Pikkula_ABME_2004

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Annals of Biomedical Engineering [AMBE] pp1282-ambe-490790 July 28, 2004 17:49 Style file version 14 Oct, 2003

Annals of Biomedical Engineering, Vol. 32, No. 8, August 2004 (©2004) pp. 1131–1140

Effects of Droplet Velocity, Diameter, and Film Height on HeatRemoval during Cryogen Spray Cooling

BRIAN M. PIKKULA,1 JAMES W. TUNNELL,1,2 DAVID W. CHANG,3 and BAHMAN ANVARI1

1Department of Bioengineering, Rice University, Houston, TX; 2Current address: G.R. Harrison Spectroscopy Laboratory,Massachusetts Institute of Technology, Cambridge, MA; and 3Department of Plastic Surgery, University of Texas

M.D. Anderson Cancer Center, Houston, TX

(Received 16 May 2003; accepted 31 March 2004)

Abstract—Cryogen spray cooling (CSC) is an effective methodto reduce or eliminate epidermal damage during laser treatmentof various dermatoses. This study sought to determine the effectsof specific cryogen properties on heat removal. Heat removal wasquantified using an algorithm that solved an inverse heat con-duction problem from internal temperature measurements madewithin a skin phantom. A nondimensional parameter, the Webernumber, characterized the combined effects of droplet velocity,diameter, and surface tension. CSC experiments with laser irra-diation were conducted on ex vivo human skin samples to assessthe effect of Weber number on epidermal protection. An empiricalrelationship between heat removal and the difference in droplettemperature and the substrate, droplet velocity, and diameter wasobtained. Histological sections of irradiated ex vivo human skindemonstrated that sprays with higher Weber numbers increasedepidermal protection. Results indicate that the cryogen film actsas an impediment to heat transfer between the impinging dropletsand the substrate. This study offers the importance of Weber num-ber in heat removal and epidermal protection.

Keywords—Dermatology, Laser therapy, Skin, Surface tension,Surfactants, Weber number.

INTRODUCTION

Laser radiation is currently utilized to remove un-wanted cutaneous structures such as hypervascular lesions,rhytides, and hair.13,20,30,39 The unwanted structures areheated by prescribing a particular wavelength which ispreferentially absorbed by the targeted chromophore (e.g.,hemoglobin, water, or melanin), and specifying an appro-priately short laser pulse to limit thermal diffusion fromthe chromophore. These targeted chromophores undergophotothermolysis, in which the energy deposited to the de-sired chromophore results in its thermal destruction.3 De-spite the spatial confinement of heat within the targetedchromophore, light absorption by the overlying epidermalmelanin which takes place over a broad spectral range26 can

Address correspondence to Bahman Anvari, Department of Bioengi-neering, MS 142, Rice University, P.O. Box 1892, Houston, TX 77251.Electronic mail: [email protected]

result in nonspecific heating of the epidermis. Furthermore,the fluence at which the threshold for epidermal damage oc-curs is lower in individuals with greater epidermal melanincontent,5,12 resulting in decreased laser treatment efficacy.

Protecting the epidermis from nonspecific heating canbe accomplished by precooling the skin prior to laserirradiation.9,19,25,37,41 Immediately upon laser exposure,the precooled epidermis ideally would be heated to atemperature below the threshold for thermal injury. Onemethod of selectively cooling the epidermis is to spray ashort (on the order of tens of milliseconds) cryogen spurtonto the skin surface.4 Cryogen spray cooling (CSC) hasproven to protect the epidermis from nonspecific thermalinjury.9,19,24,25,36,37 Although CSC can protect patients withfair to medium pigmentation levels from nonspecific ther-mal injury,19,25,36 heavily pigmented patients such as in-dividuals of Asian and African descent5,12,17 are at an in-creased risk for epidermal injury while undergoing cuta-neous laser therapy due to increased energy absorption bythe higher concentration of melanin within the epidermis.Increasing the amount of heat removal from skin by op-timization of CSC can potentially allow individuals withdarker skin to benefit from cutaneous laser therapy, and al-low for higher incident fluences than those currently usedin patients with lighter skin types.

