- Email: [email protected]
Laser-based measurement of liquid temperature or concentration at a solid–liquid interface
Experimental Thermal and Fluid Science 23 (2000) 1±9
www.elsevier.nl/locate/etfs
Laser-based measurement of liquid temperature or concentration at a solid±liquid interface C.H. Fan, J.P. Longtin
*
Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794-2300, USA Received 4 February 2000; received in revised form 20 April 2000; accepted 20 May 2000
Abstract This work presents a real-time, non-contact, laser-based thermore¯ectance technique to measure changes in temperature or concentration of stationary or ¯owing liquids at a transparent solid±liquid interface, e.g., a glass window. Variations in temperature or concentration result in a change in refractive indices of the liquid, which, in turn, alter the re¯ectivity at the interface. A 3 mW semiconductor laser diode serves as the light source, and a silicon photodiode monitors the intensity variations of the re¯ected laser beam. The temperature of three liquids, water, ethanol, and 1-propanol, are measured with very good agreement found between the laser technique and a calibrated thermistor. The concentration of a methanol±propanol solution is successfully measured as well. The maximum uncertainty is 0:6°C for the temperature measurement and 0.2% for the concentration measurement, respectively. The presented experimental con®guration is simple, inexpensive and reliable. Additionally very high spatial and temporal resolution are possible: the beam spot size can be readily reduced to 20 lm or less, and a temporal resolution of 1 ls or less can be achieved with a high-speed data acquisition system. Thus, temperature or concentration changes in a ¯owing liquid in small-scale devices such as microelectro-mechanical-systems (MEMS) and micro¯uidic structures, and the systems with fast temporal variation, e.g., rapid solidi®cation and fast mixing, can be eectively measured. Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: Interface measurement; Laser diagnostics; Liquid solution; Temperature and concentration
1. Introduction Variations in liquid temperature or concentration at a solid±liquid boundary are of primary importance in ¯uid dynamics, heat transfer, and mass diusion processes. Furthermore, the rapid development of microsystems in the recent years, including micro heat pipes [1±3], and micro¯uidics and MEMS structures [4], has resulted in the need to accurately detect changes in temperature and concentration in such systems. Several techniques are available to measure temperature, including thermocouples and related contactbased sensors, infrared thermometers, and ®ber-optic temperature sensors, however, each has its drawbacks. For the thermocouple, the measured region is determined by its dimension, and the measurement of a liquid surface or interface is dicult to achieve. Also, the * Corresponding author. Tel.: +1-631-632-9436; fax: +1-631-6328544. E-mail address: [email protected] (J.P. Longtin).
thermocouple is invasive in nature, and has a limited response time. Infrared techniques, which capture radiation emitted from an object to determine temperature, require accurate values of the liquid emissivity. However, liquid emissivity, e.g., for water, is sensitive to wavelength within the infrared spectrum [5]; moreover, transparent solids, such as glass and quartz used for windows, can absorb strongly in the infrared spectrum, making infrared techniques impractical. Fiber-optic sensors measure, e.g., the phase shift of light propagating through a sensor probe, or the radiation emitted from a ¯uorescence target to determine the temperature of an object [6±8]. A ®ber-optic sensing system, which is based on a dierential spectral transmittance/re¯ectivity technique, was developed by Wang et al. [9] to measure temperature. However, the probe had to be immersed in the test liquid, or contact the specimen until the system reached thermal equilibrium. In addition, precise ®berloss compensation was required. Other laser-based or ®ber-optic temperature measurements include techniques using diuse re¯ectance spectroscopy [10], thermal lensing [11], and laser interferometric thermometry
0894-1777/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 0 0 ) 0 0 0 1 9 - 4
2
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
Nomenclature C volume-based concentration, vol% I laser intensity, W n index of refraction R re¯ectivity at solid±liquid interface T temperature, °C; K V voltage, V Greek a b c
symbols angle of incidence at air±glass interface, deg angle of incidence at glass±liquid interface, deg angle of refraction at glass±liquid interface, deg
[12]. Longtin and Fan [13] developed a non-contact, re¯ection-based technique to measure the temperature at a free liquid surface. Regarding concentration, Bergman et al. [14,15] developed a ®ber-optic probe to measure salinity distribution in liquids. Narayanan and Narayanan [16] employed a laser-based liquid prism sucrose meter to measure sugar concentration. Liquid diusion coecients have also been measured using a decaying concentration pulse technique [17], in which the de¯ection of a laser beam through a rectangular cell was recorded, though the beam de¯ection detection was complicated and large in spatial extent. Longtin and Fan [18] presented a laser-based technique to measure liquid refractive index and concentration in a stationary cell, though their technique could not measure ¯owing liquids. Commercial refractometers determine the concentration by measuring the refraction of light passing through a liquid solution [19]. Other techniques reported in the literature include a planar laserinduced ¯uorescence technique [20], an invasive heat-marker method [21], interferometric techniques [22±24], and a phase-locked-loop ultrasonic method [25]. Although the techniques described above can produce good results, they suer from one or more of the following shortcomings: they can only measure either temperature or concentration of solids or stationary liquids, they must contact the specimen directly, they must reach thermal equilibrium before taking data, they are complicated and dicult to operate, or have expensive components. This work presents a laser-based interface measurement (LBIM) technique to measure temperature or concentration changes in the liquid directly adjacent to a transparent solid interface. The thickness of the interrogated liquid region is on the order of k=2 [26], where k 635 nm is the incident laser wavelength, giving a very good estimate of the true interface temperature itself. The measurement uncertainty is roughly 0:6°C for the temperature and 0.2% for concentration measurements, respectively. Another unique feature of this technique is that very high spatial and temporal resolution can be obtained. With a thin lens, the beam spot
h k
angle of incidence or refraction, deg laser wavelength, m
Subscripts a air g glass l liquid p p-polarized light s s-polarized light 0 initial 1 medium 1 2 medium 2
size can be reduced to 20 lm or less at the solid±liquid interface. The temporal resolution of the technique is limited by the electrical components, rather than the optical components. The photodiode and transresistance ampli®er in this work have a response time on the order of 1 ls or less. Thus, the LBIM technique shows potential for temperature or concentration measurement in small systems, including thin evaporating ®lms [27], micro heat pipes [1±3], MEMS and micro¯uidic structures [4], as well as systems requiring high temporal accuracy, such as liquid solidi®cation in thermal spray processes, rapid mixing, and laser-induced Marangoni convection. 2. Experimental setup and theory The experimental principle is based on thermore¯ectance, i.e., the variation in intensity of re¯ected light from a solid±liquid interface as a function of liquid temperature or concentration. The re¯ectivity R of the interface depends on the refractive indices of the solid and liquid, which, in turn, depend on the temperature T and concentration C. Thermore¯ectance measurements for solids surfaces and ®ber-optic sensor applications have been performed in recent years [9,28±30], however, investigations of liquids have received relatively little attention [13]. 2.1. Experimental Setup The experimental con®guration is shown in Fig. 1(a). The liquid resides in a glass beaker, with a maximum capacity of 50 ml. The beaker is placed on a hot plate stirrer with a magnetic stirring bar inside, by which the test liquid is circulated, uniformly mixed, and heated. A 3 mW Hitachi HL6316G semiconductor laser diode with a wavelength of 635 nm serves as the light source. The laser diode and integrated aspheric lens are mounted on a rotation stage, by which a desired incident angle can be obtained. The diode is driven by a Wavelength Electronics LFI4505 diode driver, and is modulated with an EG&G Model 7260 DSP look-in ampli®er. The lockin ampli®er provides a sinusoidal signal to modulate the diode laser output at a unique frequency that is detected
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
3
Fig. 1. Schematic of the experimental setup.
