Optical temperature measurements in liquid flows have been the focus of extensive research for several decades, holding particular relevance in situations where conventional devices such as thermometer sensors, including thermocouples, may not be applicable [1]. A wide range of physical phenomena present various optical opportunities for temperature determination. Examples include the analysis of vibrational energy modes with Raman scattering spectroscopy, measuring thermal radiation with IR thermometry, and the use of thermochromic liquid crystals [2]. Even though the temporal response of these techniques may differ significantly, they are in principle all adequate for the investigation of single-phase media, such as turbulent heated jets [3]. The thermometry of complex two-phase media, such as bubble flows, particle suspensions, or spray systems, however, still remains challenging [4]. Laser-induced fluorescence (LIF) techniques stand out as the favored choice offering advantages in terms of localization, species sensitivity, and control over the illuminated volume where liquid flow and transfer phenomena can entail complex geometries. LIF involves the introduction of a fluorescent dye, whose fluorescence emission displays pronounced sensitivity to temperature, in terms of variations in emission wavelengths, intensity, and lifetime.

Early measurements of liquid temperature with LIF, in the 1990s, involved point measurements using a focused laser beam [5]. Over time, advancements in camera and laser technology led to the introduction of planar laser-induced fluorescence (PLIF) for two-dimensional temperature measurements [6]. This method involves the illumination of liquid flows with a thin laser sheet confining the fluorescence emission to an area. More recently, stereoscopic systems have been developed to reconstruct three-dimensional temperature fields [7].

Within a small elementary volume denoted as $dV$, the single-photon fluorescence intensity, $dF$, can be mathematically expressed as follows:

To determine the temperature based on Eq. (1), the flow must remain single phase, while, simultaneously, the laser flux and measurement volume must be kept constant with respect to a reference measurement. As a result of these stringent restrictions, disturbances in the form of striations due to refractive index variations pose significant challenges. For two-phase flows, discontinuities in refractive indices and the presence of multiple interfaces (e.g., liquid/gas) introduce notable degrees of light scattering, making the direct use of fluorescence intensity for thermometry problematic.

To address this challenge, one can resort to ratiometric techniques [9]. These techniques, also referred to as two-color LIF thermometry (2CLIF), rely on the simultaneous measurement of the fluorescence intensity in two spectral bands, each exhibiting different sensitivities to temperature variations. This can be achieved by using either a single dye whose emission spectrum changes with temperature [10] or two dyes having separated absorption spectra and exhibiting different temperature sensitivities [11]. This approach has been applied in diverse temperature reconstruction applications [12–14]. The efficiency of ratiometric approaches relies on achieving equal scattering and absorption impacts across the two detection bands. Consequently, the utilization of these methodologies is confined to some applications of low complexity, as previously described.

For high-complexity, two-phase media, refractive index variations and multiple scattering will extend the fluorescing region beyond the laser sheet. Furthermore, the lengthening of optical paths in these types of media will favor the reabsorption and re-emission of fluorescence, encroaching on the stringent requirements of ratiometric thermometry.

An alternative solution is the use of two-photon laser-induced fluorescence (2p-LIF), a nonlinear process involving the excitation of the aforementioned temperature-sensitive fluorescent dyes via the simultaneous absorption of two infrared photons. Due to the necessity of simultaneous absorption, only areas of high photon flux, i.e., areas within the laser path, will absorb and hence emit 2p-LIF signal, granting this technique robustness toward, e.g., scattering environments, a characteristic recently employed for pointwise temperature measurements within the optically dense regions of sprays [15]. Recent advances in femtosecond laser technology have resulted in high photon flux pulses that generate enough 2p-LIF signal for detection in planes several centimeters wide, paving the way for new imaging applications especially in optically dense samples [16].

In this study, we utilize the benefits of 2p-LIF imaging to 2CLIF thermometry in order to obtain instantaneous temperature maps in complex two-phase media. With the use of Kiton Red and Rhodamine 560 (R560) as the temperature probes, we show a temperature sensitivity of $1.54 {\% }/^{\circ }$C over a temperature range of 17–60$^{\circ }$C. The use of the 2p–2CLIF technique in heating and degassing water illustrates its effectiveness in thermometry for complex and dynamic high-speed liquid flows. A macroscopic laser sheet measuring $\sim 1\times 1$ cm$^2$, with a pulse duration of $45$ fs, $1$ mJ energy and centered at $840$ nm, is incident on a cuvette filled with dissolved fluorescent dyes. The fluorescence signal is detected, via a telecentric objective (1.0$\times$ GoldTL) positioned at a 90$^{\circ }$ angle from the laser sheet, on two sCMOS cameras (Andor, Zyla 5.5) resulting in a spatial resolution of $6.5$ $\mathrm {\mu }$m per pixel. To simultaneously capture the same image on both cameras while using a single telecentric lens, a Twincam system (CairnOptics) has been implemented (Fig. 1(a)). This system comprises an imaging relay that via a beam splitter cube, generates duplicate images on both cameras. For efficient collection of the fluorescence signal in two distinct spectral bands, bandpass fluorescence filters ([575–625] nm and [488–512] nm, whose spectral properties are depicted in Fig. 1(b)) are placed in front of each camera.