The first goal of this study was to determine how cryo-gen droplet velocity and diameter influenced heat removal.Motivation to alter the droplet velocity and diameter wasas follows. Because of the low thermal diffusivity of skinand the skin phantom used in this study, a cryogen filmbuild-up on the surface occurs during spraying.1,28,35 Wespeculate that due to the cold droplets (≈–55◦C) imping-ing the residing cryogen film on the surface and the deeperportions of the film warmed by the substrate, a thermal gra-dient exists within the cryogen film. This gradient may alsobe augmented by the low thermal diffusivity of the cryogenfilm.18 Therefore, the cryogen film itself may act as bar-rier to heat transfer between the impinging droplets and thesubstrate.

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0090-6964/04/0800-1131/1 C© 2004 Biomedical Engineering Society

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1132 PIKKULA et al.

Verkruysse et al.40 postulated that droplets possessinggreater momentum penetrate deeper into the cryogen film,and come to closer proximity or even direct contact with thesubstrate. Since droplets have lower temperatures relativeto the film, the reduction in separation distance between thedroplet and the substrate will increase the thermal conduc-tance, and result in enhanced heat removal.

Increasing the droplet penetration into the film (or creat-ing a thinner film) would allow the cold droplets to come incloser proximity or even in direct contact with the substrate,thus enhancing the rate of heat removal by reducing the dis-tance the cold wave must propagate through a low thermallydiffusive cryogen film. The cryogen film composed of theresiding and impinging droplets is hypothesized to impedeheat removal; therefore, it was our aim to modify the dropletproperties, namely, increase droplet velocity or diameter toaugment the droplet penetration depth into the film.

Our second objective was to investigate the effect of thecryogen film height reduction on heat removal by reducingthe cryogen surface tension. We speculated that creatinga thinner film would allow the cryogen droplets to comein closer proximity to the substrate surface, resulting inan increased rate of heat removal by reducing the distanceof heat diffusion between the impinging cold droplets andsubstrate.

Lastly, we sought to determine if increased heat removalwould result in greater protection of the epidermis in re-sponse to laser irradiation of ex vivo human skin samples.Results of this study can be used to optimize the appro-priate range of cryogen droplet velocity and diameter foruse in conjunction with laser treatment of individuals withvarious skin types. In summary, the objective of this workwas to investigate how droplet velocity and diameter, sur-face tension, and cryogen film height influence heat removaland affect thermal damage to human skin epidermis duringlaser irradiation.

THERMOPHYSICAL PARAMETERS AND HEATREMOVAL ESTIMATION

Weber Number

To account for the changes in both the altered dropletvelocity and diameter, we used the Weber number. Studieson the general subject of spray cooling have shown that thedimensionless Weber number (We) influences the instanta-neous heat flux (q ∝ We0.6 when using Freon-113 sprayedon heated metal substrates).15 We is proportional to the ratioof the kinetic energy to the surface energy of the droplets:

We =12ρ

[43π

(dimpact

2

)3]

v2impact

σ

[4π

(dimpact

2

)2] , (1)

where ρ is the liquid density (kg m−3), dimpact the dropletdiameter (m), vimpact the droplet velocity (m s−1), and σ is

the liquid surface tension (N m−1). Eliminating constantsand reducing gives

We = ρdimpactv2impact

σ(2)

Heat Removal Estimation

Inasmuch as thermal boundary conditions such as a time-varying heat flux [q(t)] are difficult to measure directly, in-direct techniques using internal temperature measurementsare often used.32 With these techniques, an inverse heat con-duction problem (IHCP) is solved to estimate the boundarycondition from internal temperature measurements.

