RESEARCH ARTICLE

Spectroscopic properties of a perfluorinated ketone for PLIFapplications

Arnab Roy • Jonas P. R. Gustavsson •

Corin Segal

Received: 21 September 2010 / Revised: 27 June 2011 / Accepted: 1 July 2011 / Published online: 19 July 2011

� Springer-Verlag 2011

Abstract This work identifies the fluorescence charac-

teristics of a perfluorinated ketone, 2-trifluoromethyl-

1,1,1,2,4,4,5,5,5-nonafluoro-3-pentanone, further referred

to as fluoroketone. This compound is suitable for use with

the third harmonic of an Nd:YAG laser for quantitative

concentration measurements, as it exhibits strong emission

even for relatively low excitation and has a near-linear

response of fluorescence intensity with concentration. This

makes it suitable for a broad range of fluorescence appli-

cations. The absorption cross-section of 3.81 9 10-19 cm2

was found to be constant for a temperature range of

293–441 K and a pressure range of 1–18 atm. A calibration

line has been generated that relates the concentration of

gaseous and liquid fluoroketone with its absorption

coefficient.

List of symbols

P Pressure (atm)

T Temperature (K)

Pcr Critical pressure (atm)

Tcr Critical temperature (K)

Tr Reduced temperature

Pr Reduced pressure

q Density (kg/m3)

I Intensity of the laser sheet (J/m2)

k Wavelength of laser (nm)

r Absorption cross-section (cm2)

rg Absorption cross-section for the ground state (cm2)

re Absorption cross-section for the excited state (cm2)

Ng Number of molecules in the ground state

Ne Number of molecules in the excited state

N Total number of molecules

dV Collection volume

dl Differential length along the laser propagation

direction

A Area perpendicular to laser propagation direction

NA Avogadro’s number

M Molecular weight

R Universal gas constant

Nph Number of incident photons

Nfl Number of emitted photons due to fluorescence

h Planck’s constant

c Speed of light (m/s)

u Quantum yield of fluorescence

a Absorption coefficient

goptic Collection optics efficiency

S Fluoroketone vapor fluorescence signal

F, K Constants in the fluorescence equation

1 Introduction

The perfluorinated ketone discussed in the present paper is

technically referred to as 2-trifluoromethyl-1,1,1,2,4,4,5,5,5-

nonafluoro-3-pentanone, also known as FK-5-1-12 (Owens

2003). The molecular structure is shown in Fig. 1. This flu-

oroketone has several interesting features that make it a useful

compound for research (Gustavsson and Segal 2007), of

which a few are highlighted below as follows:

A. Roy (&) � C. Segal

Combustion and Propulsion Laboratory,

Department of Mechanical and Aerospace Engineering,

University of Florida, Gainesville, FL 32611, USA

e-mail: arnab1985@ufl.edu

J. P. R. Gustavsson

Florida Center for Advanced Aero-Propulsion,

2525 Pottsdamer St, Room A229, Tallahassee, FL 32310, USA

e-mail: scramjet@hotmail.com

123

Exp Fluids (2011) 51:1455–1463

DOI 10.1007/s00348-011-1163-6

• High vapor pressure at ambient temperature—making

the fluoroketone a good model for studies of the

breakup and mixing of volatile fuels and enabling high

seeding densities.

• Low critical pressure and temperature—facilitating the

study of trans- and supercritical phenomena.

• Strong fluorescence with broadband excitation—mak-

ing flow tracing using common high-power lasers, such

as the third- and fourth-order harmonics of a Nd:YAG

laser, possible.

• Inert—compatible with most common construction

materials and does not exhibit thermal decomposition

below 500�C in air (Owens 2003).

• Non-flammable—safe for use in large quantities.

• Low toxicity and environmentally acceptable.

For experiments at high temperatures and pressures,

e.g., the study of supercritical mixing (Roy and Segal

2010), the fluoroketone offers a safer alternative to acetone.