at the photodiode ampli®er output (Fig. 1(a)). The laser diode has an integrated photodiode to provide feedback to the diode driver, resulting in very stable laser intensity; the intensity from this con®guration is stable to 0:02%. A high-quality circular optical fused silica window 25.4 mm in diameter and 9.625 mm thick covers the test liquid (Fig. 1). For the experiment, the window provides high transmittance through the visible spectrum and a smooth, ¯at surface for the solid±liquid interface. Note that the optical window is not necessary for the measurement. If a high optical quality glass container is used, then the glass wall of this container can replace the optical window as a viewport. The liquid under the window can either be ¯owing or stationary with comparable results in both cases. A Newport Glan±Thompson calcite polarizer is used to linearly polarize the laser beam before it is directed onto the glass window. The re¯ected beam from glass±liquid interface is then sent to a UDT PIN6D silicon PIN photodiode (PD). The diode has an active area of 20:3 mm2 and is operated with a 15 V reverse bias voltage to improve response linearity. The PD current is sent to a transimpedance ampli®er and
converted to a voltage linearly proportional to the diode current. The RMS voltage is measured using the lock-in ampli®er discussed above. Since the lock-in ampli®er detects only those signals at the reference frequency, eects such as stray room light striking the PD, and electrical and mechanical noise are minimized. A 2 mm diameter thermistor is placed in the liquid under the glass±liquid interface to monitor the liquid temperature. The thermistor is calibrated against a NIST-traceable RTD probe over the temperature range 15±50°C, and provides a reference temperature for comparison with the LBIM technique. The thermistor resistance is recorded using a Keithley Model 2000 voltmeter (DMM) during the experiment. Readings from the lock-in ampli®er and the DMM are sent via a GPIB interface to a personal computer running LabVIEW at a sampling rate of 5 sample/s. Although the measurement system is generally insensitive to ambient noise, the system is assembled on a vibration-isolated optical bench for convenience. The liquid under test is mixed during the heating process using a magnetic stirring bars on the hot plate to minimize temperature gradients in the liquid.
4
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
2.2. Experimental theory Fluctuations in temperature result is slight refractive index variations in both the liquid and solid, which alter the re¯ectivity at the solid±liquid interface. Measured re¯ectivity changes can thus be correlated to temperature changes at the interface. Referring to Fig. 1, I0 is the incident laser intensity on the glass±liquid interface, the re¯ected beam intensity from the interface with re¯ectivity R will be RI0 . For oblique incidence at an interface, re¯ectivity depends on the polarization and the angle of incidence according to Fresnel's laws of re¯ection [31] 2 tan h1 ÿ h2 ; 1a Rp tan h1 h2
sin h1 ÿ h2 Rs sin h1 h2
2 ;
1b
where Rp and Rs are the p- and s-polarized re¯ectivity, and h1 and h2 are the angles of incidence and refraction in medium 1 and 2, respectively. Referring to Fig. 1(b), there are two interfaces present: the air±glass interface and glass±liquid interface. The laser beam strikes the glass window at an angle of incidence, a. Snell's law then relates the beam angles in the glass and liquid [31], na sin a ng sin b nl sin c;
2
where b and c are the refractive angles at the air±glass and glass±liquid interface, and na ; ng , and nl are the air, glass, and liquid indices of refraction, respectively. Note that a re¯ected beam generated at the ®rst air±glass surface is not used in this experiment, and is blocked from reaching the photodiode detector. Using Eqs. (1a), (1b) and (2), the re¯ectivity for the air±glass±liquid beam path in Fig. 1(b) can be expressed as " p p #2 A 1 ÿ A 2 ÿ B 1 ÿ B2 p p ; 3a Rp a; ng ; nl A 1 ÿ A 2 B 1 ÿ B2 " p p #2 A 1 ÿ B 2 ÿ B 1 ÿ A2 p p ; Rs a; ng ; nl A 1 ÿ B 2 B 1 ÿ A2
negligible. Therefore, for pure liquids, i.e., DC 0, changes in re¯ectivity for both p- and s-polarized light with temperature can be expressed as oR dng oR dnl DR DT ; 5 ong dT onl dT where DT is a small, ®nite temperature change at the interface. As seen in Eq. (5), the sensitivity of R to temperature is determined by both the temperature coecient dn=dT , and the change in re¯ectivity with refractive index, oR=on, for both the liquid and glass. The values of dn=dT can be treated as a constant if the total temperature change is small [32,33], while oR=on depends on polarization of the light and the angle of incidence (Eqs. (3a) and (3b)). The re¯ectivity sensitivity for p- and s-polarized light for incident angles a from 0° to 60° is shown in Fig. 2 for a 1°C temperature increase in 1-propanol. To avoid being blocked by the sides of the liquid container, an incident angle greater than 60° was not used. For s-polarized light, the sensitivity increases with the angle of incidence. Conversely, ppolarized light decreases its sensitivity with larger angles of incidence. For maximum sensitivity, then, s-polarized light with an incident angle of 60° at the air±glass interface is used for the measurements. Larger angles of incidence also facilitate blocking the ®rst air±glass interface re¯ection (Fig. 1). The LBIM technique measures the change in the surface re¯ectivity to obtain the temperature change in liquids at a glass-liquid interface. Thus at the beginning of the experiment, the system is allowed to reach thermal equilibrium at a known temperature, T0 , and corresponding reference re¯ectivity, Rs0 , at the interface and photodiode/ampli®er voltage V0 . As the liquid is heated by the hot plate stirrer, the temperature will rise gradually, which changes the re¯ectivity at the glass±liquid interface. Due to the linear response of the photodiode and transimpedance ampli®er, variations in re¯ectivity and signal voltage are related as follows [13]:
3b
where A sin a=ng and B sin a=nl , respectively, and na 1:00: In the absence of strong pressure variations, the index of refraction is a function of temperature, liquid concentration, and the wavelength of the incident light only n n T ; C; k;
4a
on on on DT DC Dk: 4b oT oC ok Since laser light is highly monochromatic and wavelength-stable, Dk 0, and the wavelength variation is Dn
Fig. 2. Sensitivity of re¯ectivity for p- and s-polarized light at glass± propanol interface for 1°C temperature change.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
5
Table 1 Optical properties of liquids and glass (fused silica) n k 632:8 Water
Ethanol
1-propanol
Methanol
Glass a b
1.331 [32]
1.358 [32]
1.384 [32]
1.325 [32] 1.45702 [37]
dn=dT 104 Kÿ1 ÿ0.8 [32] ÿ1.04 [33] ÿ3.9 [32] ÿ4.38 [34] ÿ4.53 [35] ÿ3.9 [32] ÿ4.33 [35]
Rs %
oRs =ong
oRs =onliq
0.5441a
0.0779a
ÿ0:0956a
0.3212a
0.0600a
ÿ0:0701a
0.1675a
0.0434a
ÿ0:0485a
ÿ3.9 [32] ÿ4.32 [35] 0.128b
Calculated from Eq. (3b) with a 60°. From manufacture.