We used the sequential function specification (SFS)method6 to solve the IHCP from internal temperature mea-surements at a known depth within the phantom substrate(described in the next section) at discrete times. This methodestimates the surface heat flux as a piecewise function oftime, sequentially solving for q(t) at each time point. Indoing so, the method uses “future” temperature data to es-timate the surface heat flux at the current time point,31 andminimizes the following least squares expression over fu-ture time steps. The sensitivity and accuracy of the IHCP isdescribed fully in a previous article on this technique by ourgroup.38 The total heat removal per unit area, Q (J m−2),the time-integral of q(t) at the substrate surface (z = 0),was determined over the 200-ms cryogen spurt from thesolution of the IHCP for various spraying conditions.

Thermal Conductance

Thermal conductance, ζ (t) (W m−2 K−1), between theimpinging droplet and substrate was calculated as

ζ (t) = q(t)

Ts(t) − Tdroplet, (3)

where Ts is the temperature of the substrate at z = 0 (com-puted by solving the forward heat transfer problem once q(t)was estimated) and Tdroplet is the cryogen droplet temper-ature just prior to impacting the substrate, measured by in-serting a 60-µm bead diameter thermocouple (CHAL-001,OMEGA Engineering, Inc., Stamford, CT) into thecryogen spray. Since calculation of ζ utilizes measuredand estimated temperatures [i.e., Tdroplet and T (z = 0, t),respectively], all thermal resistances between the dropletand substrate (i.e., at cryogen-substrate interface and withinthe cryogen film on the surface) are taken into account.The dynamic thermal conductance was time averaged overthe duration of the cryogen spurt, resulting in an averagevalue, ζ .

Surface Tension

The single capillary rise method is a classical methodof quantification of surface tension.22 To simplify the

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Effects of Specific Cryogenic Properties on Heat Removal 1133

measurement technique,16 the differential capillary risemethod (DCRM) was used in this study, in which two cap-illaries, arranged vertically and with different inner diam-eters, were lowered into a pool of the liquid being tested.With dissimilar diameters, the column of liquid rises higherin the capillary with the smaller inner diameter and theheight difference in the two menisci are measured.

The downward and upward forces, respectively, actingon a column of fluid in a single capillary are

force↓ = [hπr2(ρ ′ − ρ ′′)]gforce↑ = σ [2πr ] cos θ,

(4)

where σ is the surface tension of the liquid Nm−1; g thegravitational constant (9.8 ms−2); ρ′ and ρ ′′ are the liquidand vapor densities of the cryogen (1206 and 5.3 kgm−3,respectively); h1 − h2 is the difference in height of the twomenisci (m); r1 and r2 (m) are the inner radii of each of thecapillaries; and θ is the angle the liquid contacts the innerwall of the capillary. After equating the force balance andsubstituting the differences in the heights and differencesin the area and circumferences of the two capillaries, theDCRM yields the surface tension using simplified methodversus that of the single capillary method.29

σ = g(ρ ′ − ρ ′′)(h1 − h2)

2(1/r1 − 1/r2) cos θ(5)

Images of the capillaries were captured with a CCD cam-era and an attached a zoom-macro lens, described in thenext section, using ambient lighting, and NIH Scion Im-age (www.scioncorp.com) was utilized to measure h1 − h2

and θ .

EXPERIMENTAL METHODS

Cryogen Type and Delivery Systems

The cryogen used in this study was refrigerant R-134a, 1,1,1,2 tetrafluoroethane (National Refrigerants, Inc.,Rosenhayn, NJ), which is a nontoxic, environmentally com-patible, Freon substitute2,23 (boiling point ≈ −26◦C at 1atm) used clinically for epidermal protection and pain re-duction during cutaneous laser therapy. Spurt duration wasset to 200 ms, and controlled by a programmable digitaldelay generator (DG535, Stanford Research Systems, Sun-nyvale, CA).

Droplet velocity and diameter were altered by threemethods. First, immersing the cryogen canister into a warmwater bath led to increased pressure within the canister,causing a more forceful release of the cryogen at a higherejection velocity. The second method was to change thespraying distance between the substrate and cryogen de-livery device. Since droplets evaporate and cool in flight,adjusting the spraying distance also alters droplet impacttemperature. However, droplet velocity and diameter couldbe independently varied from the droplet temperature when

changing the pressure of the cryogen canister. Third, differ-ent cryogen delivery devices were used to produce dropletdiameter and velocity dependent on the design of the device.

