

to its image on the front surface of the mirror, p is the distance between images of the drop center

on the mirror and on the screen, D is the diameter of the drop image on the screen. Both d and D

are time dependent due to the spreading and the evaporation, which can be accurately measured

through the direct photo-shadowgraphic system. It is obvious that as the function of time, the

curvature radius of the liquid spherical cap can be then determined by the data of d and D:

d(t)

R(t) = (n - 1)(s + p) (3)

d(t) + D(t)

The contact angle can be calculated as

d(t)

O(t) = arcsin (4)

2R(t)

The evaporation rate can also be determined from the data of d and D. According to a simple

geometric relationship, the instant volume of the sessile drop can be written as

, h(t)]

V(t) = rch'(t){R(t) - ---_j (5)

Parallel white light beam !, CCD

Beam splitter

Parallel laser bear_

camera I

,4 -- I..----

Monitor I

Testsection_ _, r ._ [

_" ,, d Liquid reservoir r-q

D _camera

Aluminized mirror Screen

Monitor II

Video printer

Video recorder I

Video recorder II

Figure 1.-Schematic of experimental setup.

NASA/TM--1999-209636 2
Therefore, the evaporation rate is

h

v; = 2Jrhh(R - _-) + tch_(R - T) {6)

where h = R-_/R 2 -d 2 /4, (7)

R/_ -dd / 4

/i =/?-

2_d2/4

(8)

d d(d+D).

and [_:(n-1)(s+P)[d+ D _-_+- _)-_ J (9)

As an example, Figs. 2 and 3 show the direct photography from top and the laser

shadowgraphy at moment t - 4 sec., respectively, for an evaporating freon-ll3 sessile drop.

Inside convection can be seen clearly in Fig.3.

I K J I i I

Figure 2.-Direct photography from top. d(t) - 5.72 mm at t = 4 sec.

NASA/TM--1999-209636 3
Figure3.-Laser shadowgraphy,d(t) = 85.7mm att = 4 sec.

References

I. N. Zhang, and W.J. Yang, "Natural Convection in Evaporating Minute Drops," ASME

Journal of Heat Transfer, vol. 104, pp. 656-662 (1982).

2. N. Zhang, and W.J. Yang, "Microstructure of Flow Inside Minute Drops Evaporating on a

Surface," ASME Journal of Heat Transfer, vol. 105, pp. 908-910 (1983).

3. N. Zhang, and W.J. Yang, "Visualization of Evaporative Convection in Minute Drops by

Laser Shadowgraphy," Rev. Sci. Instrum., vol. 54, no. 1, pp. 93-96 (1983).

4. R.G. Picknett, and R. Bexon, "The Evaporation of Sessile or Pendant Drops in Still Air,"

J. Colloid Interface Sci., vol. 61, no. 2, pp. 336-350 (1977).

5. S.M. Rowan, M.I. Newton, and G. McHale, "Evaporation of Microdroplets and the Wetting

of Solid Surfaces," J. Phys. Chem., vol. 99, no. 35, pp. 13268-13271 (1995).

6. M.J. De Ruijter, J. De Coninck, and G. Oshanin, "Droplet Spreading: Partial Wetting Regime

Revisited," Langmuir, vol. 15, no. 6, pp. 2209-2216 (1999).

NASA/TM-- 1999-209636 4

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December 1999 Technical Memorandum

4. TITLE AND SUBTITLE

A New Approach to Measure Contact Angle and Evaporation Rate

with Flow Visualization in a Sessile Drop

6. AUTHOR(S)

Nengli Zhang and David F. Chao

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

John H. Glenn Research Center at Lewis Field

Cleveland. Ohio 44135-3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space Administration

Washington. DC 20546-0001

5. FUNDING NUMBERS

WU- 101-13-0A-O0

8. PERFORMING ORGANIZATION

REPORT NUMBER

E-11966

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

NASA TM--1999-209636

11. SUPPLEMENTARY NOTES

Prepared for the Interfaces for the Twenty-First Century: New Research Directions in Fluid Mechanics and Materials

Science sponsored by the NASA OLMSA Microgravity Research Division, NSF, Monterey, California, August 16-18,

1999. Nengli Zhang, Ohio Aerospace Institute, 22800 Cedar Point Road, Cleveland, Ohio 44142 (work funded under

NASA Cooperative Agreement NCC3-620): David F. Chao, NASA Glenn Research Center. Responsible person.

David E Chao, organization code 6712, (216) 433-8320.

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13. ABSTRACT (Maximum 200 words)

The contact angle and the spreading process of sessile droplet are very crucial in many technological processes, such as painting and coating, material

processing, film-cooling applications, lubrication, and boiling. Additionally. as if is well known that the surface free energy of polymers cannot be

directly measured for their elastic and viscous restraints. The measurements of liquid contact angle on the polymer surfaces become extremely

importan! to evaluate the surface tree energy of polymers through indirect methods linked with the contact angle data. Due to the occurrence of liquid

evaporation is inevitable, the effitcts of evaporation on the contact angle and the spreading become very important for more complete understanding of

these processes. It is of interest to note that evaporation can induce Marangoni-B_nard convection in sessile drops. However. the impacts of the inside

convection on the wening and spreading processes are not clear. The experimental methods used by previous investigators cannot simuhaneously

measure the spreading process and visualize the convection inside. Based on the laser shadowgraphic system used by the present author, a very simple

optical procedure has been developed to measure the contact angle, the spreading speed, the evaporation rate. and to visualize inside convection of a

sessile drop simuhaneously. "lwo CCD cameras were used to synchronously record the real-time diameter of the sessile drop, which is essential for

determination of both spreading speed and evaporation rate. and the shadowgraphic image magnified by the sessile drop acting as a thin piano-convex

lens. From the shadowgraph, the inside convection of the drop can be observed if any and the image outer diameter, which linked to the drop profile,

can be measured, Simple equations have been derived to calculate the drop profile, including the instantaneous contact angle, height, and volume of the

sessile drop, as well as the evaporation rate. The influence of the inside convection on the wetting and spreading processes can be figured out through

comparison of the drop profiles with and without inside convection when the sessile drop is placed at different evaporation conditions.

14. SUBJECT TERMS

Spreading: Contact angle; Evaporation rate; Flow visualization

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