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Research Papers: Techniques and Procedures

# Effect of Surface Roughness on Single Cryogen Droplet Spreading

[+] Author and Article Information
Jie Liu

Department of Mechanical Engineering, University of California, Riverside, CA 92521liuj@engr.ucr.edu

Walfre Franco

Beckman Laser Institute and Medical Clinic, University of California, Irvine, 1002 Health Sciences Road East, Irvine, CA 92612wfranco@uci.edu

Guillermo Aguilar

Department of Mechanical Engineering, University of California, Riverside, CA 92521gaguilar@engr.ucr.edu

J. Fluids Eng 130(4), 041402 (Apr 11, 2008) (9 pages) doi:10.1115/1.2903810 History: Received April 18, 2006; Revised October 08, 2007; Published April 11, 2008

## Abstract

Cryogen spray cooling is an auxiliary procedure to dermatologic laser surgery, which consists of precooling the superficial skin layer (epidermis) during laser irradiation of subsurface targets to avoid nonspecific epidermal thermal damage. While previous studies have investigated the interaction of cryogen sprays with microscopically smooth human skin models, it is important to recognize that real human skin surface is far from smooth. With the objective to provide physical insight into the interaction between cryogen sprays and human skin, we study the effect of surface roughness on the impact dynamics of single cryogen droplets falling on skin models of various roughnesses $(0.5–70μm)$. We first develop a theoretical model to predict the maximum spread diameter $(Dm)$ following droplet impingement based on a similarity approximation to the solution of a viscous boundary layer that incorporates friction as the major source of viscous dissipation on a rough surface. Then, we measure the droplet diameter, impact velocity, and $Dm$ of cryogen droplets falling by gravity onto skin models. Experimental data prove that the proposed model predicts $Dm$ with good accuracy, suggesting that the effects of surface roughness and friction on $Dm$ are properly taken into account for the range of surface roughness studied herein.

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## Figures

Figure 1

Sketch of shape and energy of droplet before impact and at maximum spread diameter Dm

Figure 3

Droplet with D=1.41mm and V=0.9m∕s and Re=9200 and We=258 impact onto three surfaces with Ra=0.5μm (left), Ra=30μm (middle), and Ra=70μm (right) for various times in the range of 0–20ms

Figure 2

Experimental facilities for experiments of cryogen droplet impact dynamics without evaporation. 1, pressure gauge; 2, cryogen tank; 3, nozzle; 4, clear PVC tower; 5, temperature sensor; 6, pressured gas; 7, illumination; 8, impact surface; 9, high speed camera; 10, pressure relieve valve; 11, pressure gauge; 12, needle valve; 13, ball valve.

Figure 4

Spread diameter versus spread time for surface roughnesses of Ra=0.5μm, 4.2μm, 8.2μm, 30μm, 50μm, and 70μm, with droplet with D=1.41mm and V=0.9m∕s

Figure 5

Spread velocity versus spread time for surface roughnesses of Ra=0.5μm, 4.2μm, 8.2μm, 30μm, 50μm, and 70μm, with droplet with D=1.41mm and V=0.9m∕s

Figure 6

Prediction of β with undetermined coefficient C in Eq. 27: Case 1: D=1.41mm and V=0.9m∕s; Re=9200 and We=258. Case 2: D=1.41mm and V=2.38m∕s; Re=20,000 and We=1210. Case 3: D=1.91mm and V=2.38m∕s; Re=26,500 and We=1670.

Figure 7

Flowchart of algorithm to determine the coefficients c, K1, and K2 for experiment results

Figure 8

Experimental and model predicted results of β for three cases: Case 1: D=1.41mm and V=0.9m∕s; Re=9200 and We=258. Case 2: D=1.41mm and V=2.38m∕s; Re=20,000 and We=1210. Case 3: D=1.91mm and V=2.38m∕s; Re=26,500 and We=1670.

Figure 9

Comparison of our experimental results with previous models (15,17,19) for the same three cases described in Table 2 with Ra=0.5μm

Figure 10

Comparison of the β using the present model with experimental data from current and previous works (20,22-24)

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