DRs DV : Rs0 V0
6
The temperature changes in Eq. (5) thus can be obtained using the measured variations in voltage ÿ1 oRs dng oRs dnl DV Rs0 : 7 DT ong dT onl dT V0 The values of dn=dT for the test liquids, water, ethanol, and l-propanol, and dR=dn at the interfaces for an incident angle a 60° are listed in Table 1. For liquid solutions, changes in the refractive index occur from changes in both temperature and concentration. If, however, the concentration term dominates, i.e., on on DC DT ; oC oT
8
then concentration can successfully be measured using Eq. (7). Note that the liquid concentrations do not aect the refractive index of glass, thus the dng =dC term does not appear. In the case of concentration measurement with large temperature variations, temperature ¯uctuations can be accounted for by measuring temperature independently, e.g., with a thermocouple. 3. Results and Discussion The liquids used to demonstrate the temperature measurement technique are water, ethanol, and l-propanol, and the window material is fused silica. First, the importance of temperature change in the glass is discussed. For fused silica, dn=dT 1:3 10ÿ5 Kÿ1 , which is over 30 times smaller than dn=dT for ethanol and 1propanol. Even water, with its unusually low dn=dT of ÿ0:8 10ÿ4 Kÿ1 , is still nearly eight times greater. For
the very popular BK 7 glass, dn=dT is even smaller at 2 10ÿ6 Kÿ1 . From the symmetry in Eqs. (3a) and (3b), and noting that ng na ; oR=ong is on the order of oR=onl . To a good approximation, then, contributions to the re¯ectivity change from the glass can be neglected in Eq. (5). Incorporating window temperature changes from the glass is straightforward, however, dn=dT for the window material is required. Changes in the window temperature will also change the amount of re¯ected light at the air±glass interface, which alters the intensity entering the window, and results in a false reported temperature change. Following a similar argument as above, however, the re¯ectivity change with temperature in silica and glass is negligibly small, and this eect can be ignored. The area of the interface interrogated by the LBIM technique is determined by the laser spot size at the glass±liquid interface. In this work, the beam spot size was 0:5 mm in diameter, and is readily adjusted with the aspheric lens in the diode housing. The minimum spot size is limited by the laser wavelength and focusing optics; a spot size of 20 lm or less can be readily achieved using lens combinations and/or a high numerical aperture microscope objective. Such small spot sizes provide extremely high spatial resolution. Alternatively, the spot size can be expanded to several millimeters in diameter, in which case the reported temperature is an average value for the illuminated surface. The maximum spot size is determined by the interface-laser distance, and the ability to collect and send the re¯ected beam to the photodiode. The temporal resolution of the technique is determined by the electrical components, rather than optical limitations. The PD and transimpedance ampli®er have a response time on the order of 1 ls or less, while the lock-in ampli®er and digital voltmeter have a response time of 1 ms. For the experiments in this work, a sampling rate of 5 samples/s was sucient. If a faster response time is desired, then a high-speed data
6
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
acquisition system can be used in which temporal resolutions of 1 ls can readily be obtained. Temperature measurement results are presented for three sample liquids: water, ethanol, and 1-propanol. The typical test duration ranges from 9 to 16 min with temperature increasing from 7°C to 10°C above the ambient temperature. Relevant liquid properties are taken from the literature, and are shown in Table 1 [32± 35]. Before each test run, the liquid system is allowed to stabilize thermally at room temperature for at least 30 min, with the magnetic stirrer keeping the ¯uid in motion. For the test, data acquisition is started, and heat is applied from the hot plate for several minutes, and then shut o. The results of temperature measurement for water and ethanol are shown in Figs. 3 and 4 respectively. In each graph, the solid line represents the LBIM temperature and the dashed line represents the reference thermistor temperature. The LBIM temperature is the raw data from the system, i.e., no averaging or smoothing is performed. Since the LBIM technique measures only changes in liquid temperature, an initial temperature is provided by the calibrated thermistor; this explains the common temperature at t 0. As can be seen, the agreement is good for the test liquids. During the heating process, a variation of 0:5±1:0°C between the LBIM and the thermistor temperature is observed, which is most likely due to temperature variations between the thermistor and interface laser beam locations. In fact, very good agreement is found at the start and end of the test, when no heat is applied, and the liquid temperature is more uniform. The sensitivity of the LBIM technique is illustrated with the temperature measurement for water, which has a dn=dT value only 25% that of the other liquids, resulting in a correspondingly weaker signal. Although there is slightly more noise on the signal for water, the result is still good. The presence of the glass interface substantially reduces noise compared to an air±water interface, which the authors found in a previous work to be very noisy for water [13]. This suggests that surface motion
and/or surface evaporation ± not present for the glass± liquid interface ± contribute signi®cantly to signal noise for an air±liquid interface. In Fig. 5, the sensitivity to small temperature changes for l-propanol is illustrated. In this case, the liquid is allowed to cool from several degrees above ambient for 60 s, with the magnetic stirrer keeping the liquid well mixed. To minimize noise ¯uctuations, a ®ve-point moving average is performed on the collected data. The LBIM and thermistor temperature agree to within 0:1°C, which suggests the technique can measure small temperature ¯uctuations as well, with appropriate data processing. For the concentration measurement, the experiment con®guration is identical to that for the temperature measurement, except that the heater is not used. To demonstrate the technique for concentration measurement methanol and l-propanol are used, as n varies linearly with concentration for this combination of liquids. The index of refraction as a function of concentration for this liquid system was measured with an
Fig. 3. Temperature measurement of water.
Fig. 5. Temperature measurement of 1-proponal over a small range.
Fig. 4. Temperature measurement of ethanol.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
7
4. Experimental uncertainty
Fig. 6. Real-time concentration measurement of a methanol±propanol solution.
independent technique [18], and found to be dnl =dC ÿ5:9 10ÿ4 l/vol%, which is the value used in Eq. (7). The liquid temperature was also measured with the thermistor during the experiment, which drifted less than 1:0°C during a given run. Results of the measurement are shown in Fig. 6. At ®rst, a known volume of l-propanol is placed in the liquid container. The re¯ected laser intensity from this pure liquid±glass interface served as the reference value, after which the concentration was varied by adding a given volume of methanol using a micropipettor and the magnetic stirrer to uniformly mix the liquids. Fig. 6(a) shows the real-time concentration variation at the interface, with the methanol concentration increased in steps of 0.4%. A 10-point average value is computed after the concentration reaches steady state, which is then taken to be the measured values (dots) shown in Fig. 6(b), in which the x-axis represents the true methanol concentration, and the y-axis represents the measured concentration from the laser technique. The ideal results should follow the line y x, as shown in the ®gure. For all results, the dierence between the measured and true concentration is less than 0.2%.
The thermistor, after calibration, has an uncertainty of 0:05°C over the calibration range of 15±50°C. Accurate values of the index of refraction of glass and liquids, and the glass temperature coecient, dn=dT , are reported in the literature, and their uncertainty is negligible. However, the liquid temperature coecients, dnl =dT , taken from the literatures vary by 10±20%. A 10% variation in dnl =dT can change the measured temperature by roughly 8%. Values of dn=dT reported by Solimini [32] were used in this work. Another source of error is noise in the photodiode ampli®er signal, which primarily arises from ¯uctuations in the laser diode and the driver. The measured laser intensity is actively stabilized, and has a measured ¯uctuation of 0.02%. The measured S=N ratio for the ampli®er is greater than 90 dB. Other noises, including vibration and small disturbances in the beam path aect the measurement as well. To quantify these contributions to noise, the temperature of an isothermal interface was measured over a 10 min interval. The re¯ectivity varied less than 0.1%, corresponding to temperature uncertainties of 0:6°C for water, and 0:1°C for ethanol and 1-propanol. A more stable laser source, e.g., by thermoelectrically cooling the laser diode, would likely reduce noise and improve temperature resolution. The laser diode is mounted on a rotation stage with an uncertainty of 0:5° in incident angle, which contributes a small error in re¯ectivity at the interface (Eq. (3a) and (3b)). The maximum laser diode power is 3 mW, and the absorption coecients of all liquids at the diode wavelength are of the order of 10ÿ3 cmÿ1 [32,33], thus liquid heating by the probe laser can be neglected. The extinction ratio of linear polarizer is greater than 105 , thus the uncertainty from light not polarized in the preferred direction is negligible as well. Considering the main sources of error, the computed root-sum-square uncertainties in temperature changes are approximately 0:6°C for water, 0:3°C for ethanol, and 0:2°C for 1-propanol, respectively. Regarding concentration measurement, there is some noise and overshoot just after the liquid concentration is changed as shown in Fig. 6(a), which is due to small concentration and/or temperature ¯uctuations as the liquid mixes near the interface. This ¯uctuation diminishes after 60 s. Another source of error is evaporation of methanol in the solution, which can reduce the true concentration during the experiment, resulting in smaller measured values near the end of the test (Fig. 6(b)). Considering all sources of error, the uncertainty in concentration is 0.2%. 5. Practical signi®cance The LBIM technique is well suited for interface temperature measurement through common glasses and silica windows. It provides a non-invasive, true interface temperature measurement. Two applications of note
8
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
include using the LBIM technique to measure the liquid±solid temperature at an extended evaporating meniscus, e.g., hexane evaporating on a clean glass slide, and measuring temperature in a heat pipe or other closed system that has a sight glass or ¯at glass interface. Other examples include monitoring temperature or concentration changes in biological/chemical systems and measurements requiring high temporal accuracy that occur at a solid±liquid interface, such as rapid solidi®cation during thermal spray processing. A measurement of Marangoni convection induced by temperature and/or concentration changes also can be eectively made by LBIM technique. Since the spot size can be made extremely small, e.g., 20 lm, the technique can be used for temperature or concentration measurement in very small systems, such as micro heat pipes [1±3], microchannels [36], and MEMS and micro¯uidic systems [4]. For example, the temperature of 100 lm wide liquid-®lled channels etched in silicon and capped with quartz or glass can be measured with the appropriate focusing optics for a small laser spot size; such measurements are very dicult with traditional instruments, such as thermocouples or RTDs. Since the technique is based on a semiconductor laser, integrating the LBIM technique on a chip for analysis is another possibility, provided lens and/or waveguides can be constructed to direct the laser light. Another interesting application, though not explored here, is the measurement of temperature at the interface between two immiscible liquids. The physics governing the re¯ection and experimental con®guration are identical to the glass±liquid interface. Substantial liquid motion at the interface may result in increased noise; however, temperature resolution comparable to the glass±liquid case should be obtainable for reasonably quiescent liquids. 6. Conclusions This work presents a real-time, laser-based technique to measure temperature or concentration changes in liquids adjacent to a transparent solid. In this work, a probe laser beam is sent through a glass window, where a portion is re¯ected o the liquid±solid interface. Temperature or concentration changes in the liquid result in re¯ectivity changes that are monitored with a photodiode and correlated to temperature in pure liquids or concentration in liquid solutions. In most cases, temperature changes in the glass will not aect the measurement. Temperature measurement results are presented for pure water, ethanol, and 1-propanol with very good results found when compared to a calibrated, reference thermistor immersed in the liquid near the interface. Uncertainties in the measurement are approximately 0:6°C for water, 0:3°C for ethanol, and 0:2°C for 1-propanol, respectively. For binary liquid solutions, the concentration can also be measured, provided temperature changes in the liquid are small, and results for a methanol±propanol solution are found
to be in good agreement with expected results. The experimental con®guration is simple, inexpensive, and reliable. The technique is suited for a variety of applications, especially those requiring high spatial and temporal resolution or a small interrogation region.