Three types of cryogen delivery devices were used. Thefirst device (Device 1) was a standard automobile fuel injec-tor with a 1-mm diameter orifice and an attachment nozzlewith a length of 2 mm and 1.5-mm orifice diameter thatproduced a uniform spray cone with the following spraycharacteristics (±standard deviation) at ambient conditions:average droplet diameter of 26 ± 2.1 µm and Sauter meandiameter of 66 ± 17 µm at a spraying distance of 100 mm.27

The Sauter mean diameter is commonly used to quantifydroplet size during spraying processes and is calculated asthe diameter of a single droplet whose volume to surfacearea ratio is equal to the sum of the volume over the sum ofthe surface area of all droplets in the droplet set:

SMD =∑N

i=1 D3i ni∑N

i=1 D2i ni

, (6)

where D is the median droplet diameter of the given bin,n the number of droplets in that bin, i the bin number, andN is the total number of bins. The second device (Device2) consisted of a fuel injector with a 1.3-mm orifice diam-eter (without an attachment nozzle) producing an averagedroplet diameter of 34.0 ± 3.7 µm and Sauter mean diam-eter of 116.1 ± 16 µm at a spraying distance of 90 mm.27

The third spraying system (Device 3) consisted of the sec-ond device above with a 40-mm long attachment nozzle anda 1.1-mm diameter orifice. This device produced an averagedroplet diameter of 32 ± 4 µm and a Sauter mean diameterof 101 ± 22 µm at a spraying distance of 90 mm.

Droplet Impact Velocity and Diameter

Droplet impact velocity (ν impact) measurements wereconducted by imaging the droplets (at spraying distancesof 40–130 mm or 90 mm for the case when the cryo-gen canister temperature was altered) using a CCD cam-era, a 2× focal length extender (EX2C, Computar CBCAMERICA Corp., Commack, NY), and a macrozoom lens(Zoom 7000, Navitar, Japan) (Fig. 1). Resolution of theimaging system (interpixel distance) was 3.7 µm/pixel, de-termined by dividing the image height (1.9 mm) by thenumber of pixel rows (515). Illumination sources were two10 ns flashlamps (TWINLITE, High-Speed Photo-Systeme,Wedel, Germany), which were coupled with a beam splitterto project along the optical axis of the CCD camera. Thecryogen was sprayed perpendicular to the optical axis be-tween the flashlamp and CCD camera. Triggering the twoflashlamps to spark within predetermined time intervals (1–4 µs with respect to each other) exposed the droplets twiceon the same image. Velocity was subsequently calculated asthe ratio of the droplet travel distance to the delay betweenthe two flashes. The droplet size was determined from the

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FIGURE 1. Schematic of the setup used for droplet velocitymeasurements.

same images by quantifying the diameters in pixels andconverting the values into microns.

Phantom Substrate

A phantom substrate composed of epoxy resin withimbedded microthermocouples was used to record inter-nal temperature profiles in response to CSC (Fig. 2). Thethermal diffusivity (α) of the epoxy substrate, 0.843 ×10−7 m2 s−1 (EP30, Master Bond Inc., Hackensack NJ),was within the range of human skin, 6.9 × 10−8 to 1.1 ×10−7· m2 s−1.14 This phantom type has been used exten-sively in previous studies.27,33,34,40 Type K thermocouples(ChromegaAlomega, Omega Engineering, Inc., Stam-ford, CT) with 30-µm bead diameters, positioned at 20, 90,200, and 400 µm (all ± 5 µm) below the phantom surfacewere used to measure internal temperatures in response toCSC. The measured temperature profiles were subsequentlyused as input data for the inverse model, described in theprevious section, to estimate the heat flux at the substrate-cryogen interface. The entire substrate was warmed to 33◦Cprior to each experiment by applying heated air to thephantom.

