# Photothermal Imaging of Transient and Steady State Convection Dynamics in Primary Alkanes

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Alkane Series and Power Study Protocol

#### 2.2. Pulse Study Protocol

#### 2.3. Excitation and Probe Lasers

#### 2.4. Camera

#### 2.5. Acquisition and Analysis Software

#### 2.6. Primary Alkane Samples

## 3. Results

#### 3.1. Concrete Example of Video Data: Hexane

#### 3.2. Alkane Series

#### Pulse Duration

#### 3.3. Power Study

#### 3.4. Video Data

## 4. Discussion

#### Conjecture about the Physical Processes

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the experimental setup. The excitation beam is from a QSL103A-1030 nm Q-Switched Picosecond Microchip Laser System (Thorlabs). The probe laser is from a 5V 650 nm laser diode (HiLetgo). The shutter is driven by a solenoid controlled by the computer. The camera is a DCC1240M High-Sensitivity CMOS Camera, 1280 × 1024 pixel array sensor (Thorlabs). The camera is controlled by the computer.

**Figure 2.**Still frames from the raw (

**left**), background subtracted (

**middle**) and transient isolated (

**right**) data files for one particular run of neat n-hexane at full excitation power. Each of the three frames is at precisely the same time (approximately 3.4 s into the run or 1.4 s after the laser first enters the sample). At this time in the run, the laser is on and towards the bottom of the frame (best seen in the left and middle images). The transient wavefront (top of thermal plume head) has progressed about 3/4 of the way up the frame. Note that the middle image clearly shows both the transient and stationary responses, while the rightmost image isolates only the transient response.

**Figure 3.**Still frames from the transient isolated data files for one particular run of neat n-hexane at full excitation power. From left to right, the three frames show the progression of the transient signal with wavefront tracking. The yellow curve represents a second-order polynomial best fit to the wavefront; the cyan curve is similar except for the trailing edge of the transient signal. The red is the center of mass motion of the transient signal.

**Figure 4.**Aggregate wavefront position values from the 10 runs of n-pentane (blue), n-nonane (green), and n-tetradecane (red). The remaining alkanes are not shown for visual clarity. Very slightly for n-nonane and more pronounced for n-tetradecane, one sees an initial downward curvature. This is followed by a parabolic curvature showing upward acceleration. It is very slight for n-tetradecane. These aggregate data along with the remaining alkanes, were fit to produce the results listed in Table 1 and Figure 5.

**Figure 5.**Acceleration values, ${a}_{\mathrm{WF}}$, for the primary alkanes (except for n-pentadecane) plotted as a function of alkane (

**left panel**), viscosity (

**middle panel**) Prandtl number (

**right pannel**). The measured acceleration is roughly linear with number of carbons, N, in the alkane (fit function: ${a}_{\mathrm{WF}}=-0.015N+0.21$). The 95% confidence intervals on the fit parameters are ($-0.017$, $-0.012$) and (0.18, 0.24), respectively. It is nearly of the form $\frac{1}{x}$ as a function of viscosity, $\eta $, (fit funtion: ${a}_{\mathrm{WF}}=\frac{0.036}{\eta}$). The 95% confidence interval on the fit parameter is (0.033, 0.039) In addition, because the Prandtl number is nearly linear with viscosity, it, too, is nearly of the form $\frac{1}{x}$ (fit function: ${a}_{\mathrm{WF}}=\frac{0.71}{\mathrm{Pr}}$), confidence interval (0.67, 0.76)) The error bars represent the 95% confidence interval for the fit parameters.

**Figure 6.**Initial averaged (10 runs) signal strength for various pulse durations for n-pentane (•), n-hexane (⧫), and n-heptane (■). The signals are all normalized such that n-pentane with a 2.0 s pulse is unity. Error bars represent plus and minus the standard deviation of the signal strength over the 10 run averaging. The signal is a combination of the transient and steady-state features. To within error, the signal is roughly constant.

**Figure 7.**Process of row binning to create the row marginal spectra shown in Figure 8. Each point on the spectra is the average value for the full row in the video frame. There are 1024 rows that are converted to a 1024-point spectrum to create the row marginal.

**Figure 8.**Row marginals for times when the transient and steady-state features are well distinguished. Position refers to the position on the camera with pixels converted to centimeters (0.000354 cm/pixel). The laser power, ${P}_{L}$, for the top row from left to right is 0.59 W, 0.43 W, and 0.30 W. The power for the bottom row, left to right, is 0.21 W and 0.14 W. Per the specification sheet of the Thorlabs S140C powerhead, the uncertainty in the power is approximately 7%. The bottom rightmost graph is the linear best fit to the ratio of the transient component to the stationary state component. The ratio, r, is calculated as the area under the transient part of the marginal (right side of graph) over the area under the stationary part of the marginal (left side of graph). The best-fit line is $r=4.2{P}_{L}+0.6$. The 95% confidence intervals on the fit parameters are (3.1, 5.3) and (0.2, 1.0), respectively.