An additional benefit of having an additional tracer species

makes it easier to match the absorption cross-section to the

length scale and tracer density; it also ensures acceptable

beam attenuation and fluorescence signal strength.

The purpose of this study is to provide detailed infor-

mation about the absorption coefficients of the gas and

liquid phases of fluoroketone for PLIF applications. The

criteria that have been mentioned by Karasso and Mungal

(1997) in their work with other tracers have been verified

for fluoroketone and have been found to be satisfactory for

quantitative PLIF measurements with certain modifica-

tions. Finally, a calibration line has been obtained that

relates the absorption coefficients to the vapor densities for

a wide range of temperatures and pressures.

2 Photophysics of fluoroketone and PLIF

implementation

Fluorescence is a radiative decay process of atoms or

molecules that have been excited to a higher-energy state,

generally by photons of a shorter wavelength. Fluoroke-

tone, at room temperature and atmospheric pressure, has a

broadband excitation from 260 to 355 nm. Fluorescence is

emitted from 350 to 550 nm.

A differential volume dV is considered, equal to the

differential length dl traversed by the laser, times the area A

perpendicular to the direction of laser propagation. The

number of electrons in the ground state be Ng and excited

state be Ne, with absorption cross-sections of rg and re,

respectively. If the number of photons incident on one face

of this volume be Nph, then the number of electrons excited

from the ground state can be calculated as:

DNe ¼Nph

ANgrg ð1Þ

Similarly, the number of electrons removed from the

excited state due to stimulated emission is:

�DNe ¼Nph

ANere ð2Þ

Laser-independent loss processes during the excitation like

spontaneous emission, intersystem crossing, internal

conversion, and collisional quenching have not been taken

into consideration since we assume that the pulse duration of

the laser is short compared with these processes. Hence, laser

fluency through the area A can be calculated as:

dNe

dt¼ dNph

dtNgrg � Nere

� �:1

A¼

N0ph

ANgrg � Nere

� �ð3Þ

The total number of electrons N = Ng ? Ne is assumed to

remain constant, i.e., photo dissociation effects have been

neglected. Thus, rearranging the above equation yields:

dNe

dt¼

N 0ph

ANrg � Ne re þ rg

� �� �ð4Þ

During steady state, i.e., at saturation, the above equation is

equated to zero, yielding:

Nrg ¼ Ne;sat re þ rg

� �or Ne;sat ¼ N

rg

re þ rg

� �ð5Þ

When Eq. (4) is solved with the initial condition Ne(0) = 0,

the solution is:

Ne ¼ Nrg

re þ rg

� �1� e�

N0ph

reþrgð ÞtA

� ð6Þ

If expressed in terms of total number of photons delivered

in one pulse, the above equation can be represented as:

Ne ¼ Nrg

re þ rg

� �1� e�

Nph reþrgð ÞA

� ð7Þ

The function obtained in Eq. (7) has been plotted in Fig. 2.

To establish a region where the curve can be approximated

as being linear, a straight line is drawn tangentially to the

curve through the origin until it intersects the saturation

line, and a point Nphs is found as shown in the figure. Hence,

for the linear regime, Nph � Nphs . Thus, Eq. (7) can then be

approximated as:

Ne ¼ Nrg

re þ rg

� �1� 1þ

Nph re þ rg

� �

A

� ¼ NrgNph

A

ð8Þ

Fig. 1 The molecular structure of the fluoroketone 2-trifluoromethyl-

1,1,1,2,4,4,5,5,5-nonafluoro-3-pentanone investigated in this paper

1456 Exp Fluids (2011) 51:1455–1463

123

If this is expressed in terms of number density of electrons

(n), we arrive at the form of the equation used by Hanson

et al. (1996):

Ne ¼ nrgNphdl ð9Þ

In all our experiments, the excitation was in the non-linear

regime, and hence, Eq. (7) was used instead of (9). Thus,

using this model for excitation, the equation for

fluorescence can be written as:

Nfl ¼ Nrg

re þ rg

� �1� e�

Nph reþrgð ÞA

� u ð10Þ

Here, u is the fluorescence yield. According to some works

(Thurber et al. 1996; Koch and Hanson 2003; Frackowiak

et al. 2008), u is taken to be a function of the laser

wavelength, pressure, and temperature of the substance.

