Use of infrared thermography for the study of evaporation in a square capillary tube

https://doi.org/10.1016/j.ijheatmasstransfer.2010.01.008Get rights and content

Abstract

In this paper we report experimental results on evaporation of a volatile wetting liquid in a capillary tube of square internal cross section, when conditions are such that liquid films develop along the tube internal corners under the effect of capillary forces, as the bulk meniscus recedes inside the tube. Combining an infrared thermography technique with visualizations by ombroscopy makes it possible to determine the time-space evolution of the temperature minimum on the capillary outer surface together with the bulk meniscus position within the tube. When the tube is held horizontal, the temperature minimum stays at the tube entrance and the evaporation rate reaches a stationary value. In contrast with the horizontal case, the position of the temperature minimum changes when the bulk meniscus has sufficiently receded inside the tube when the tube is vertical and opened at the top. The rate of evaporation then decreases significantly. This is explained by the thinning of the corner films in the vertical tube entrance region, under the conjugated effects of gravity and viscous forces up to the depinning of the films from the tube entrance. When the tube is held horizontal, the capillary effects are dominant and the film thickness remains essentially constant in the tube entrance region. This analysis is supported by a simple model of liquid flow within the corner films.

Introduction

Evaporation from a meniscus plays an important role in many applications such as capillary pumped loops, heat pipes, fuel cells and drying of porous media. In this context, the study of evaporation of a liquid confined in a single microchannel can be regarded as a first step before more complex situations such as, for example, networks of interconnected capillaries [1]. In recent years, evaporation driven by mass transfer has been studied experimentally in microchannels of rectangular cross section [2], as well as in capillary tubes of square cross section [3]. All these works, see also [4], indicate that evaporation in a channel with corners is much faster than in a channel of circular cross section. This is attributed to the effects of “thick” liquid films trapped along the channel corners under the action of capillary effects. Because of these films, modelling of evaporation in a channel of polygonal cross section is significantly more involved than for the classical circular tube. A model of liquid flow with evaporation in a channel of square cross section was presented in [5] in relation with the modelling of drying of porous media. Depending on the competition between the capillary, viscous and gravity forces, various evaporation regimes can be distinguished. The regime dominated by the capillary forces was mainly considered in [6], whereas a modelling of other regimes was presented in [7]. Tubes of triangular or hexagonal cross sections have been considered as well, see [8] where first results on the influence of contact angle are also presented. However, there is a lack of experimental data and, consequently, of quantitative comparisons between the available models and experimental data. In this context, the general objective of the present work is to contribute to fill this gap by combining careful experimental studies with a proper modelling. First results in this direction were reported in [9] but only for a tube in vertical position. Here we consider also the case of a tube in a horizontal position and use the IR thermography technique to analyze in more details the evaporation process. A preliminary version of the present paper was presented in [10]. Here much more details are given, together with additional experimental results.

More specifically, we study evaporation in capillary tubes of square or circular cross section, the internal side length of which is 1 mm, a value lower than the capillary length. As discussed in several previous works (see e.g. [8] and references therein) and sketched in Fig. 1, thick liquid films can be trapped by capillarity along the four internal corners of a square tube as the bulk meniscus recedes inside the tube under the effect of evaporation. These corner films provide paths for the liquid between the receding bulk meniscus and the entrance of the tube. The liquid is transported within the films under the action of the pressure gradient induced by the meniscus curvature variation along the films. This effect is therefore termed capillary pumping. As a result, the phase change occurs preferentially at the entrance of the tube as long as the corner liquid films remain attached at the tube entrance. This very efficient transport mechanism of liquid by the films is naturally absent in a circular tube, in which the transport mechanism between the receding bulk meniscus and the tube entrance is the poorly efficient molecular diffusion in the gas phase (this case is usually referred to as the “Stefan tube” problem [11]). This explains why evaporation can be several orders of magnitude faster in a tube with corners compared to a circular tube (see [8]). Adsorbed thin films may also be present over the internal surfaces of the tube not covered by the thick films. However, the hydraulic conductivity of the adsorbed films is very small compared to that of the thick films in tubes of internal side length much greater than the typical thickness of adsorbed films (a few nanometers), as considered here. Hence the effect of the adsorbed films can be neglected in the present case. As discussed in [8], the wetting contact angle of the liquid must be sufficiently low for the corner films to develop. The value of the contact angle below which the corner films can exist depends on the corner internal angle. For a tube of square cross section (corners internal angle = 90°), the liquid contact angle θ must be less than 45°. The results presented in this paper have been obtained for evaporation of hexane in borosilicate glass tubes, i.e. for an almost perfectly wetting liquid (θ0°). Evaporation is self-induced in a stagnant air atmosphere at ambient temperature and atmospheric pressure. Hence, there is no external forced convective flow imposed near the tube entrance.

