Investigation of thermocapillary convective patterns and their role in the enhancement of evaporation from pores

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Abstract

The present work investigates the evaporation process from a liquid meniscus formed in capillary tubes of various sizes. A very strong convection within the liquid phase is observed; it is proposed that the non-uniform evaporation from the meniscus leads to a temperature gradient along the interface causing a surface tension gradient, which is the driving mechanism for the convection. The observed convection is shown to be clearly correlated to the evaporation rate and the volatility of the liquid. Unlike Marangoni convection observed by imposing a temperature gradient, this is a self-induced driving gradient caused by evaporative cooling effect.

The Marangoni roll in the liquid phase has been visualized and characterized using seeding particles. It is shown in the present study that the observed convection contribute in enhancing the heat–mass transfer from the pore. The experimental results show that when the meniscus recedes inside the pore, the convection slows down and eventually stops. A theoretical model is developed to describe the temperature gradient, which establishes due to the evaporative cooling effect between the centre and the wedge of the meniscus. The results of the model show a good qualitative agreement with the experimental observations.

Introduction

In recent years, there has been an increasing interest for the phenomena involved in the evaporation of thin films because of potential applications in many two phase heat transfer devices involving phase change. Although a lot of works have been done in the area (Chu, 1986; Mirzamoghadam and Catton, 1988; Swanson and Herdt, 1992; Pratt and Hallinan, 1997; Hallinan et al., 1998; Lee et al., 1999; Wei and Ma, 2002a, Wei and Ma, 2002b; Wei et al., 2002), many open questions remain to be addressed because of the difficulties encountered in resolving and quantifying the micro-flows involved. Exploring this area and understanding the basic mechanisms involved is a key to improve the heat transfer capability of devices involving phase change in confined environments. In an early work Potash and Wayner (1972) investigated the transport processes that occurred in a two-dimensional evaporating meniscus and adsorbed thin film on a superheated flat glass plate immersed in a liquid. It was assumed that the local heat flux across the meniscus is fixed by the thermal resistance of the liquid. The work was able to conclude that a change in the profile of the meniscus brings about a pressure drop that is sufficient to circulate the fluid replacing the liquid that has evaporated and hence allows the evaporation to continue. It was also shown that in the intrinsic meniscus region fluid flow is brought about by thermocapillarity while in the evaporating thin film region the fluid flow is entirely caused by the disjoining pressure gradient between the film and the vapour. This is the force resulting from the pull of the adhesion forces between the adsorbed liquid molecules in the thin liquid film and the tube wall, i.e. liquid–solid interfacial forces, and it leads to the motion of liquid in the thin liquid film region. This result is backed up by previous research by Potash and Wayner which showed that, depending on the magnitudes of the heat and mass transfer coefficients, thermocapillary flows are unimportant in the upper region of the meniscus. Cook et al. (1981) were concerned with the heat transfer characteristics of the contact line region of an evaporating extended meniscus, given its large and efficient heat sink capabilities which could be made use of in industrial applications. Wayner and Tung (1985) studied how the bulk composition of a liquid mixture affects stationary, steady-state evaporating thin films. It was found that even small changes in the bulk composition could lead to significant changes in heat and mass transfer in the contact line region, and hence that the profile of the contact line is a strong function of both the evaporation rate and composition. It was also noted, however, that gradients in either temperature or concentration can lead to shear stresses at the interfaces and recirculation flows in the liquid which improve the stability of the meniscus in the contact line region. Khrustalev and Faghri, 1994, Khrustalev and Faghri, 1996 investigated thermocapillary convection using grooved plates heated on the bottom. They set about establishing the influence of the liquid and vapour flows resulting from this effect on heat transfer from the meniscus formed by the liquid in the groove. They found that the convection currents formed in the liquid just below the meniscus could increase the heat transfer coefficient by up to 30%. This is presumably due to the assistance that the convection currents give in bringing liquid from the bulk region right up to the interface where the heat transfer occurs, and then removing it again. They also found that if there are very large temperature differences between the wall and the vapour saturation temperature, then recirculation of the vapour could appear above the meniscus in the region where the meniscus meets the container wall. This is a very important factor in the design of micro-heat pipes because of the effects it will have on heat transfer capacity from the meniscus.Szymczyk (1991) and Molenkamp (1998) showed that in containers with diameter greater than a few millimeters, Rayleigh convection or buoyancy dominates the convection process. Marangoni and Rayleigh convections are always coupled when a temperature difference exists inside a media with a free surface in g-environment. However, Rayleigh convection plays a more important role when the flow characteristic dimension is large; instead, Marangoni convection is predominant at smaller scales.The evaporation of a liquid meniscus formed in a capillary tube is the case investigated in the present paper. The liquid evaporates essentially in the thin film region of the meniscus in contact with the tube wall and we tried to quantify the phenomena involved. The focus of the present work is to investigate the evaporation in small capillary tubes with internal diameter ranging from 200 to 900 μm of volatile liquids (ethanol, methanol, acetone and n-pentane). The meniscus region in the liquid phase has been the object of the study. The convection roll has been characterized using tracers and the spinning frequency was measured. The evaporation rate was monitored following the receding meniscus. The objective is to correlate the evaporation process to the observed convection and to demonstrate how the latter contribute to the heat–mass transfer enhancement from the pore.