Acknowledgements The authors gratefully acknowledge ®nancial support for this work from the National Science Foundation through contract CTS-9702644.
References [1] J.P. Longtin, B. Badran, F.M. Gerner, A one-dimension model of a micro heat pipe during steady-state operation, J. Heat Transfer 116 (3) (1994) 709±715. [2] D.A. Benson, R.T. Mitchell, M.R. Tuck, D.W. Palmer, G.P. Peterson, Ultrahigh-capacity micromachined heat spreaders, Microscale Thermophys. Eng. 2 (1) (1998) 21±30. [3] R. Hopkins, A. Faghri, D. Khrustalev, Flat miniature heat pipes with micro capilary grooves, J. Heat Transfer 121 (1) (1999) 102± 109. [4] C.M. Ho, Y.C. Tai, Micro-Electro-Mechanical-Systems (MEMS) and ¯uid ¯ows, Annu. Rev. Fluid Mech. 30 (1998) 579±612. [5] G.M. Hale, M.R. Querry, Optical constants of water in the 200nm to 200-lm wavelength region, Appl. Opt. 12 (3) (1973) 555± 563. [6] K.T.V. Grattan, The use of ®ber optic techniques for temperature measurement, Meas. Control 20 (6) (1987) 32±39. [7] D.A. Krohn, Fiber Optic Sensors ± Fundamentals and Applications, Inst. Soc. Am. (1988). [8] K.A. Wickersheim, W.D. Hyatt, Commercial applications of ®beroptic temperature measurement, Proceddings of SPIE ± The International Society for Optical Engineering Fiber Optic Sensors IV, 1267, 1990, pp. 84±96. [9] A. Wang, G.Z. Wang, K.A. Murphy, R.O. Claus, Fiber-optic temperature sensors based on dierential spectral transmittance/ re¯ectivity and multiplexed sensing systems, Appl. Opt. 34 (13) (1995) 2295±2300. [10] T.P. Pearsall, S.R. Saban, J. Booth, B.T. Beard Jr., S.R. Johnson, Precision of noninvasive temperature measurement by diuse re¯ectance spectroscopy, Rev. Sci. Instr. 66 (10) (1995) 4977± 4980. [11] J.M. Harris, N.J. Dovichi, Thermal lens calorimetry, Anal. Chem. 52 (6) (1980) 695A±706A. [12] A.N. Magunov, Laser interferometric thermometry of semiconductors and dielectrics, Instr. Exp. Technol. 41 (3) (1998) 297± 308. [13] J.P. Longtin, C.H. Fan, Laser-based temperature measurement at a liquid surface, in: 11th International Heat Transfer Conference, Kyongyu, Korea, August 1998, pp. 119±123. [14] T.L. Bergman, F.P. Incropera, W.H. Stevenson, Miniature ®ber-optic refractormeter for measurement of salinity in doublediusive thermohaline systems, Rev. Sci. Instr. 56 (2) (1985) 291± 296. [15] T.L. Bergman, D.R. Munoz, F.P. Incropera, R. Viskanta, Measurement of salinity distribution in salt-strati®ed. doublediusive systems by optical de¯ectometry, Rev. Sci. Instr. 57 (10) (1986) 2538±2542.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9 [16] V.A. Narayanan, R. Narayanan, Laser-based liquid prism sucrosemeter ± a precision optical method to ®nd sugar concentration, J. Chem. Edu. 74 (2) (1997) 221±223. [17] M. Capobianchi, T.F. Irvine Jr., N.K. Tutu, G.A. Greene, A new technique for measuring the ®ckan diusion coecient in binary liquid solutions, Exp. Thermal Fluid Sci. 18 (1) (1998) 33±47. [18] J.P. Longtin, C.H. Fan, Precision laser-based concentration and refractive index measurement of liquids, Microscale Thermophys. Eng. 2 (4) (1998) 261±272. [19] J.E. Geake, Linear refractometers for liquid concentration measurement, Chem. Eng. (297) (1975) 305±308. [20] A. Lozano, S.H. Smith, M.G. Mungal, R.K. Hanson, Concentration measurements in a transverse jet by planar laser-induced ¯uorescence of acetone, AIAA J. 32 (1) (1993) 218±221. [21] V.A. Vink, G.A. Sokolov, Yu.S. Fomochev, Measurement of the concentration of ¯owing liquid solutions by a heat-marker method, J. Appl. Chem. USSR 58 (2) (1985) 357±359. [22] T. Konishi, S. Naka, A. Ito, K. Saito, Transient two-dimensional fuelconcentration measurement technique, Appl. Opt. 36 (33) (1997) 8815±8819. [23] T.A. Wilson, W.F. Reed, Low-Cost, Interferometric dierential refractometer, Am. J. Phys. 61 (11) (1993) 1046±1148. [24] R.J. Harris, G.T. Johnston, G.A. Kepple, P.C. Krok, H. Mukai, Infrared thermooptic coecient measurement of polycrystalline ZnSe, ZnS, CdTe, CaF2 , and BaF2 , single crystal KCl, and T1-20 Glass, Appl. Opt 16 (2) (1977) 436±438. [25] K. Ikeda, Ultrasonic measurement of concentration in solutions by a phase-locked loop method, Jpn. J. Appl. Phys 36 (5B) (1997) 3180±3183.
9
[26] E. Hecht, Optics, Second ed, Addison-Wesley, Reading, MA, 1987. [27] I.Y. Kim, P.C. Wayner, Shape of an evaporating completely wetting extended meniscus, J. Thermophys. Heat Transfer 10 (2) (1996) 320±325. [28] T.Q. Qiu, C.P. Grigoropoulos, C.L. Tien, Novel technique for noncontact and microscale temperature measurements, Exp. Heat Transfer 6 (3) (1993) 231±241. [29] A.S. Lee, J.L. Hostetler, P.M. Norris, Temperature measurement by thermore¯ectance at near grazing angles, in: Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition, Atlanta. GA, 1996, pp 77±82. [30] A.S. Lee, P.M. Norris, A new optical method for measuring surface temperature at large incident probe angles, Rev. Sci. Instr. 68 (2) (1997) 1307±1311. [31] F.A. Jenkins, H.I. White, Fundamentals of Optics, Fourth ed, McGraw-Hill, New York, 1976. [32] D. Solimini, Loss measurements of organic materials at 6328 A, J. Appl. Phys. 37 (1966) 3314±3315. [33] J. Stone, Measurement of the absorption of light in low-loss liquids, J. Opt. Soc. Am. 62 (3) (1972) 327±333. [34] M.E. Lusty, M.H. Dunn, Refractive indices and thermo-optical properties of dye laser solvents, Appl. Phys. B 44 (3) (1987) 193±198. [35] J. Sun, J.P. Longtin, T.F. Irvine Jr., Laser-based thermal pulse measurement of liquid thermophysical properties, Int. J. Heat Mass Transfer 44 (2001) 645±657. [36] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, Elec. Dev. Lett. 2 (5) (1981) 126±129. [37] I.H. Malitson, Interspecimen comparison of the refractive index of fused silica, J. Opt. Soc. Am. 55 (10) (1965) 1205±1209.