Reduction of Cryogen Surface Tension

Surfactants reduce the intermolecular forces within a liq-uid, and when in contact with a surface, cause the spreadingof the liquid under gravity or other external forces. Surfac-tants were added to the cryogen liquid to reduce the cryo-gen film height and increase the droplet Weber number, andsubsequently, investigate the effects on the amount of heat

FIGURE 2. Schematic of experimental setup used to measureinternal temperatures within the phantom substrate.

removal. Three surfactants (Table 1), Brij 30, Tween 20, andpolyethylene glycol (PEG) 300, were chosen for this studybased on their solubility in R-134a, current applications indrug delivery, and low toxicity.7 These three surfactants areamong the highest for solubility in R-134a.7

Several concentrations (w/w) were used for each surfac-tant (Table 1). The upper limit of each surfactant concentra-tion in R-134a was determined by the maximum reportedsolubility.7 If excessive foaming was present after spurt ter-mination, a decreased concentration was used.

Surfactants were added to the pressurized canisters by“cold filling” which consisted of attaching a regulator tothe canister, and placing it in a cooler filled with dryice to reduce the vapor pressure of the cryogen to atmo-spheric levels. After several minutes, temperature of thefluid within the canister was well below the boiling point ofR-134a allowing the removal of the regulator and exposingthe contents to atmospheric pressure without releasing itscontents. Surfactants were subsequently added via a cali-brated pipette to create a surfactant/R-134a mixture in a w/wproportion.

In some experiments, surfactants were spread on the sub-strate surface to reduce the cryogen surface tension. In thesecases, two drops (≈50–60 µl) of surfactant were placed ontoa Kimwipe (Kimberly-Clark, Roswell, GA), and spreadmanually on the substrate to provide an even distribution ofsurfactant on the surface (area ≈16 cm2). When the surfac-tant was spread on the surface, the resulting surface tensionwas not measurable. Whether the surfactant was added tothe cryogen or spread on the substrate surface, a Kimwipewas used to remove any residue from the substrate from theprior spurt.

Normalized Cryogen Film Height

Although the absolute cryogen film height was not mea-sured, we normalized the film height for a certain sprayingcondition compared to those under different spraying condi-tions. The apparent cryogen film height (H ) on the substratewas estimated as

H = m

Aρ, (7)

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TABLE 1. Surfactants used in the study.

Chemical Maximum reported7 solubility in % w/w ProportionsCommon name Chemical name composition R-134a (% w/w proportion) used

Brij 30 Polyoxyethylene(4) C12H25(OCH2CH2)4OH 1.8% 0.3%, 1.8%lauryl ether

Tween 20 Polyoxyethylene(20) C58H114O26 0.1% 0.02%, 0.1%sorbitan monolaurate

PEG 300 Poly(oxy-1,2-ethanediyl), H(CH2CH2O)6OH 4% 0.5%, 1%alpha-hydro-omega-hydroxy

where m (kg) is the cryogen mass output from the orificeof the cryogen delivery device, A (m2) is the area coveredby the cryogen film on the substrate, and ρ (kg m−3) is thecryogen density.

The value of apparent height was normalized to that ofDevice 2, which produced the lowest Weber number at roomtemperature to obtain the normalized cryogen film height,ϕ. Cryogen mass output from the orifice for each of thethree delivery devices under different canister temperatureswas measured for 200 ms spurts. The total mass loss ofthe cryogen from the canister was divided by the numberof 200 ms spurts actuated (approximately 10), resulting inmass output per spurt. The sprayed area on the surface of thesubstrate immediately after spurt termination was measuredby a CCD image under ambient lighting conditions. Thismethodology was based on the assumption that regardlessof the mass output for each of the cryogen delivery devices,an equal fraction of cryogen was evaporated in flight.

Laser Irradiation of ex Vivo Human Skinin Conjunction with CSC

We sought to determine if altering the cryogen dropletand velocity (hence, Weber number) could change theamount of epidermal protection ex vivo in response to laserirradiation. Skin samples were obtained from consenting pa-tients undergoing autograft breast reconstruction using ab-dominal skin. CSC and laser irradiation were subsequentlyperformed on the samples. The study was carried out undera protocol approved by the institutional review boards ofRice University and The University of Texas M. D. Ander-son Cancer Center.