Section snippets

Experimental apparatus and procedure The borosilicate glass capillaries used in the present investigation were bought from Drummund Scientific. These were cleaned using an ultrasonic bath with de-ionized water for 30 min at 65 °C and dried in an oven at 60 °C for 2 h. The tubes were stored in a clean vial and used within few days. To avoid contamination, capillaries were filled from the end opposite to that where the meniscus was positioned for observation.The roughness of the internal tube surface was characterized using a

Results In Experiment (1) (see Fig. 3) the meniscus moves inside the pore as evaporation takes place. The meniscus moves in two distinct stages; first, it changes shape but remains stuck at the capillary mouth due to the strong adhesion forces. When the receding apparent contact angle is reached, it starts to recede inside the pore. As the meniscus recedes evaporation continues however, vapour has to diffuse to the mouth of the capillary. As a result, the partial vapour pressure at the liquid–vapour

Theoretical model The thermocapillary motion observed in our experiments is due to a thermal gradient established along the meniscus interface, which takes its origin in the strong evaporation occurring at the triple line region while the centre of the spherical cap undergoes a weaker evaporation. Evaporation takes place at the interface then vapour diffuses to the mouth of the capillary. In the following, we will attempt to calculate the temperature at the triple line region by a heat diffusion model. The

Discussion The evaporation along the meniscus formed inside a confined space such as a pore is not uniform. It is larger near the wall than in the middle of the capillary (Sartre et al. (2000)). The results about the evaporation rate reproduced in Fig. 8 confirm this assumption. Indeed if the evaporation was uniform along the meniscus, we should have a linear relation between the evaporation rate and the meniscus surface area, the latter being proportional to the square of the tube radius. The evaporation

Conclusion Some fundamental aspects of the evaporation of volatile liquids from a meniscus formed in a confined space such as a capillary tube have been experimentally investigated. This is critical for a wide range of technological applications involving phase change in confined environment. The complex phenomena taking place in such applications can be modelled investigating a far simpler case such as the evaporation from a meniscus formed in a capillary tube. Four different liquids (ethanol, methanol,

Acknowledgements The authors acknowledge the Engineering and Physical Sciences Research Council support through Grant/N02122. Prof. W. Easson (The University of Edinburgh) help to access PIV facility is recognized.

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hi

Capillary convection, thermocapillary convection, and Marangoni convection are related phenomena but not exactly the same.

Capillary Convection: Capillary convection refers to the motion of fluids in small capillary tubes or narrow channels due to capillary forces. It occurs when the surface tension of the liquid dominates over other forces, such as gravity. Capillary convection is driven by the pressure gradient caused by the curvature of the liquid meniscus at the liquid-air interface in the capillary.

Thermocapillary Convection: Thermocapillary convection, also known as thermo-capillary convection or thermocapillary flow, refers to fluid motion induced by surface tension variations caused by temperature gradients. When a temperature gradient exists at the interface between two immiscible fluids or between a fluid and a solid surface, it can lead to variations in surface tension. These surface tension variations can drive fluid motion, resulting in thermocapillary convection.

Marangoni Convection: Marangoni convection, also known as the Marangoni effect, occurs due to surface tension gradients in a liquid caused by variations in surface concentration of a surface-active substance (surfactant) or temperature differences. When there is a gradient in surface tension, it induces fluid motion in the liquid to equalize the surface tension. This convection can be observed in systems such as thin liquid films, liquid droplets, or liquid layers with surfactants.

Respected Suresh Ahuja

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Respected Amjed A. Kadhim

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