www.elsevier.nl/locate/etfs
Laser-based measurement of liquid temperature or concentration at a solid±liquid interface C.H. Fan, J.P. Longtin
*
Department of Mechanical Engineering, State University of New York at Stony Brook, Stony Brook, NY 11794-2300, USA Received 4 February 2000; received in revised form 20 April 2000; accepted 20 May 2000
Abstract This work presents a real-time, non-contact, laser-based thermore¯ectance technique to measure changes in temperature or concentration of stationary or ¯owing liquids at a transparent solid±liquid interface, e.g., a glass window. Variations in temperature or concentration result in a change in refractive indices of the liquid, which, in turn, alter the re¯ectivity at the interface. A 3 mW semiconductor laser diode serves as the light source, and a silicon photodiode monitors the intensity variations of the re¯ected laser beam. The temperature of three liquids, water, ethanol, and 1-propanol, are measured with very good agreement found between the laser technique and a calibrated thermistor. The concentration of a methanol±propanol solution is successfully measured as well. The maximum uncertainty is 0:6°C for the temperature measurement and 0.2% for the concentration measurement, respectively. The presented experimental con®guration is simple, inexpensive and reliable. Additionally very high spatial and temporal resolution are possible: the beam spot size can be readily reduced to 20 lm or less, and a temporal resolution of 1 ls or less can be achieved with a high-speed data acquisition system. Thus, temperature or concentration changes in a ¯owing liquid in small-scale devices such as microelectro-mechanical-systems (MEMS) and micro¯uidic structures, and the systems with fast temporal variation, e.g., rapid solidi®cation and fast mixing, can be eectively measured. Ó 2000 Elsevier Science Inc. All rights reserved. Keywords: Interface measurement; Laser diagnostics; Liquid solution; Temperature and concentration
1. Introduction Variations in liquid temperature or concentration at a solid±liquid boundary are of primary importance in ¯uid dynamics, heat transfer, and mass diusion processes. Furthermore, the rapid development of microsystems in the recent years, including micro heat pipes [1±3], and micro¯uidics and MEMS structures [4], has resulted in the need to accurately detect changes in temperature and concentration in such systems. Several techniques are available to measure temperature, including thermocouples and related contactbased sensors, infrared thermometers, and ®ber-optic temperature sensors, however, each has its drawbacks. For the thermocouple, the measured region is determined by its dimension, and the measurement of a liquid surface or interface is dicult to achieve. Also, the * Corresponding author. Tel.: +1-631-632-9436; fax: +1-631-6328544. E-mail address: [email protected] (J.P. Longtin).
thermocouple is invasive in nature, and has a limited response time. Infrared techniques, which capture radiation emitted from an object to determine temperature, require accurate values of the liquid emissivity. However, liquid emissivity, e.g., for water, is sensitive to wavelength within the infrared spectrum [5]; moreover, transparent solids, such as glass and quartz used for windows, can absorb strongly in the infrared spectrum, making infrared techniques impractical. Fiber-optic sensors measure, e.g., the phase shift of light propagating through a sensor probe, or the radiation emitted from a ¯uorescence target to determine the temperature of an object [6±8]. A ®ber-optic sensing system, which is based on a dierential spectral transmittance/re¯ectivity technique, was developed by Wang et al. [9] to measure temperature. However, the probe had to be immersed in the test liquid, or contact the specimen until the system reached thermal equilibrium. In addition, precise ®berloss compensation was required. Other laser-based or ®ber-optic temperature measurements include techniques using diuse re¯ectance spectroscopy [10], thermal lensing [11], and laser interferometric thermometry
0894-1777/00/$ - see front matter Ó 2000 Elsevier Science Inc. All rights reserved. PII: S 0 8 9 4 - 1 7 7 7 ( 0 0 ) 0 0 0 1 9 - 4
2
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
Nomenclature C volume-based concentration, vol% I laser intensity, W n index of refraction R re¯ectivity at solid±liquid interface T temperature, °C; K V voltage, V Greek a b c
symbols angle of incidence at air±glass interface, deg angle of incidence at glass±liquid interface, deg angle of refraction at glass±liquid interface, deg
[12]. Longtin and Fan [13] developed a non-contact, re¯ection-based technique to measure the temperature at a free liquid surface. Regarding concentration, Bergman et al. [14,15] developed a ®ber-optic probe to measure salinity distribution in liquids. Narayanan and Narayanan [16] employed a laser-based liquid prism sucrose meter to measure sugar concentration. Liquid diusion coecients have also been measured using a decaying concentration pulse technique [17], in which the de¯ection of a laser beam through a rectangular cell was recorded, though the beam de¯ection detection was complicated and large in spatial extent. Longtin and Fan [18] presented a laser-based technique to measure liquid refractive index and concentration in a stationary cell, though their technique could not measure ¯owing liquids. Commercial refractometers determine the concentration by measuring the refraction of light passing through a liquid solution [19]. Other techniques reported in the literature include a planar laserinduced ¯uorescence technique [20], an invasive heat-marker method [21], interferometric techniques [22±24], and a phase-locked-loop ultrasonic method [25]. Although the techniques described above can produce good results, they suer from one or more of the following shortcomings: they can only measure either temperature or concentration of solids or stationary liquids, they must contact the specimen directly, they must reach thermal equilibrium before taking data, they are complicated and dicult to operate, or have expensive components. This work presents a laser-based interface measurement (LBIM) technique to measure temperature or concentration changes in the liquid directly adjacent to a transparent solid interface. The thickness of the interrogated liquid region is on the order of k=2 [26], where k 635 nm is the incident laser wavelength, giving a very good estimate of the true interface temperature itself. The measurement uncertainty is roughly 0:6°C for the temperature and 0.2% for concentration measurements, respectively. Another unique feature of this technique is that very high spatial and temporal resolution can be obtained. With a thin lens, the beam spot
h k
angle of incidence or refraction, deg laser wavelength, m
Subscripts a air g glass l liquid p p-polarized light s s-polarized light 0 initial 1 medium 1 2 medium 2
size can be reduced to 20 lm or less at the solid±liquid interface. The temporal resolution of the technique is limited by the electrical components, rather than the optical components. The photodiode and transresistance ampli®er in this work have a response time on the order of 1 ls or less. Thus, the LBIM technique shows potential for temperature or concentration measurement in small systems, including thin evaporating ®lms [27], micro heat pipes [1±3], MEMS and micro¯uidic structures [4], as well as systems requiring high temporal accuracy, such as liquid solidi®cation in thermal spray processes, rapid mixing, and laser-induced Marangoni convection. 2. Experimental setup and theory The experimental principle is based on thermore¯ectance, i.e., the variation in intensity of re¯ected light from a solid±liquid interface as a function of liquid temperature or concentration. The re¯ectivity R of the interface depends on the refractive indices of the solid and liquid, which, in turn, depend on the temperature T and concentration C. Thermore¯ectance measurements for solids surfaces and ®ber-optic sensor applications have been performed in recent years [9,28±30], however, investigations of liquids have received relatively little attention [13]. 2.1. Experimental Setup The experimental con®guration is shown in Fig. 1(a). The liquid resides in a glass beaker, with a maximum capacity of 50 ml. The beaker is placed on a hot plate stirrer with a magnetic stirring bar inside, by which the test liquid is circulated, uniformly mixed, and heated. A 3 mW Hitachi HL6316G semiconductor laser diode with a wavelength of 635 nm serves as the light source. The laser diode and integrated aspheric lens are mounted on a rotation stage, by which a desired incident angle can be obtained. The diode is driven by a Wavelength Electronics LFI4505 diode driver, and is modulated with an EG&G Model 7260 DSP look-in ampli®er. The lockin ampli®er provides a sinusoidal signal to modulate the diode laser output at a unique frequency that is detected
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
3
Fig. 1. Schematic of the experimental setup.
at the photodiode ampli®er output (Fig. 1(a)). The laser diode has an integrated photodiode to provide feedback to the diode driver, resulting in very stable laser intensity; the intensity from this con®guration is stable to 0:02%. A high-quality circular optical fused silica window 25.4 mm in diameter and 9.625 mm thick covers the test liquid (Fig. 1). For the experiment, the window provides high transmittance through the visible spectrum and a smooth, ¯at surface for the solid±liquid interface. Note that the optical window is not necessary for the measurement. If a high optical quality glass container is used, then the glass wall of this container can replace the optical window as a viewport. The liquid under the window can either be ¯owing or stationary with comparable results in both cases. A Newport Glan±Thompson calcite polarizer is used to linearly polarize the laser beam before it is directed onto the glass window. The re¯ected beam from glass±liquid interface is then sent to a UDT PIN6D silicon PIN photodiode (PD). The diode has an active area of 20:3 mm2 and is operated with a 15 V reverse bias voltage to improve response linearity. The PD current is sent to a transimpedance ampli®er and
converted to a voltage linearly proportional to the diode current. The RMS voltage is measured using the lock-in ampli®er discussed above. Since the lock-in ampli®er detects only those signals at the reference frequency, eects such as stray room light striking the PD, and electrical and mechanical noise are minimized. A 2 mm diameter thermistor is placed in the liquid under the glass±liquid interface to monitor the liquid temperature. The thermistor is calibrated against a NIST-traceable RTD probe over the temperature range 15±50°C, and provides a reference temperature for comparison with the LBIM technique. The thermistor resistance is recorded using a Keithley Model 2000 voltmeter (DMM) during the experiment. Readings from the lock-in ampli®er and the DMM are sent via a GPIB interface to a personal computer running LabVIEW at a sampling rate of 5 sample/s. Although the measurement system is generally insensitive to ambient noise, the system is assembled on a vibration-isolated optical bench for convenience. The liquid under test is mixed during the heating process using a magnetic stirring bars on the hot plate to minimize temperature gradients in the liquid.