One of each Fitzpatrick skin types V and VI (mediumbrown and dark brown, respectively) at room temperaturewere irradiated using the Candela (Wayland, MA) Vbeampulsed dye laser (595 nm wavelength). The temporal pulseprofile in this laser consists of a macropulse in which atrain of four 100-µs micropulses are placed in equal timeintervals within the macropulse. In our experiments, themacropulse was set to 6 ms; hence, delivering four 100-µsmicropulses. Depending on the size of the excised skin,one or two sites were cooled and irradiated using a com-bination of 10 or 15 J cm−2, and 100- or 200-ms cryogen

spurts immediately preceding the laser pulse. Each cool-ing and irradiation combination utilized either of the twocryogen delivery devices which produced droplets with thegreatest (Device 1) and least (Device 2) Weber numberswith the cryogen canister at room temperature. Followinglaser irradiation, 6-mm punch biopsies were excised andfixed in 10% buffered formalin and hematoxylin & eosinstained for histological analysis of thermal damage. Ther-mally mediated morphological damage was characterizedby a score of 0 (no observable damage), 1 (nuclei shrink-age), 2 (<10% dermal-epidermal separation), 3 (10% to50% dermal-epidermal separation), and 4 (>50% dermal-epidermal separation). The percentage of separation wasquantified by the linear distance ratio of the separated to in-tact tissue at the dermal–epidermal junction for the portionof the histological section exposed to laser irritation.

RESULTS

Cryogen Surface Tension

Published surface tension values for R-134a fromMcLinden et al.21 and Chae et al.8 were extrapolated to−26◦C which resulted in values of 15.5 and 15.4 mNm−1,respectively. Published values concur with the surfacetension measurements of R-134a in this study, 15.5 ±0.3 mNm−1 (Table 2), verifying our method and results. Forthe cases where the surfactant was spread on the substratesurface, cryogen surface tension was not measurable. Themaximum reduction in surface tension, when the surfactantwas added to the cryogen canister was approximately 16%.We nevertheless found no correlation between heat removaland cryogen surface tension (data not shown). Additionally,no correlation was found with ϕ and cryogen surface tension(data not shown).

Droplet impact velocity (ν impact) data for pure R-134aand with a 1% w/w PEG 300/cryogen mixture were 33.9 ±3.5 ms−1 and 35.9 ± 3.7 ms,−1 respectively, at a sprayingdistance of 90 mm. A standard t-test (p < 0.05) showed nostatistical difference between the resulting velocities. How-ever, the standard deviation of ≈10% provides a relativelylarge variation in the spurt to spurt velocities. When analyz-ing the Weber number, discussed in the next section, a 10%

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1136 PIKKULA et al.

TABLE 2. Surface tension of R-134a after addition ofsurfactants.

Concentration of surfactant Surface tensionin R-134a (% w/w) ± SD (mNm−1)

0 (pure R-134a) 15.5 ± 0.30.3 (Brij 30) 13.1 ± 0.91.8 (Brij 30) Not measurable

due to foaming0.02 (Tween 20) 13.7 ± 0.90.1 (Tween 20) 15.2 ± 0.40.5 (PEG 300) 15.6 ± 0.81 (PEG 300) 13 ± 0.6

standard deviation in velocity is sufficient to overshadowthe effects of the reduction in cryogen surface tension.

Weber Number

As the cryogen canister temperature was increased, thecryogen was expelled with a greater velocity, but producedfiner droplets. As the spraying distance was increased, bothdroplet velocity and diameter decreased due to air-induceddrag force and droplet evaporation in flight. By only chang-ing the temperature of the cryogen canister, altering thespraying distance, or using one of the three different cryo-gen delivery devices, we were unable to independently varyvimpact and droplet diameter just prior to impact (dimpact);however, using a combination of the three methods we wereable to independently vary these spray parameters. Rangesof vimpact and dimpact were 12–72 m s−1 and 23–52 µm, re-spectively, for cryogen canister temperatures of 15–50◦Cand spraying distances of 40–130 mm while using the threecryogen delivery devices.

