Analysis of the effects of evaporative cooling on the evaporation of liquid droplets using a combined field approach

Abstract

During liquid evaporation, the equations for the vapor concentration in the atmosphere and for the temperature in the liquid are coupled and must be solved in an iterative manner. In the present paper, a combined field approach which unifies the coupled fields into one single hybrid field and thus makes the iteration unnecessary is proposed. By using this approach, the influences of the evaporative cooling on the evaporation of pinned sessile droplets are investigated, and its predictions are found in good agreement with the previous theoretical and experimental results. A dimensionless number Ec which can evaluate the strength of the evaporative cooling is then introduced, and the results show that both the evaporation flux along the droplet surface and the total evaporation rate of the droplet decrease as the evaporative cooling number Ec increases. For drying droplets, there exists a critical value EcCrit below which the evaporative cooling effect can be neglected and above which the significance of the effect increases dramatically. The present work may also have more general applications to coupled field problems in which all the fields have the same governing equation.

Evaporation of binary mixtures and precision measurement by crystal resonator

“…Since E c is around 1, which enters the regime that evaporation cooling may considerably reduce the saturation pressure and thus reduce the evaporative flux. According to the studies of evaporative cooling effect on a sessile methanol droplet, the range of temperature difference within the droplet is about 2 degree kelvin [42], which corresponds to $10 to 15% reduction of evaporative flux [41], and $3% increase of the local viscosity. By neglecting evaporative cooling, our modeling results would have over-predicted (instead of under-predicted) the evaporation rate.…”

“…where the Fourier number F o ¼ sa ð'Þ =d 2 , Brinkman number B r ¼ l ð'Þ U 2 =ðj ð'Þ MT ð'Þ Þ, and the Evaporation cooling number [41] E c ¼ L v D ðgÞ c 1 =j ð'Þ . The parameters T ð'Þ and u are scaled temperature and velocity fields, respectively, and q ðgÞ M is the scaled methanol vapor mass concentration at the interface.…”

Combined effects of underlying substrate and evaporative cooling on the evaporation of sessile liquid droplets

“…50 If we consider T 1 , T 2 , and T 3 as the temperature in the air, in the liquid and in the substrate, respectively, the abovementioned eqn (1)-(9) represent a heat conduction field in the surrounding air with thermal conductivity of E c , in the liquid droplet with a thermal conductivity of 1, and in the substrate with thermal conductivity of k R . The larger the value of E c , the more significant the negative feedback effect of evaporative cooling, which reduces the evaporation rate.…”

“…50 The contact angle y indicates the spatial configuration of the droplet. The number E c characterizes the strength of the evaporative cooling and its value is determined only by the thermal properties of the liquid and the atmosphere.…”

“…50 Because the heat supply to the droplet surface is closely related to the thermal properties of the substrate, it can thus exert remarkable influences on the evaporation of the droplet. 50 Because the heat supply to the droplet surface is closely related to the thermal properties of the substrate, it can thus exert remarkable influences on the evaporation of the droplet.…”