4
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
2.2. Experimental theory Fluctuations in temperature result is slight refractive index variations in both the liquid and solid, which alter the re¯ectivity at the solid±liquid interface. Measured re¯ectivity changes can thus be correlated to temperature changes at the interface. Referring to Fig. 1, I0 is the incident laser intensity on the glass±liquid interface, the re¯ected beam intensity from the interface with re¯ectivity R will be RI0 . For oblique incidence at an interface, re¯ectivity depends on the polarization and the angle of incidence according to Fresnel's laws of re¯ection [31] 2 tan h1 ÿ h2 ; 1a Rp tan h1 h2
sin h1 ÿ h2 Rs sin h1 h2
2 ;
1b
where Rp and Rs are the p- and s-polarized re¯ectivity, and h1 and h2 are the angles of incidence and refraction in medium 1 and 2, respectively. Referring to Fig. 1(b), there are two interfaces present: the air±glass interface and glass±liquid interface. The laser beam strikes the glass window at an angle of incidence, a. Snell's law then relates the beam angles in the glass and liquid [31], na sin a ng sin b nl sin c;
2
where b and c are the refractive angles at the air±glass and glass±liquid interface, and na ; ng , and nl are the air, glass, and liquid indices of refraction, respectively. Note that a re¯ected beam generated at the ®rst air±glass surface is not used in this experiment, and is blocked from reaching the photodiode detector. Using Eqs. (1a), (1b) and (2), the re¯ectivity for the air±glass±liquid beam path in Fig. 1(b) can be expressed as " p p #2 A 1 ÿ A 2 ÿ B 1 ÿ B2 p p ; 3a Rp a; ng ; nl A 1 ÿ A 2 B 1 ÿ B2 " p p #2 A 1 ÿ B 2 ÿ B 1 ÿ A2 p p ; Rs a; ng ; nl A 1 ÿ B 2 B 1 ÿ A2
negligible. Therefore, for pure liquids, i.e., DC 0, changes in re¯ectivity for both p- and s-polarized light with temperature can be expressed as oR dng oR dnl DR DT ; 5 ong dT onl dT where DT is a small, ®nite temperature change at the interface. As seen in Eq. (5), the sensitivity of R to temperature is determined by both the temperature coecient dn=dT , and the change in re¯ectivity with refractive index, oR=on, for both the liquid and glass. The values of dn=dT can be treated as a constant if the total temperature change is small [32,33], while oR=on depends on polarization of the light and the angle of incidence (Eqs. (3a) and (3b)). The re¯ectivity sensitivity for p- and s-polarized light for incident angles a from 0° to 60° is shown in Fig. 2 for a 1°C temperature increase in 1-propanol. To avoid being blocked by the sides of the liquid container, an incident angle greater than 60° was not used. For s-polarized light, the sensitivity increases with the angle of incidence. Conversely, ppolarized light decreases its sensitivity with larger angles of incidence. For maximum sensitivity, then, s-polarized light with an incident angle of 60° at the air±glass interface is used for the measurements. Larger angles of incidence also facilitate blocking the ®rst air±glass interface re¯ection (Fig. 1). The LBIM technique measures the change in the surface re¯ectivity to obtain the temperature change in liquids at a glass-liquid interface. Thus at the beginning of the experiment, the system is allowed to reach thermal equilibrium at a known temperature, T0 , and corresponding reference re¯ectivity, Rs0 , at the interface and photodiode/ampli®er voltage V0 . As the liquid is heated by the hot plate stirrer, the temperature will rise gradually, which changes the re¯ectivity at the glass±liquid interface. Due to the linear response of the photodiode and transimpedance ampli®er, variations in re¯ectivity and signal voltage are related as follows [13]:
3b
where A sin a=ng and B sin a=nl , respectively, and na 1:00: In the absence of strong pressure variations, the index of refraction is a function of temperature, liquid concentration, and the wavelength of the incident light only n n T ; C; k;
4a
on on on DT DC Dk: 4b oT oC ok Since laser light is highly monochromatic and wavelength-stable, Dk 0, and the wavelength variation is Dn
Fig. 2. Sensitivity of re¯ectivity for p- and s-polarized light at glass± propanol interface for 1°C temperature change.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
5
Table 1 Optical properties of liquids and glass (fused silica) n k 632:8 Water
Ethanol
1-propanol
Methanol
Glass a b
1.331 [32]
1.358 [32]
1.384 [32]
1.325 [32] 1.45702 [37]
dn=dT 104 Kÿ1 ÿ0.8 [32] ÿ1.04 [33] ÿ3.9 [32] ÿ4.38 [34] ÿ4.53 [35] ÿ3.9 [32] ÿ4.33 [35]
Rs %
oRs =ong
oRs =onliq
0.5441a
0.0779a
ÿ0:0956a
0.3212a
0.0600a
ÿ0:0701a
0.1675a
0.0434a
ÿ0:0485a
ÿ3.9 [32] ÿ4.32 [35] 0.128b
Calculated from Eq. (3b) with a 60°. From manufacture.