 

Fig. 1. (a) Illustration of the experimental setup used for generating a macroscopic laser sheet measuring approximately $1\times 1$ cm$^2$. An ultra-short, $1$ mJ laser pulse ($45$ fs) from a ytterbium-doped fiber seeded laser centered at $840$ nm is focused into the cuvette with a cylindrical lens (CL). Illustration of the calibration and application cases has been added. Detection is achieved in two spectral channels via a CairnOptics Twincam setup, two spectral filters, and two Andor Zyla sCMOS cameras. The experimental setup used for the temperature calibration and for the study of the heating of non-degassed water is also depicted. (b) Spectrum of the laser excitation source as well as the fluorescence spectra of Rhodamine 560 and Kiton Red. The shaded areas represent the spectral positions of the bandpass filters. (c) Graphical representation of the image processing routine used for 2p–2CLIF ratiometric temperature calibration.

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For 2p-LIF applications, Eq. (1) must be updated:

In this study, the mixing of Kiton Red (KR at a concentration of $10^{-6}$ mol/L) and Rhodamine 560 (R560 at a concentration of $10^{-5}$ mol/L) was used as the temperature-sensitive mixture. In relation to the excitation laser, their measured spectra are illustrated in Fig. 1(b). The calibration was conducted in a cell placed on a temperature-controlled heating plate with a path length of less than $1$ mm between the laser sheet and the cell wall. In order to ensure temperature homogeneity, a magnetic stirrer is inserted along with a thermocouple (Fig. 1(a)). Figure 2(a), top panel, represents the variation of the fluorescence signal on each spectral band as a function of temperature. As observed, the fluorescence signal emitted on spectral band 1 ([575–625] nm, related to KR) decreases with temperature, while the signal in spectral band 2 ([488–512] nm, related to Rh560) increases slightly. Figure 2(b) presents the evolution of the mean intensity on each image as well as the logarithm of the normalized ratio (see Fig. 1(c) for a graphical representation of the image processing). The fitting of the calibration curve yields a temperature sensitivity of 1.54 ${\% }/^{\circ }$C from 17 to 60$^{\circ }$C. The divergence of this value from literature [8] is attributed to the contamination by fluorescence from Rhodamine 560 in the fluorescence band designated for Kiton Red (Fig. 1(b)), reducing the temperature sensitivity on this specific spectral band. Furthermore, this reduction in temperature sensitivity is also due to the laser system we employed for this investigation. Indeed, fluorescence is occurring in the partially saturated excitation regime which could explain this sensitivity decrease for Kiton Red [3]. The temperature calibration obtained in Fig. 2 is applicable within the experimental condition described here. Any change in the fluorescent dyes, liquid solvent, and spectral bands of detection will necessitate a new calibration, following the same methodology. As for the effect of the optical path, the necessity of a new calibration will depend on whether the amount of light reabsorbed in the detection bands can be neglected.

 

Fig. 2. (a) Image ratios at various temperatures, calculated via the routine illustrated in Fig. 1(c). (b) Evolution of fluorescent intensity in both spectral bands where the logarithmic ratios are plotted on the right axis as a function of water temperature. This fitted line results in a sensitivity of 1.54${\% }/^{\circ }$C.