Other works (Melton and Lipp 2003) have stated that u is a

function of the laser intensity I. In this work, u has been

taken to be a function of all the above-mentioned

parameters, i.e., u = f(P, T, I, k). The number of

incident photons, Nph, can be written as follows:

Nph ¼I

ðhc=kÞA ð11Þ

Here I is the laser intensity, and (hc/k) is the energy of an

incident photon at the laser wavelength k. It shall also be

assumed in this work that rg ? re & rg or simply r. The

transmission efficiency of the collection optics and the

collection angle also have to be taken into account. If goptic

is the collection optic efficiency and (X/4p) is the fractional

solid angle for collection, the total number of photons

collected due to fluorescence can be written as:

Nfl;coll ¼ goptic

X4p

� �N 1� e�I k

hcð Þrh i

u ð12Þ

The collection optics efficiency, fractional solid angle,

photon to signal count conversion factor, and other

constants are grouped into a factor F. If the x-direction is

taken as the direction of propagation of the laser and the

y-direction is the direction perpendicular to the x axis and

in the plane of the laser sheet, then I = f(x, y). The total

number of the absorbing molecules N is proportional to the

density of the vapor fluoroketone q(x, y). Then, the

equation for fluorescence signal recorded on a pixel for a

specific laser excitation wavelength can be written as:

S px; py

� �¼ Fq x; yð Þu 1� e�I k

hcð Þrh i

ð13Þ

Equation (10) has a different form than that adopted by

others (Karasso and Mungal 1997; Muhlfriedel and

Baumann 2000) due to its non-linearity. In the current

work, the density (q) of the fluoroketone vapor is changed

by changing the temperature and pressure of the chamber.

Moreover, if the absorbing species is uniformly distributed

throughout the chamber, then the q is not a function of the

position (x, y). The decrease in the intensity of the laser

sheet along its line of propagation also needs to be

considered (Crimaldi 2008). For conditions where

scattering can be neglected, the drop in laser intensity

due to absorption should follow the Beer–Lambert’s law,

which can be expressed as:

I x; yð Þ ¼ I 0; yð Þe�R x

0rndx ð14Þ

The limits of the integral for our experiment have been taken

to be from the window (x = 0) to any position x along the line

of propagation of the laser. For the experiments described

below, since the concentration of fluoroketone vapor is

uniform inside the chamber, n is not a function of the position

x. Hence, Eq. (14) can be simplified as:

I x; yð Þ ¼ I 0; yð Þe�rnx ð15Þ

Thus, by plugging this expression of I(x, y) into Eq. (10),

the following relation is obtained:

S px; py

� �¼ Fqu 1� e�I 0;yð Þ k

hcð Þre�rnxh i

ð16Þ

In this case, for a single phase, the absorption cross-section

has been assumed to be a constant. This has also been

verified through our tests. Thus, Eq. (16) can be simplified

as:

S px; py

� �¼ Fqu 1� e�ke�rnx� �

ð17Þ

Here, all the constants in the exponent term have been

grouped under a single constant k. Obtaining concentration

values from the fluorescence signal by PLIF measurements

requires an accurate determination of u. In the current

work, focus has been given to the study of u under varying

Fig. 2 Variation of the number of excited electrons with the number

of exciting photons

Exp Fluids (2011) 51:1455–1463 1457

123

fluoroketone vapor concentrations. The value of u can be

affected by processes such as quenching, which is a non-

radiative relaxation process resulting from the collision

between the fluoroketone and a second species such as

oxygen. Thus, any air present inside the chamber may lead

to quenching effects. Phosphorescence is another radiative

relaxation process with characteristic times much longer

than fluorescence. It has been reported (Thurber and Hanson

1999) that the influence of quenching on phosphorescence

in acetone is more significant than on fluorescence. A sim-

ilar phenomenon is assumed for fluoroketone. Photolysis

has also been neglected in this analysis. In most non-

reacting environments, where the concentration of vapor is

essentially uniform inside the chamber and laser excitation

is within certain limits, it may be expected that u is a

constant. This has been validated in the current work

through various calibration tests. The calibration procedure

involves obtaining the fluorescence signal for various flu-

oroketone vapor densities and laser intensities. In the

absence of saturation, if both u and r are constants, the

fluorescence signal should be linear with the vapor density

(for fixed laser intensity). It is only then that the image

processing for density calculations is reliable.

3 Experimental setup

The experimental setup is shown in Fig. 3. The schematic

is shown in Fig. 3a, and a picture of the setup is shown in

Fig. 3b.

The details of the setup were given previously (Segal

and Polikhov 2008; Roy and Segal 2009), and hence, only

a brief description is included here. The high-pressure

chamber is constructed to withstand pressures up to

100 atm and temperatures up to 600 K. For optical access,

there are three windows in the chamber that provide a field

of view of 22 mm wide and 86 mm long. All experiments

were carried out using a round liquid injector with a

diameter of 2.0 mm. The flow is laminar before entering

the injector, and turbulence is not expected to develop

while the fluid passes through the relatively short,

15.4 mm, injector tip. The third harmonic of Nd:YAG laser

was used to excite the fluorescence. Earlier tests have

shown that emission spectrum of FK-5-1-12 within

400–500 nm does not reveal significant dependence on

pressure and temperature (Gustavsson and Segal 2007).

Based on emission spectra, an optical filter with 420 nm

centerline and 10 nm FWHM width was kept before the

Princeton Instruments Intensified CCD camera lens to

eliminate any elastic scattering. The ICCD Camera has a

resolution of 512 9 512 pixels and an acquisition rate of

10 Hz synchronized with the laser. The gate width of

150 ns was chosen to capture the entire duration of fluo-

rescence while reducing the background light significantly.

A thin laser sheet of 0.1 mm thickness and 25 mm width

was focused on the injector centerline.

4 Results and discussion

4.1 Laser sheet absorption through the gas phase

To study the laser absorption through the fluoroketone gas

phase, the chamber was partly filled with fluoroketone;

after a while, the vapor and liquid phases reach equilib-

rium. The vapor concentration inside the chamber was

controlled by adjusting the chamber wall temperature. To

obtain higher values of vapor concentration, the chamber

walls were heated to the saturated vapor temperature,

which in turn heated the liquid phase, producing more

vapor. This also increased the pressure inside the chamber

since the volume is constant.

The laser sheet was then passed through the nearly

uniform vapor phase to obtain the intensity profile of the

sheet and also to observe how the intensity of the fluo-

rescence changes as the laser passes through the chamber.

Figure 4 shows the laser sheet profiles taken at four

Fig. 3 Test chamber schematic

(a) and its overall view (b). The

liquid and gas injection ports

have also been shown. The

25 mm square chamber with

228 mm length can be heated

and pressurized to 600 K and

100 atm, respectively

1458 Exp Fluids (2011) 51:1455–1463

123

different temperatures and pressures, averaged for a total of

50 images. The laser enters the chamber at column 1 and

leaves at column 512.

Figure 4a shows the profile at 2.7 atm chamber pressure

and 85�C chamber temperature. The vapor density in this

case is 0.032 g/cm3. The figure shows that the laser profiles

at the four different column positions are very similar to each

other. There are some variations in intensity, but the overall

effect is not as significant as the other cases to follow.

Figure 4b shows the profile at 5.9 atm chamber pressure

and 110�C chamber temperature, at a vapor density of

0.074 g/cm3. This plot shows a greater variation of the

laser profile shape and intensity, implying that the

absorption has increased.