DRs DV : Rs0 V0
6
The temperature changes in Eq. (5) thus can be obtained using the measured variations in voltage ÿ1 oRs dng oRs dnl DV Rs0 : 7 DT ong dT onl dT V0 The values of dn=dT for the test liquids, water, ethanol, and l-propanol, and dR=dn at the interfaces for an incident angle a 60° are listed in Table 1. For liquid solutions, changes in the refractive index occur from changes in both temperature and concentration. If, however, the concentration term dominates, i.e., on on DC DT ; oC oT
8
then concentration can successfully be measured using Eq. (7). Note that the liquid concentrations do not aect the refractive index of glass, thus the dng =dC term does not appear. In the case of concentration measurement with large temperature variations, temperature ¯uctuations can be accounted for by measuring temperature independently, e.g., with a thermocouple. 3. Results and Discussion The liquids used to demonstrate the temperature measurement technique are water, ethanol, and l-propanol, and the window material is fused silica. First, the importance of temperature change in the glass is discussed. For fused silica, dn=dT 1:3 10ÿ5 Kÿ1 , which is over 30 times smaller than dn=dT for ethanol and 1propanol. Even water, with its unusually low dn=dT of ÿ0:8 10ÿ4 Kÿ1 , is still nearly eight times greater. For
the very popular BK 7 glass, dn=dT is even smaller at 2 10ÿ6 Kÿ1 . From the symmetry in Eqs. (3a) and (3b), and noting that ng na ; oR=ong is on the order of oR=onl . To a good approximation, then, contributions to the re¯ectivity change from the glass can be neglected in Eq. (5). Incorporating window temperature changes from the glass is straightforward, however, dn=dT for the window material is required. Changes in the window temperature will also change the amount of re¯ected light at the air±glass interface, which alters the intensity entering the window, and results in a false reported temperature change. Following a similar argument as above, however, the re¯ectivity change with temperature in silica and glass is negligibly small, and this eect can be ignored. The area of the interface interrogated by the LBIM technique is determined by the laser spot size at the glass±liquid interface. In this work, the beam spot size was 0:5 mm in diameter, and is readily adjusted with the aspheric lens in the diode housing. The minimum spot size is limited by the laser wavelength and focusing optics; a spot size of 20 lm or less can be readily achieved using lens combinations and/or a high numerical aperture microscope objective. Such small spot sizes provide extremely high spatial resolution. Alternatively, the spot size can be expanded to several millimeters in diameter, in which case the reported temperature is an average value for the illuminated surface. The maximum spot size is determined by the interface-laser distance, and the ability to collect and send the re¯ected beam to the photodiode. The temporal resolution of the technique is determined by the electrical components, rather than optical limitations. The PD and transimpedance ampli®er have a response time on the order of 1 ls or less, while the lock-in ampli®er and digital voltmeter have a response time of 1 ms. For the experiments in this work, a sampling rate of 5 samples/s was sucient. If a faster response time is desired, then a high-speed data
6
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
acquisition system can be used in which temporal resolutions of 1 ls can readily be obtained. Temperature measurement results are presented for three sample liquids: water, ethanol, and 1-propanol. The typical test duration ranges from 9 to 16 min with temperature increasing from 7°C to 10°C above the ambient temperature. Relevant liquid properties are taken from the literature, and are shown in Table 1 [32± 35]. Before each test run, the liquid system is allowed to stabilize thermally at room temperature for at least 30 min, with the magnetic stirrer keeping the ¯uid in motion. For the test, data acquisition is started, and heat is applied from the hot plate for several minutes, and then shut o. The results of temperature measurement for water and ethanol are shown in Figs. 3 and 4 respectively. In each graph, the solid line represents the LBIM temperature and the dashed line represents the reference thermistor temperature. The LBIM temperature is the raw data from the system, i.e., no averaging or smoothing is performed. Since the LBIM technique measures only changes in liquid temperature, an initial temperature is provided by the calibrated thermistor; this explains the common temperature at t 0. As can be seen, the agreement is good for the test liquids. During the heating process, a variation of 0:5±1:0°C between the LBIM and the thermistor temperature is observed, which is most likely due to temperature variations between the thermistor and interface laser beam locations. In fact, very good agreement is found at the start and end of the test, when no heat is applied, and the liquid temperature is more uniform. The sensitivity of the LBIM technique is illustrated with the temperature measurement for water, which has a dn=dT value only 25% that of the other liquids, resulting in a correspondingly weaker signal. Although there is slightly more noise on the signal for water, the result is still good. The presence of the glass interface substantially reduces noise compared to an air±water interface, which the authors found in a previous work to be very noisy for water [13]. This suggests that surface motion
and/or surface evaporation ± not present for the glass± liquid interface ± contribute signi®cantly to signal noise for an air±liquid interface. In Fig. 5, the sensitivity to small temperature changes for l-propanol is illustrated. In this case, the liquid is allowed to cool from several degrees above ambient for 60 s, with the magnetic stirrer keeping the liquid well mixed. To minimize noise ¯uctuations, a ®ve-point moving average is performed on the collected data. The LBIM and thermistor temperature agree to within 0:1°C, which suggests the technique can measure small temperature ¯uctuations as well, with appropriate data processing. For the concentration measurement, the experiment con®guration is identical to that for the temperature measurement, except that the heater is not used. To demonstrate the technique for concentration measurement methanol and l-propanol are used, as n varies linearly with concentration for this combination of liquids. The index of refraction as a function of concentration for this liquid system was measured with an
Fig. 3. Temperature measurement of water.
Fig. 5. Temperature measurement of 1-proponal over a small range.
Fig. 4. Temperature measurement of ethanol.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
7
4. Experimental uncertainty
Fig. 6. Real-time concentration measurement of a methanol±propanol solution.
independent technique [18], and found to be dnl =dC ÿ5:9 10ÿ4 l/vol%, which is the value used in Eq. (7). The liquid temperature was also measured with the thermistor during the experiment, which drifted less than 1:0°C during a given run. Results of the measurement are shown in Fig. 6. At ®rst, a known volume of l-propanol is placed in the liquid container. The re¯ected laser intensity from this pure liquid±glass interface served as the reference value, after which the concentration was varied by adding a given volume of methanol using a micropipettor and the magnetic stirrer to uniformly mix the liquids. Fig. 6(a) shows the real-time concentration variation at the interface, with the methanol concentration increased in steps of 0.4%. A 10-point average value is computed after the concentration reaches steady state, which is then taken to be the measured values (dots) shown in Fig. 6(b), in which the x-axis represents the true methanol concentration, and the y-axis represents the measured concentration from the laser technique. The ideal results should follow the line y x, as shown in the ®gure. For all results, the dierence between the measured and true concentration is less than 0.2%.
The thermistor, after calibration, has an uncertainty of 0:05°C over the calibration range of 15±50°C. Accurate values of the index of refraction of glass and liquids, and the glass temperature coecient, dn=dT , are reported in the literature, and their uncertainty is negligible. However, the liquid temperature coecients, dnl =dT , taken from the literatures vary by 10±20%. A 10% variation in dnl =dT can change the measured temperature by roughly 8%. Values of dn=dT reported by Solimini [32] were used in this work. Another source of error is noise in the photodiode ampli®er signal, which primarily arises from ¯uctuations in the laser diode and the driver. The measured laser intensity is actively stabilized, and has a measured ¯uctuation of 0.02%. The measured S=N ratio for the ampli®er is greater than 90 dB. Other noises, including vibration and small disturbances in the beam path aect the measurement as well. To quantify these contributions to noise, the temperature of an isothermal interface was measured over a 10 min interval. The re¯ectivity varied less than 0.1%, corresponding to temperature uncertainties of 0:6°C for water, and 0:1°C for ethanol and 1-propanol. A more stable laser source, e.g., by thermoelectrically cooling the laser diode, would likely reduce noise and improve temperature resolution. The laser diode is mounted on a rotation stage with an uncertainty of 0:5° in incident angle, which contributes a small error in re¯ectivity at the interface (Eq. (3a) and (3b)). The maximum laser diode power is 3 mW, and the absorption coecients of all liquids at the diode wavelength are of the order of 10ÿ3 cmÿ1 [32,33], thus liquid heating by the probe laser can be neglected. The extinction ratio of linear polarizer is greater than 105 , thus the uncertainty from light not polarized in the preferred direction is negligible as well. Considering the main sources of error, the computed root-sum-square uncertainties in temperature changes are approximately 0:6°C for water, 0:3°C for ethanol, and 0:2°C for 1-propanol, respectively. Regarding concentration measurement, there is some noise and overshoot just after the liquid concentration is changed as shown in Fig. 6(a), which is due to small concentration and/or temperature ¯uctuations as the liquid mixes near the interface. This ¯uctuation diminishes after 60 s. Another source of error is evaporation of methanol in the solution, which can reduce the true concentration during the experiment, resulting in smaller measured values near the end of the test (Fig. 6(b)). Considering all sources of error, the uncertainty in concentration is 0.2%. 5. Practical signi®cance The LBIM technique is well suited for interface temperature measurement through common glasses and silica windows. It provides a non-invasive, true interface temperature measurement. Two applications of note
8
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9
include using the LBIM technique to measure the liquid±solid temperature at an extended evaporating meniscus, e.g., hexane evaporating on a clean glass slide, and measuring temperature in a heat pipe or other closed system that has a sight glass or ¯at glass interface. Other examples include monitoring temperature or concentration changes in biological/chemical systems and measurements requiring high temporal accuracy that occur at a solid±liquid interface, such as rapid solidi®cation during thermal spray processing. A measurement of Marangoni convection induced by temperature and/or concentration changes also can be eectively made by LBIM technique. Since the spot size can be made extremely small, e.g., 20 lm, the technique can be used for temperature or concentration measurement in very small systems, such as micro heat pipes [1±3], microchannels [36], and MEMS and micro¯uidic systems [4]. For example, the temperature of 100 lm wide liquid-®lled channels etched in silicon and capped with quartz or glass can be measured with the appropriate focusing optics for a small laser spot size; such measurements are very dicult with traditional instruments, such as thermocouples or RTDs. Since the technique is based on a semiconductor laser, integrating the LBIM technique on a chip for analysis is another possibility, provided lens and/or waveguides can be constructed to direct the laser light. Another interesting application, though not explored here, is the measurement of temperature at the interface between two immiscible liquids. The physics governing the re¯ection and experimental con®guration are identical to the glass±liquid interface. Substantial liquid motion at the interface may result in increased noise; however, temperature resolution comparable to the glass±liquid case should be obtainable for reasonably quiescent liquids. 6. Conclusions This work presents a real-time, laser-based technique to measure temperature or concentration changes in liquids adjacent to a transparent solid. In this work, a probe laser beam is sent through a glass window, where a portion is re¯ected o the liquid±solid interface. Temperature or concentration changes in the liquid result in re¯ectivity changes that are monitored with a photodiode and correlated to temperature in pure liquids or concentration in liquid solutions. In most cases, temperature changes in the glass will not aect the measurement. Temperature measurement results are presented for pure water, ethanol, and 1-propanol with very good results found when compared to a calibrated, reference thermistor immersed in the liquid near the interface. Uncertainties in the measurement are approximately 0:6°C for water, 0:3°C for ethanol, and 0:2°C for 1-propanol, respectively. For binary liquid solutions, the concentration can also be measured, provided temperature changes in the liquid are small, and results for a methanol±propanol solution are found
to be in good agreement with expected results. The experimental con®guration is simple, inexpensive, and reliable. The technique is suited for a variety of applications, especially those requiring high spatial and temporal resolution or a small interrogation region.