The paper is organized as follows. The experimental set-up and techniques are presented first. An ombroscopy visualization technique is used to track the volume of liquid contained in the capillary during evaporation and thus to measure the evaporation rate. A distinguishing feature of the present work is to couple this rather standard ombroscopy technique with an infrared (IR) thermography technique. The use of the IR technique in the present context is detailed in the third section of the paper. Then, in Section 4, we present some representative results illustrating the interest of combining the two types of visualizations for analyzing evaporation in capillary tubes. The paper ends with an analysis of the results using a simple model of liquid flows within the corner films.

Before going into the details of the present work, it is interesting to notice that an IR technique has already been used for studying evaporation in capillary tubes. In [12], IR measurements of temperature along the meniscus interface of volatile liquids in capillary tubes of circular cross section were reported. Interestingly, these measurements show that the temperature is not uniform along the meniscus interface and lower at the meniscus triple line where the evaporation rate is greater than in the middle of the meniscus. Hence the IR technique was shown to be a valuable tool for detecting the temperature sink effect associated with evaporation, a feature we also use in the present study. However, the results reported in [12] were for circular tubes (as opposed to square tubes in the present case) and for a stationary meniscus located at the tube entrance (as opposed to receding ones in the present case).

Section snippets

Experimental set-up

The 10cm long square capillary tubes used in the present study are made of borosilicate glass: the internal side length and the wall thickness of the tubes are 1mm and 0.2mm respectively (Vitrocom). A tube with a circular cross section (internal diameter 1mm, wall thickness 0.2mm) is also used as a reference case for some experiments.

A capillary tube is glued by an epoxy resin directly to a syringe tip. The syringe is placed on a precision syringe pump (PHD 2000, Harvard Apparatus), allowing

Infrared thermography

Measuring accurately the temperature, and its spatial variations, at the outer surface of the capillary tube requires to analyse the different contributions of the radiative flux impinging on the IR camera detector when imaging the capillary tube on one hand and the black body on the other hand (during calibration). The analysis detailed below in Section 3.1 takes into account the effects of “unwanted” fluxes and permits to set-up the method used to process the IR images. Then, the exploitation

Experimental results

In this section, some experimental results obtained using the experimental set-up and techniques detailed above are presented. Typical evolutions of the bulk meniscus position z0 as a function of time, in a capillary tube positioned either vertically or horizontally, are shown in Fig. 5. When the tube is positioned horizontally (crosses in Fig. 5), the bulk meniscus position z0 evolves linearly with time: the evaporation rate, which is proportional to dz0/dt, is therefore constant (note the

Discussion

Qualitatively, the interpretation of the experimental results is as follows. In the horizontal case, it is conjectured that the thickness of the corner film remains essentially constant whatever the position of the bulk meniscus within the tube is. As a result, the phase distribution at the tube entrance does not change significantly as the bulk meniscus recedes. Since the evaporation rate is controlled by what happens at the tube entrance region, a constant evaporation rate must follow from

Conclusion

In the present work, the use of an IR thermography technique, coupled with visualizations by ombroscopy, enabled us to highlight the dynamic of thick liquid corner films as well as their impact on the evaporation process. A specific infrared thermography data processing based on the proper consideration of all important radiative fluxes has been developed in order to measure the temperature of the capillary tube external wall with a good accuracy. This permits to track the bulk meniscus

Acknowledgment

Financial support from GIP ANR “Intensifilm” (Project ANR-06-BLAN-0119-01) is gratefully acknowledged.

References (21)

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