Effect of Dynamic Contact Angle on Single Bubbles during Nucleate Pool Boiling

Nucleate pool boiling at low heat flux is typically characterized by cyclic growth and departure of single vapor bubbles from the heated wall. It has been experimentally observed that the contact angle at the bubble base varies during the ebullition cycle. In the present numerical study, dynamic advancing and receding contact angles obtained from experimental observations are specified at the base of a vapor bubble growing on a wall. The complete NavierStokes equations are solved and the liquid-vapor interface is captured using the level-set technique. The effect of dynamic contact angle on the bubble dynamics and vapor removal rate are compared to results obtained with static contact angle. The results show that bubble base exhibits a slip/stick behavior with dynamic contact angle though the overall effect on the vapor removal rate is small. Higher advancing contact angle is found to increase the vapor removal rate. INTRODUCTION Bubbles nucleate from the cavities at the wall during nucleate pool boiling. During its growth period, the bubbles stay attached to the wall at the base. The bubble base diameter increases initially, then stays constant for a period of time and finally decreases as the bubble departs. Intense evaporation is believed to take place near the bubble base that results in very high wall heat flux. The liquid-vapor interface at the bubble base experiences dynamic advancing and dynamic receding contact angles at the wall during bubble growth and 1 departure stages. The dynamic contact angle is different from static or equilibrium contact angle, which depends on the liquid, vapor and the material of the solid surface. Use of a single contact angle may not be justified, as even under equilibrium conditions, the static advancing contact angle is different (larger) from the static receding contact angle. Figure 1 shows a nucleating bubble at the wall during pool boiling [1]. The frame on the left shows a bubble just after nucleation. The bubble base is expanding in this case, and the contact angle at the wall is receding. The frame on the right shows the same bubble just prior to departure. The bubble base is contracting in this case and the contact angle is advancing. It can be seen from the figures that the advancing contact angle is larger than the receding one. Receding contact angle Advancing contact angle Fig. 1 – Advancing and receding contact angle Copyright © 2004 by ASME The surface tension force acting at the bubble base depends on the dynamic contact angle. This affects the overall bubble dynamics and the wall heat transfer. The present numerical calculations are performed to study the effect of the dynamic contact angle at the bubble base as compared to a static contact angle. LITERATURE REVIEW A brief literature survey is presented to review some of the papers dealing with static and dynamic contact angles associated with evaporating liquid-vapor interface on a heated surface. Schulze et al. [2] empirically determined the equilibrium contact angle for certain low energy solids and pure liquids. They varied the roughness of the polymer solid surfaces and used a sessile drop experiment to measure the advancing and receding contact angles. The contact angle hysteresis was assumed to be dependent on the surface roughness and the equilibrium contact angle was linearly approximated setting the hysteresis to be zero. Shoji and Zhang [3] experimentally measured contact angle of water on copper, glass, aluminum and Teflon surfaces. The receding contact angle was found to decrease with surface roughness while the advancing contact angle remained almost constant. They also developed a model for evaluating surface wettability by introducing a surface roughness parameter and a surface energy parameter. They concluded that the advancing and receding contact angles are unique for any liquid-solid combination and the surface condition. Kandlikar and Stumm [4] developed a model to analyze the forces acting on a vapor bubble during subcooled flow boiling. They also measured experimentally the upstream and downstream contact angles as a function of flow velocity. They found that the upstream and downstream contact angles went through a maxima and minima respectively with increase in flow velocity. Brandon and Marmur [5] simulated contact angle hysteresis for a two-dimensional drop on a chemically heterogeneous surface. The intrinsic contact angle was assumed to vary periodically with distance from the center of the drop. The changes in free energy of the system, the contact angle and the size of the base of the drop were calculated with increase and decrease in volume of the drop. The authors concluded that the quasi-static analysis of the dependence of the free energy of the system on the drop volume could explain the contact angle hysteresis measurements. Ramanujapu and Dhir [6] studied dynamic contact angle at the base of a vapor bubble during nucleate pool boiling. A silicon wafer was used as the test surface with micromachined cavities for nucleation. The bubble base diameter was measured as a function of time and the interface velocity was calculated. The results show that though the contact angle varied during different stages of bubble growth, it was weakly dependent on the interface velocity. They concluded that contact angle could be determined primarily based on the sign of the interface velocity. 2 Son et al. [7] carried out complete numerical simulation of a single bubble on a horizontal surface during nucleate pool boiling. They assumed a static contact angle at the bubble base and accounted for the microlayer evaporation by including the disjoining pressure effect. The results showed that the departing bubble became larger with increase in contact angle. Sobolev et al. [8] measured dynamic contact angle of water in thin quartz capillaries with radii varying from 200 to 40 nm. The value of dynamic contact angle was found to depend on the degree of surface coverage by the absorbed water molecules. At velocities lower than 5 microns/s, the dynamic contact angle was found to be linearly dependent on the velocity whereas, at higher velocities, it was found to be rate independent. Kandlikar [9] developed a theoretical model of CHF with dynamic receding contact angle. The model was based on the assumption that CHF occurs when the force due to the momentum change pulling the bubble interface into the liquid along the heated surface exceeds the sum of the forces from surface tension and gravity holding the bubble. He assumed the dynamic receding contact angle for various liquid-solid systems. The model indicated decrease in CHF with increase in contact angle. Kandlikar and Steinke [10] made photographic observations of liquid droplets impinging on a heated surface. They studied the effects of surface roughness and surface temperatures on the dynamic advancing and receding contact angles. They found that the equilibrium contact angle first decreased and then increased with surface roughness. The dynamic advancing and receding contact angles were found to be equal for high wall superheats at critical heat flux conditions. Barazza et al. [11] determined advancing contact angle during spontaneous capillary penetration of liquid between two parallel glass plates by measuring the transient height attained by it. The data was fitted into an averaged NavierStokes model integrated over a cross section away from the liquid front. The calculated contact angle values failed to predict the dependence of the dynamic contact angle on velocity as suggested by classical hydrodynamics and molecular theories in the nonwetting case. Lam et al. [12] carried out dynamic one-cycle and cyclic contact angle measurements for different solids and liquids. Four different patterns of receding contact angle were obtained: (a) time dependent receding contact angle; (b) constant receding contact angle; (c) stick/slip pattern and (d) no receding contact angle. The authors identified liquid sorption and retention as the primary cause of contact angle hysteresis. Abarajith and Dhir [13] studied the effect of various contact angles on single bubbles during nucleate pool boiling. The contact angle was kept fixed throughout the bubble growth and departure process. The effect of microlayer evaporation was included in the study. The contact angle was related to the magnitude of the Hamaker constant, which was found to change with surface wettability. Copyright © 2004 by ASME Kandlikar and Kuan [14] experimentally studied an evaporating meniscus on a smooth heated rotating copper surface. They studied the size and shape of the meniscus and its receding and advancing contact angles. The meniscus is comparable to a nucleating bubble base near its contact line region. The results show that for a stationary meniscus, the contact angle was almost independent of the flow rate and heat flux. In the case of a moving meniscus, large difference was observed between the advancing and receding contact angles.