Acknowledgements The authors gratefully acknowledge ®nancial support for this work from the National Science Foundation through contract CTS-9702644.
References [1] J.P. Longtin, B. Badran, F.M. Gerner, A one-dimension model of a micro heat pipe during steady-state operation, J. Heat Transfer 116 (3) (1994) 709±715. [2] D.A. Benson, R.T. Mitchell, M.R. Tuck, D.W. Palmer, G.P. Peterson, Ultrahigh-capacity micromachined heat spreaders, Microscale Thermophys. Eng. 2 (1) (1998) 21±30. [3] R. Hopkins, A. Faghri, D. Khrustalev, Flat miniature heat pipes with micro capilary grooves, J. Heat Transfer 121 (1) (1999) 102± 109. [4] C.M. Ho, Y.C. Tai, Micro-Electro-Mechanical-Systems (MEMS) and ¯uid ¯ows, Annu. Rev. Fluid Mech. 30 (1998) 579±612. [5] G.M. Hale, M.R. Querry, Optical constants of water in the 200nm to 200-lm wavelength region, Appl. Opt. 12 (3) (1973) 555± 563. [6] K.T.V. Grattan, The use of ®ber optic techniques for temperature measurement, Meas. Control 20 (6) (1987) 32±39. [7] D.A. Krohn, Fiber Optic Sensors ± Fundamentals and Applications, Inst. Soc. Am. (1988). [8] K.A. Wickersheim, W.D. Hyatt, Commercial applications of ®beroptic temperature measurement, Proceddings of SPIE ± The International Society for Optical Engineering Fiber Optic Sensors IV, 1267, 1990, pp. 84±96. [9] A. Wang, G.Z. Wang, K.A. Murphy, R.O. Claus, Fiber-optic temperature sensors based on dierential spectral transmittance/ re¯ectivity and multiplexed sensing systems, Appl. Opt. 34 (13) (1995) 2295±2300. [10] T.P. Pearsall, S.R. Saban, J. Booth, B.T. Beard Jr., S.R. Johnson, Precision of noninvasive temperature measurement by diuse re¯ectance spectroscopy, Rev. Sci. Instr. 66 (10) (1995) 4977± 4980. [11] J.M. Harris, N.J. Dovichi, Thermal lens calorimetry, Anal. Chem. 52 (6) (1980) 695A±706A. [12] A.N. Magunov, Laser interferometric thermometry of semiconductors and dielectrics, Instr. Exp. Technol. 41 (3) (1998) 297± 308. [13] J.P. Longtin, C.H. Fan, Laser-based temperature measurement at a liquid surface, in: 11th International Heat Transfer Conference, Kyongyu, Korea, August 1998, pp. 119±123. [14] T.L. Bergman, F.P. Incropera, W.H. Stevenson, Miniature ®ber-optic refractormeter for measurement of salinity in doublediusive thermohaline systems, Rev. Sci. Instr. 56 (2) (1985) 291± 296. [15] T.L. Bergman, D.R. Munoz, F.P. Incropera, R. Viskanta, Measurement of salinity distribution in salt-strati®ed. doublediusive systems by optical de¯ectometry, Rev. Sci. Instr. 57 (10) (1986) 2538±2542.
C.H. Fan, J.P. Longtin / Experimental Thermal and Fluid Science 23 (2000) 1±9 [16] V.A. Narayanan, R. Narayanan, Laser-based liquid prism sucrosemeter ± a precision optical method to ®nd sugar concentration, J. Chem. Edu. 74 (2) (1997) 221±223. [17] M. Capobianchi, T.F. Irvine Jr., N.K. Tutu, G.A. Greene, A new technique for measuring the ®ckan diusion coecient in binary liquid solutions, Exp. Thermal Fluid Sci. 18 (1) (1998) 33±47. [18] J.P. Longtin, C.H. Fan, Precision laser-based concentration and refractive index measurement of liquids, Microscale Thermophys. Eng. 2 (4) (1998) 261±272. [19] J.E. Geake, Linear refractometers for liquid concentration measurement, Chem. Eng. (297) (1975) 305±308. [20] A. Lozano, S.H. Smith, M.G. Mungal, R.K. Hanson, Concentration measurements in a transverse jet by planar laser-induced ¯uorescence of acetone, AIAA J. 32 (1) (1993) 218±221. [21] V.A. Vink, G.A. Sokolov, Yu.S. Fomochev, Measurement of the concentration of ¯owing liquid solutions by a heat-marker method, J. Appl. Chem. USSR 58 (2) (1985) 357±359. [22] T. Konishi, S. Naka, A. Ito, K. Saito, Transient two-dimensional fuelconcentration measurement technique, Appl. Opt. 36 (33) (1997) 8815±8819. [23] T.A. Wilson, W.F. Reed, Low-Cost, Interferometric dierential refractometer, Am. J. Phys. 61 (11) (1993) 1046±1148. [24] R.J. Harris, G.T. Johnston, G.A. Kepple, P.C. Krok, H. Mukai, Infrared thermooptic coecient measurement of polycrystalline ZnSe, ZnS, CdTe, CaF2 , and BaF2 , single crystal KCl, and T1-20 Glass, Appl. Opt 16 (2) (1977) 436±438. [25] K. Ikeda, Ultrasonic measurement of concentration in solutions by a phase-locked loop method, Jpn. J. Appl. Phys 36 (5B) (1997) 3180±3183.
9
[26] E. Hecht, Optics, Second ed, Addison-Wesley, Reading, MA, 1987. [27] I.Y. Kim, P.C. Wayner, Shape of an evaporating completely wetting extended meniscus, J. Thermophys. Heat Transfer 10 (2) (1996) 320±325. [28] T.Q. Qiu, C.P. Grigoropoulos, C.L. Tien, Novel technique for noncontact and microscale temperature measurements, Exp. Heat Transfer 6 (3) (1993) 231±241. [29] A.S. Lee, J.L. Hostetler, P.M. Norris, Temperature measurement by thermore¯ectance at near grazing angles, in: Proceedings of the 1996 ASME International Mechanical Engineering Congress and Exposition, Atlanta. GA, 1996, pp 77±82. [30] A.S. Lee, P.M. Norris, A new optical method for measuring surface temperature at large incident probe angles, Rev. Sci. Instr. 68 (2) (1997) 1307±1311. [31] F.A. Jenkins, H.I. White, Fundamentals of Optics, Fourth ed, McGraw-Hill, New York, 1976. [32] D. Solimini, Loss measurements of organic materials at 6328 A, J. Appl. Phys. 37 (1966) 3314±3315. [33] J. Stone, Measurement of the absorption of light in low-loss liquids, J. Opt. Soc. Am. 62 (3) (1972) 327±333. [34] M.E. Lusty, M.H. Dunn, Refractive indices and thermo-optical properties of dye laser solvents, Appl. Phys. B 44 (3) (1987) 193±198. [35] J. Sun, J.P. Longtin, T.F. Irvine Jr., Laser-based thermal pulse measurement of liquid thermophysical properties, Int. J. Heat Mass Transfer 44 (2001) 645±657. [36] D.B. Tuckerman, R.F.W. Pease, High-performance heat sinking for VLSI, Elec. Dev. Lett. 2 (5) (1981) 126±129. [37] I.H. Malitson, Interspecimen comparison of the refractive index of fused silica, J. Opt. Soc. Am. 55 (10) (1965) 1205±1209.