Figure 4c shows the profile at 10.4 atm chamber pres-

sure and 150�C chamber pressure, when the vapor density

is 0.l3 g/cm3. This plot is significantly different from the

previous two and shows clear signs of laser intensity drop

and profile shape change. A large decrease in intensity and

a major change in profile shape are observed. The profile

variations reduce considerably, and it becomes more

uniform.

Figure 4d shows the profile at 14.7 atm chamber pres-

sure and 165�C. The vapor density is the highest in this

case and is equal to 0.207 g/cm3. The temperature is nearly

critical with respect to the critical temperature of 168�C,

but the pressure is still subcritical compared with the crit-

ical pressure of 18.4 atm. The laser intensity drops to 30%

of the 100th column at column 200 and is reduced to

approximately 10% at the 300th column.

To understand the effects of absorption on fluorescence,

it is therefore necessary to isolate each parameter and study

them separately. In the following sections, the dependence

of fluorescence on vapor density and laser intensity has

been investigated, and a relation between absorption

coefficient and vapor density has been obtained.

4.1.1 Fluorescence intensity dependence on vapor density

To understand how the fluorescence signal depends on the

vapor density, the camera was zoomed to a region very

close to the window where the laser sheet entered the

chamber. This region was chosen so that the laser sheet

would not be attenuated by absorption. The results are

shown in Fig. 5. The plot shows a weak second-order

dependence of the fluorescence signal with the vapor

density. For low values of vapor density, the curve closely

approximates a straight line, while for higher values,

approaching the critical point, non-linearities start to

become important (Tran et al. 2008).

From Eq. (16), it can be seen that for fixed values of

incident laser intensity I(0, y), optics efficiency F and

absorption cross-section r, the fluorescence signal S is

proportional to the density if the quantum yield u is a

constant. Thus, at x = 0, i.e., at the window through which

the laser sheet enters, Eq. (16) reduces to:

Fig. 4 Intensity variations of

the laser sheet profile as it

passes through the chamber.

The laser enters the chamber at

column 1, and exits the chamber

at column 500. It can be

observed that the variations are

significant as the concentration

of vapor increases. The pressure

and temperature conditions for

the cases are a 2.7 atm, 85�C,

b 5.9 atm, 110�C, c 10.4 atm,

150�C and d 14.7 atm, 165�C

Exp Fluids (2011) 51:1455–1463 1459

123

S px; py

� �¼ Fqu 1� e�k

� �or S px; py

� �¼ Kq ð18Þ

Here, all the constants have been grouped under K. From

the plot, it is seen that u is a constant for vapor density

values to about 0.15 g/cm3, but starts to vary when the

densities are higher. Since the vapor density in the current

experiments was changed by heating the chamber walls, it

can be stated that, closer to the critical point of fluoroke-

tone, u deviates only slightly from a constant.

4.1.2 Fluorescence intensity dependence with laser power

To obtain the fluorescence intensity dependence on laser

power, the density of the fluoroketone vapor inside the

chamber was kept fixed and the incident laser intensity

I(0, y) was varied. An exponential dependence of the signal

with laser power is observed as shown in Fig. 6. As men-

tioned earlier, the fluorescence is clearly not in the linear

regime.

For fixed values of density q, constant optics efficiency

F and absorption cross-section r, the fluorescence signal S

is dependent on the incident laser intensity I(0, y) as shown

in Eq. (18) below if the quantum yield u is a constant.

S px; py

� �¼ a 1� e�bI 0;yð Þh i

ð19Þ

All constants have been grouped under a and b. Referring

back to the plot in Fig. 6, the data points and the curve

fitted to these points according to Eq. (19) show close

agreement. It can hence be concluded that the value of u is

constant over the range of laser power used for the current

experiments.