The influence of Weber number on heat removal is shownin Fig. 3. In general, heat removal increased with higher

FIGURE 3. Log–log plot of heat removal, Q, versus Weber num-ber for a 200-ms cryogen spurt.

FIGURE 4. Log–log plot of time-averaged thermal conduc-tance, ζ, versus Weber number for a 200-ms spurt.

Weber number. A similar trend was present between theWeber number and the time averaged thermal conductance(Fig. 4), indicating that there was reduced thermal resistancebetween the impinging droplets and substrate when We wasincreased. The time-averaged thermal conductance for theduration of the cryogen spurt resulted in a coefficient ofvariation of less than 0.08 for the cryogen delivery devices.

Normalized Cryogen Film Height

The scatter plot in Fig. 5 illustrates that increased Webernumber reduced ϕ on the surface of the substrate. Similarly,as ϕ was decreased, heat removal and ζ increased (Fig. 6).Results demonstrated no correlation between actual cryo-gen mass output and heat removal (data not shown) whichis due to the substrate being in a flooded state.

Predicting Heat Removal

Altering the spraying distance, cryogen canister temper-ature, and using three different cryogen delivery devicesprovided 50 different sets of experimental parameters (i.e.,Q for a given combination of �T , dimpact, and ν impact)where �T (in the range of 75–92◦C) is the temperaturedifference between the impinging droplet just prior to im-pact and the initial substrate temperature (33◦C). A nonlin-ear least-squares data fitting algorithm, using the Gauss–Newton method in MatLab (Natick, MA), produced theproportionality

Q ∝ 0.739�T d0.1261impact v0.1601

impact , (8)

where dimpact is the droplet diameter (m), and vimpact isthe cryogen droplet velocity just prior to impact (m s−1).Analysis of dimpact and vimpact indicated that they were in-dependent values (R2 = 0.16). Equation (8) is dependenton the droplet parameters prior to impact regardless of howthe droplets were generated. The sensitivity of Q on dimpact

andν impact is less than 13% for an exponent increase of 10%.

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FIGURE 5. The normalized cryogen film height, ϕ, versus theWeber number of the cryogen spray.

We emphasize that Eq. (8) is valid for the epoxy substrateused in this study with α = 0.843 × 10−7 m2 s−1.

Ex Vivo Epidermal Protection

Protection of epidermis from laser-induced thermal in-jury in Fitzpatrick type V skin (Fig. 7) was increasedwhen using Device 1, which produced the spray with agreater Weber number when using a 100-ms spurt and afluence of 10 Jcm−2. Note the complete dermal–epidermalseparation [Fig. 7(A)] and areas of collagen coagulationin the upper papillary dermis due to heat diffusing fromthe melanosomes in combination with suboptimal cooling.Most of the epidermis was spared when using a device (De-vice 1) producing a greater Weber number (Fig. 7B). Usingequal spurt durations and laser fluences on each treatmentpair, histological damage scores were compared betweenthe two cryogen delivery devices which produced the great-est and least Weber number droplets in this study. Resultsdemonstrated an average increase in epidermal protection

FIGURE 6. Heat removal (black) and average thermal conduc-tance, ζ (grey), for a 200-ms spurt versus the normalized cryo-gen film height, ϕ.

(±standard deviation) of �protect = 1.93 ± 1.77 when us-ing the highest Weber number device (Device 1) as com-pared to the lowest Weber number device (Device 2). Forinstance, a decrease in the thermal damage score of approx-imately 2 would reduce epidermal damage from between10 and 50% dermal–epidermal separation to that of just nu-clei shrinkage. Comparing �protect to a null hypothesis (noincrease in epidermal protection when using a spray withhigher Weber number droplets), �protect was statisticallylarger (p < 0.05). The relatively large standard deviationfrom the mean value of �protect is likely due to biologicalvariation and a digression of up to ±3% from nominal laserfluences. In all cases, the device that produced the highestWeber number provided equal or greater epidermal protec-tion when compared to the device that produced the lowestWeber number droplets.