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Instantaneous two-photon fluorescence thermometry was carried out in a transparent cuvette filled with non-degassed water seeded with the two fluorescent dyes. Employing non-degassed water in our experimental setup facilitates the generation of a substantial quantity of air bubbles dispersed throughout the liquid, mimicking a complex medium. Additionally, these bubbles yield temperature gradients of greater magnitude compared to vapor bubbles arising from the conventional water boiling processes, a regime where temperature gradients are confined to a few degrees around the boiling point. Subsequently, a resistive heater is introduced into the cuvette (Fig. 1(a)). At the onset of the experiment, the water is maintained at an initial temperature of approximately $20^{\circ }$C. Around 10 s after the beginning of image acquisition, the heating element is triggered, initiating a temperature increase. The resistive heater functions in a cyclic manner, emitting heat at a constant frequency over time. The periods during which the heater is actively generating heat are denoted as “ON” in the illustrated images presented in Fig. 3. Throughout the experiment, high-resolution fluorescence images are systematically captured at a frequency of $5$ Hz. Figure 3 shows a selection of the images from the acquired series. Initially, the water exhibits a uniform temperature distribution around $20^{\circ }$C. At the edges of the laser sheet, the fluorescence signal drops rapidly due to the second-order relation between the laser and fluorescence intensity (and consequently signal-to-noise ratio). Upon heater activation, a discernible transformation in the liquid’s thermal field becomes evident with the formation of convective cells and the emergence of hot plumes, mainly visible from 40 s and onward. Notably, this heating process is concomitant with the production of bubbles within the liquid, which become entrained in the fluid flow.

 

Fig. 3. Selection of images acquired of the temperature field of water heated by a resistive heater. The gray box at $t=76$ s along with the corresponding red curve to the right indicates an equilibrium temperature gradient after heating has been completely turned off. This is in stark contrast to the flat temperature gradient of the water before heating has commenced (green curve).

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When the heater is completely deactivated at $t = 70$ s, a distinct vertical temperature stratification becomes evident, eventually stabilizing at $t = 76$ s. The temperature profile in the region highlighted by the gray zone and corresponding temperature plot to the right (red curve of Fig. 3) reveals a significant temperature decrease, transitioning from 50$^{\circ }$C at the free liquid surface to 20$^{\circ }$C at the base of the cuvette. This observed temperature gradient was verified through thermocouple measurements conducted immediately after the experimental trials and is in stark contrast to the corresponding constant temperature profile at $t=0$ s (shown in green). The temporal evolution of temperature in three regions of interest are represented in Supplement 1.

Due to the instantaneous nature and robustness against scattering of 2p–2CLIF, temperature measurements in the vicinity of air bubbles, i.e., within complex two-phase media, become possible. Three distinct time points within the acquisition, specifically $t = 51.0, 51.2, \rm {and}\,51.4$ s are analyzed with respect to bubble formation within three designated regions, denoted as zones (i), (ii), and (iii) (Fig. 4). (i) is placed within the cool environment, (ii) is positioned immediately after the hot wavefront, and (iii) encompasses the bubble inception site. The temperature profiles derived from these areas are displayed in the histograms underneath, along with the zoomed-in images of the different areas. This investigation shows that bubbles emerging directly from the heating element are situated within an environment characterized by significantly elevated temperatures compared to regions beyond the immediate vicinity of the bubbles. Indeed, an average temperature of $54^{\circ }$C prevails within the bubble-rich zone, whereas a temperature of $45^{\circ }$C is measured adjacent to this zone.

 

Fig. 4. Detailed views at specific instances ($51.0$, $51.2$, and $51.4$ s) reveal the presence of bubble dynamics with respect to the heater being on or off. Zoomed-in sections (i, ii, and iii at $t=51.2$ s) and corresponding temperature histograms are provided, revealing the temperature gradients of this transient processes.

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In conclusion, our investigation represents a significant advancement in the domain of optical temperature measurements within complex two-phase flows. The integration of two-photon laser-induced fluorescence (2p-LIF) imaging with two-color laser-induced fluorescence (2CLIF) thermometry presents a novel and powerful methodology for achieving instantaneous temperature mapping. We have shown that this approach proves effective in capturing the temperature dynamics in two-phase flows, addressing challenges posed by refractive index variations, multiple interfaces, and light-scattering phenomena. In this work, we have used the temperature-sensitive dyes Kiton Red and Rhodamine 560, achieving a temperature sensitivity of $1.54 {\% }/^{\circ }$C over temperatures ranging from 17 to 60$^{\circ }$C. By applying this mixture and technique to the heating and degassing of water, with the intentional introduction of bubbles, we reveal detailed insights into the thermal behavior of the liquid, including the formation of convective cells, emergence of hot plumes, and temperature stratification surrounding air bubbles. In comparison to single-photon approaches, fluorescence excitation with two photons has the main advantage of being applicable to the scattering medium such as dense spray (Fig. 2 in Supplement 1) as it eliminates absorption beyond the area subtended by the laser sheet. Moreover, the proposed approach, i.e., employing a powerful femtosecond laser, offers significant temporal resolution gains for the study of transient phenomena. We believe that 2p–2CLIF thermometry contributes to the expanding toolkit of optical temperature measurement techniques, offering a robust solution for the study of complex, transient, high-speed two-phase media in various liquid media.