4.1.3 Calibration of absorption coefficient

To closely examine how the variation of laser intensity

occurs across the length and width of the chamber, a

sample image is chosen and analyzed. Figure 7 shows plots

of the laser sheet fluorescence intensity at a chamber

pressure of 14.7 atm and a chamber temperature of 165�C.

The actual intensity plots have been shown on the left, and

the normalized intensity plots have been shown on the

right. All images have a resolution of 512 9 512 pixels.

The plot on the top left corner shows the variation of

fluorescence intensity from top to bottom for all the col-

umns of the image, i.e., 512. Similarly, the plot on the

bottom left corner shows the variation of fluorescence

intensity from left to right for all the rows of the image, i.e.,

512. The normalized images were obtained by dividing the

pixel intensity of a specific column or row by the maximum

intensity for that column or row, respectively, and then

taking their mean.

From the normalized laser fluorescence intensity varia-

tion from left to right, it can be seen that there is a decrease

from 1 to about 0.05 within 300 pixels of laser propagation

distance. Since the chamber is filled with uniform density

vapor, this variation can be solely attributed to the actual

laser intensity drop. Hence, it can be inferred that the laser

intensity variation across the chamber cannot be neglected

as it was for the experiments with binary species, e.g., a

fluoroketone jet injected into inert nitrogen gas done in the

same facility (Roy and Segal 2010). This calls for a rig-

orous treatment to deal with such variations in fluorescence

intensity for a specified chamber temperature and pressure,

as described in the following sections.

It has been shown in previous two sections that the value

of u is essentially a constant, and thus, Eq. (17) is valid. It

can then be stated that:

S px; py

� �¼ Aq 1� e�ke�rnx� �

ð20Þ

where the new constant A = Fu. Hence, it is seen that for a

specific row of the image, and hence, for a specific value of

Fig. 5 Fluorescence signal versus fluoroketone vapor density. For

low values of vapor density, the curve closely approximates a straightline, while for higher values, especially near the critical point, non-

linearities start to become important

Fig. 6 Fluorescence signal versus laser power. A non-linear depen-

dence of the signal with laser power is observed in the operating range

used for the current experiments

1460 Exp Fluids (2011) 51:1455–1463

123

I(0, y), the fluorescence signal also undergoes an expo-

nential drop in intensity along the line of propagation of the

laser sheet. This has been verified through the obtained

experimental data.

From the normalized laser intensity diagram (from left to

right), we select a portion of the plot where a uniform

decrease in fluorescence intensity is noted. A curve is then

fitted to the data points according to Eq. (20) as shown in

Fig. 8. The exponential coefficient in the equation of the

fitted curve is essentially the absorption coefficient. This

value of the absorption coefficient is valid for the specified

concentration of vapor at a particular chamber pressure and

temperature, i.e., 14.7 atm and 165�C. The higher the pres-

sures and temperatures are, the greater is the concentration of

vapor and thus the value of the absorption coefficient.

Absorption coefficients for various vapor concentrations

were obtained by the above-mentioned process, and a

calibration curve was obtained as shown in Fig. 9. Cali-

bration line for the absorption coefficient plotted against

density. It can be seen that the calibration curve is a straight

line, indicating that the slope is a constant throughout the

vapor phase. Now, the absorption coefficient and cross-

section are related as:

a ¼ r� n ¼ r� NA

M

� � q

It is seen that the slope of the calibration curve is pro-

portional to the absorption cross-section r. This validates

the assumption, which was made earlier in the analysis,

that the absorption cross-section is also constant throughout

the vapor phase.

Using this data and the molecular weight of fluoroketone

(316 g mol-1), the value of the absorption cross-section in

the vapor phase was calculated to be 3.81 9 10-19 cm2

mol-1. The fluorescence yield was thus found to be con-

stant up to vapor densities of 0.25 g/cm3.

