Visualization of Milk Drop Crowning Effect

MEAM 302 Fluid Mechanics

Elizabeth Beattie | Nikolay Vladimirov | Brett Wittmershaus

Introduction

A splash is a physical phenomena in fluid mechanics, which remains unnoticed by the

unaided eye. Splashing plays a critical role in applications such as industrial chemical sprayers

and the dispersion of pollutants and diseases. Since the development of elegant and innovative

fluid visualization photographic techniques, it is possible to view the physical behavior of a

splash via specialized equipment. In the mid-1930s, Harold Edgerton was the first to pioneer this

visualization technology through his experiments to record the splash of a drop of milk with a

thin film liquid surface (Bedi & Calcago, 1998). This study examines the Edgerton Milk Drop

Crown effect, in which a sequence of milk drops were dispensed onto a thin film of the same

fluid. Lasting only two hundredths of a second, the beauty of the milk drop coronet is unable to

be seen with the naked eye and requires specialized equipment. Additionally, the objective of

this work is to explain the physical mechanisms which lead to the formation of the milk crown

stage of splashing.

Visualization Methods

The equipment used to capture the crown effect consisted of a Canon 400D DSLR still

camera, a Tamron 28-75mm lens, a Canon EF 25 II Extension Tube, and a Sanyo VPC-

HD2000A Xacti video camera. A flat, black plastic dish measuring four inches in diameter and

0.118 inches in depth was filled with a thin film of milk. A sequence of milk drops was

dispensed, from a height of 12 inches, onto the center of the dish and the resulting effects were

captured. To capture the still image side, the camera was set to the following configuration:

75mm focal length, 22F aperture, 100 ISO, and 1/200 second exposure time with flash. The

video camera was set to record at 300 fps. The images were recorded in black and white to

ensure high contrast and quality.

Results and Discussion

The accompanying pictures and video adequately illustrate the stages of formation of the

milk drop crown phenomenon after a sequence of milk drops were dispensed onto an undisturbed

thin film of milk (see Appendix). The effect can be most simply and effectively explained by a

control volume analysis. Considering the dish filled with a thin film and the drop of milk at

impact to be the control volume, conservation of momentum holds for each stage of crown

formation. The fluid film is initially at rest. Once the first drop impacts the thin film surface, the

drop and film simultaneously experience a large acceleration and impulse force which occurs at

0.02 seconds. This impulse force directs fluid radially outward and upward following the

curvature of the drop. Fluid directed radially outward forms the Peregrine layer (Deegan, Brunet,

& Eggers, 2008). The radial collisions between the fluid elements in the Peregrine layer also

direct the fluid in the direction of the curvature of the impacting drop. The upward fluid

acceleration creates a thin cylindrical sheet with a flat rim. This rim is unstable and large drops

develop around the rim in a periodic pattern, which resembles a crown. The formation of these

large droplets is consistent with the Rayleigh-Plateau instability. Since milk is heavier than air,

the surface tension causes milk around the unstable rim to break into uniform sized droplets.

Conclusion

Despite the technically rigorous apparati (Krechetnikov & Homsy, 2009; Deegan, et al.,

2008) that have been used to capture this beautiful effect, the underlying mechanisms

contributing to the crown formation remain partially unknown. Most interestingly, the milk

crown is considered a phenomenon in fluid mechanics since it exists for a range of Webers and

Reynolds numbers and is conditionally dependent on parameters such as fluid viscosity, density,

and impact velocity (Deegan, Brunet, & Eggers, 2008).

References

Bedi, J., & Calcago, C. (1998). Harold Doc Edgerton. Retrieved December 4, 2011, from http://edgerton-digital-collections.org/docs-life/strobe-in-industry

Deegan, R. D., Brunet, P., & Eggers, J. (2008). Complexities of splashing. Nonlinearity, 21(1),

C1-C11. doi:10.1088/0951-7715/21/1/C01

Krechetnikov, R., & Homsy, G. (2009). Crown-forming instability phenomena in the drop splash

problem. Journal of Colloid and Interface Science, 331(2), 555-559.

doi:10.1016/j.jcis.2008.11.079