**Figure 9.**Acceleration of the transient feature for n-pentane as a function of incident laser power. (

**Left panel**): The acceleration is linearly proportional to the incident laser power. Fit parameters: $y=0.27x-0.008$. The 95% confidence intervals on the fit parameters are (0.21, 0.31) and ($-0.03$, 0.01), respectively. The error bars represent the 95% confidence interval for the ${a}_{\mathrm{WF}}$ fit parameter. (

**Right panel**): Representative aggregate wavefront position data from which the ${a}_{\mathrm{WF}}$ in the left panel are calculated. Blue, 0.59 W; green, 0.30 W; red, 0.14 W. Per the specification sheet of the Thorlabs S140C powerhead, the uncertainty in the power is approximately 7%.

**Table 1.**Physical properties and wavefront dynamical information of the alkanes used in this work. The abbreviations are defined as follows: MW (g/mol): molecular weight, $\rho $ (g/cm${}^{3}$): density, $\eta $ (cP): dynamic viscosity, Pr: Prandtl number, n: refractive index, MP/BP (°C): melting point/boiling point, and ${a}_{\mathrm{WF}}$ (cm/s${}^{2}$): wavefront acceleration. Values for the physical properties were obtained from Wolfram Alpha [42] via ChatGPT 4.0 [43].

Name | Formula | MW | $\mathit{\rho}$ | $\mathit{\eta}$ | Pr | n | MP/BP | ${\mathit{a}}_{\mathbf{WF}}$ |
---|---|---|---|---|---|---|---|---|

n-Pentane | C${}_{5}$H${}_{12}$ | 72.15 | 0.626 | 0.224 | 4.6 | 1.358 | −130/36 | 0.148 |

n-Hexane | C${}_{6}$H${}_{14}$ | 86.18 | 0.659 | 0.300 | 5.732 | 1.375 | −95/69 | 0.129 |

n-Heptane | C${}_{7}$H${}_{16}$ | 100.2 | 0.684 | 0.387 | 7.39 | 1.387 | −91/98 | 0.091 |

n-Octane | C${}_{8}$H${}_{18}$ | 114.23 | 0.703 | 0.508 | 9.5 | 1.398 | −57/126 | 0.084 |

n-Nonane | C${}_{9}$H${}_{20}$ | 128.26 | 0.718 | 0.665 | 11.9 | 1.405 | −53/151 | 0.058 |

n-Decane | C${}_{10}$H${}_{22}$ | 142.29 | 0.73 | 0.838 | 15.2 | 1.411 | −30/174 | 0.058 |

n-Undecane | C${}_{11}$H${}_{24}$ | 156.31 | 0.74 | 1.098 | 19.3 | 1.417 | −26/196 | 0.037 |

n-Dodecane | C${}_{12}$H${}_{26}$ | 170.34 | 0.75 | 1.383 | 23.9 | 1.421 | −9.6/216 | 0.026 |

n-Tridecane | C${}_{13}$H${}_{28}$ | 184.37 | 0.756 | 1.724 | – | 1.425 | −5/234 | 0.023 |

n-Tetradecane | C${}_{14}$H${}_{30}$ | 198.39 | 0.762 | 2.128 | – | 1.429 | 5.5/253 | 0.001 |

n-Pentadecane | C${}_{15}$H${}_{32}$ | 212.42 | 0.769 | – | – | 1.431 | 9/270 | – |

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**MDPI and ACS Style**

Dominguez Lopez, J.; Gealy, M.W.; Ulness, D.J.
Photothermal Imaging of Transient and Steady State Convection Dynamics in Primary Alkanes. *Liquids* **2023**, *3*, 371-384.
https://doi.org/10.3390/liquids3030022

**AMA Style**

Dominguez Lopez J, Gealy MW, Ulness DJ.
Photothermal Imaging of Transient and Steady State Convection Dynamics in Primary Alkanes. *Liquids*. 2023; 3(3):371-384.
https://doi.org/10.3390/liquids3030022

**Chicago/Turabian Style**

Dominguez Lopez, Johan, Mark W. Gealy, and Darin J. Ulness.
2023. "Photothermal Imaging of Transient and Steady State Convection Dynamics in Primary Alkanes" *Liquids* 3, no. 3: 371-384.
https://doi.org/10.3390/liquids3030022