Fig. 7 Detailed analysis of

laser fluorescence intensity at

14.7 atm, 165�C. Actual

intensities have been plotted on

the left and the normalized

intensities have been plotted on

the right. All plots show

significant variation in laser

fluorescence intensity across the

chamber

Fig. 8 Normalized intensity points versus the length traversed by the

laser sheet in pixels. When an exponential trendline is fitted to the

plot, the absorption coefficient is obtained as given by the Beer–

Lambert’s law

Exp Fluids (2011) 51:1455–1463 1461

123

4.2 Laser sheet absorption through the liquid phase

The value of the absorption coefficient changes signifi-

cantly when the laser sheet passes through fluoroketone in

the liquid phase. The tests for investigating the absorption

coefficient in the liquid phase were performed by passing

the laser sheet through a cuvette filled with liquid flu-

oroketone at room temperature (293 K) and atmospheric

pressure (1 atm). The density of the liquid can be taken to

be constant at 1.64 g/cm3, and hence, any variation of

fluorescence intensity can again be attributed to the actual

variation of laser sheet intensity.

The decrease in fluorescence intensity inside the cuvette

can be accounted for in a way similar to the gas phase by

trying to obtain the value of the absorption coefficient. As

was done before, a plot of normalized fluorescence inten-

sity versus the distance traversed by the laser was obtained.

A region where the decrease in intensity was uniform was

selected. These data points were then fitted using an

exponential fit as shown in Fig. 10. Similar to the gas

phase, the exponential coefficient in the equation of the

fitted curve is essentially the absorption coefficient. It is

again noteworthy to mention that this absorption coeffi-

cient is only valid for the liquid of uniform density at

293 K.

Since it has been verified that the absorption cross-sec-

tion for the vapor phase of fluoroketone is a constant, it is

safe to assume that it would also be a constant for the liquid

phase (but different from the vapor phase). Hence, only

two points are required to complete the calibration line.

One point is obtained through the above-mentioned plot,

and another one would be the origin (as the absorption

coefficient should be zero if the density is zero), and the

slope of this line would again be proportional to the

absorption cross-section. The value of the cross-section

was found to be 1.47 9 10-20 cm2.

Thus, a complete analysis of the absorption cross-sec-

tions and coefficients of the vapor and liquid phases of

fluoroketone has been performed. These values can be used

for any experiments involving this specific fluid under

similar experimental conditions.

5 Conclusions

A study of the optical properties of a perfluorinated ketone

was undertaken at subcritical conditions and near critical

conditions. A theoretical analysis of fluorescence in the

non-linear regime of excitation energy was developed. The

criteria that need to be satisfied to use this ketone as a

means for studying quantitative PLIF applications were

verified. These include the linear variation of fluorescence

intensity with concentration for fixed laser intensity, and

the exponential variation of fluorescence intensity with

laser intensity for a fixed concentration. Both these criteria

were found to be true for the vapor phase of fluoroketone

from densities ranging from 20 to 200 kg/m3 and laser

intensities varying from 20 to 140 mJ/pulse. This was done

to justify that the quantum fluorescence yield is a constant

within the range of laser intensity and concentrations that

were used for our experiments. A calibration curve was

obtained for the vapor phase of fluoroketone from densities

ranging from 0.03 to 0.24 g/cm3. This curve was a straight

line, verifying that the slope of the line, which is essentially

the absorption cross-section, is a constant as assumed in the

beginning. A similar technique was also applied to the

liquid phase of fluoroketone. The absorption cross-section

of the vapor phase was found to be 3.81 9 10-19 cm2 and

that of the liquid phase was found to be 1.47 9 10-20 cm2.

Fig. 9 Calibration line for the absorption coefficient plotted against

densityFig. 10 Plot showing the normalized intensity points versus the

length traversed by the laser sheet through the cuvette in pixels. When

an exponential trendline is fitted to the plot, the absorption coefficient

is obtained as given by the Beer–Lambert’s law

1462 Exp Fluids (2011) 51:1455–1463

123

These values of absorption coefficients and cross-sections

can thus be used for any experiments involving this fluid

under similar experimental conditions.

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