DISCUSSION

The Weber number is sensitive to the variations in dropletvelocity (especially at higher velocities), and slight changesin velocity could completely mask the effects of reducingthe cryogen surface tension. On the basis of the results ofthis study, increased heat removal was not observed withdecreased cryogen surface tension due to the effects of thevariations in velocity of the cryogen droplets. These vari-ations appear to obscure the expected increase in heat re-moval by the altered cryogen surface tension; nevertheless,we have observed that a thinner film generated by a high We-ber number spray allows for increased heat removal (Fig. 6).Additionally, at high Weber numbers (i.e., We > 10) suchas the values described in this text (We > 800), the changesin kinetic energy dominate the changes in surface energy ofthe droplet. When We → 1, we would expect an equal effectof the two energies, and if We < 1, the surface tension willdominate.

The spray impacts the film and substrate, and its energyis transferred in the radial direction creating a larger sprayedarea; therefore, film diameters increase with greater Webernumbers, resulting in thinner films.11 Our results agree withRef. 11 and indicate that a thinner film is beneficial in in-creasing heat removal (Fig. 6), supporting the theory that thecryogen film acts as an impediment to heat transfer (Fig. 4),where thermal conductance increases with increased Webernumber (i.e., thermal resistance decreases with higher We-ber number values). Possible methods to enhance heat re-moval by CSC would be to decrease the cryogen film height,or equivalently, induce deeper droplet penetration into thefilm, both of which may be occurring using droplets withgreater Weber numbers.

From Eq. (8), the relative contribution of the parametersinfluencing heat removal can be determined. Consideringthe range of dimpact and ν impact and their respective expo-nents, the influence of ν impact on heat removal is approxi-mately six times that of dimpact, which was ascertained by

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1138 PIKKULA et al.

FIGURE 7. H&E histological sections of ex vivo Fitzpatrick type V skin cooled with a 100-ms cryogen spurt immediately prior topulsed laser irradiation with a fluence of 10 J cm−2 for Weber numbers of (A) 1,100 (Q = 26.9 kJ/m2), and (B) 5,100 (Q = 33.2 kJ/m2).Arrows indicate areas of slight nuclei shrinkage and dermal-epidermal separation.

the ratio of the mean values of dimpact to ν impact raised to theirrespective powers in Eq. (8). The parameter �T was by farthe most influential factor in determining heat removal.

Our experiments have shown that sprays with a higherWeber number increase the heat removal from a skin phan-tom. Results using ex vivo human skin samples suggestsprays with a higher Weber number does augment heat re-moval from skin, resulting in a statistically significant in-creased epidermal protection in response to laser irradiation.These results are encouraging in that the ability to increaseheat removal may allow individuals with darker skin typesto benefit from cutaneous laser therapy, and lighter skinned

patients will be able to tolerate greater light dosages, whichin turn, may reduce the number of treatment sessions. Ad-ditionally, transient adverse effects such as hyperpigmen-tation (lasting up to 1 year) in darker skin tones10 by laserirradiation are expected to be minimized or eliminated withincreased heat removal due to a further reduction in tem-perature at the basal layer.

CONCLUSION

Results of this study indicate the cryogen film acts as animpediment to heat transfer between the impinging droplets

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and the substrate. The cryogen droplet Weber number isa vital spray parameter that influences heat removal. Exvivo epidermal protection by CSC is augmented by utilizingdroplets with higher Weber numbers.

ACKNOWLEDGMENTS

This study was supported in part by the Instituteof Arthritis, Musculoskeletal, and Skin Disease (1R01-AR47996) at NIH; Texas Higher Education CoordinatingBoard, Candela Corporation to B.A.; and a Student Re-search Grant from the American Society for Lasers inMedicine and Surgery to B.M.P.

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