Evaporation of a thin droplet on a thin substrate with a high thermal resistance

被引：33
作者：
Dunn, G. J. [1 ]
Wilson, S. K. [1 ]
Duffy, B. R. [1 ]
Sefiane, K. [2 ]
机构：
[1] Univ Strathclyde, Dept Math, Glasgow G1 1XH, Lanark, Scotland
[2] Univ Edinburgh, Sch Engn, Edinburgh EH9 3JL, Midlothian, Scotland
来源：
PHYSICS OF FLUIDS | 2009年 / 21卷 / 05期
基金：
英国工程与自然科学研究理事会;
关键词：
drops; evaporation; heat transfer; SESSILE; MODEL; FLOW;
D O I：
10.1063/1.3121214
中图分类号：
O3 [力学];
学科分类号：
08 ; 0801 ;
摘要：
A mathematical model for the quasisteady evaporation of a thin liquid droplet on a thin substrate that incorporates the dependence of the saturation concentration of vapor at the free surface of the droplet on temperature is used to examine an atypical situation in which the substrate has a high thermal resistance relative to the droplet (i.e., it is highly insulating and/or is thick relative to the droplet). In this situation diffusion of heat through the substrate is the rate-limiting evaporative process and at leading order the local mass flux is spatially uniform, the total evaporation rate is proportional to the surface area of the droplet, and the droplet is uniformly cooled. In particular, the qualitative differences between the predictions of the present model in this situation and those of the widely used "basic" model in which the saturation concentration is independent of temperature are highlighted.
引用
收藏
页数：7
相关论文
共 25 条
[1]   INFLUENCE OF EVAPORATION ON CONTACT-ANGLE [J].
BOURGESMONNIER, C ;
SHANAHAN, MER .
LANGMUIR, 1995, 11 (07) :2820-2829
[2]   Experimental investigation of the effect of thermal properties of the substrate in the wetting and evaporation of sessile drops [J].
David, S. ;
Sefiane, K. ;
Tadrist, L. .
COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, 2007, 298 (1-2) :108-114
[3]   Contact line deposits in an evaporating drop [J].
Deegan, RD ;
Bakajin, O ;
Dupont, TF ;
Huber, G ;
Nagel, SR ;
Witten, TA .
PHYSICAL REVIEW E, 2000, 62 (01) :756-765
[4]   Capillary flow as the cause of ring stains from dried liquid drops [J].
Deegan, RD ;
Bakajin, O ;
Dupont, TF ;
Huber, G ;
Nagel, SR ;
Witten, TA .
NATURE, 1997, 389 (6653) :827-829
[5]   A mathematical model for the evaporation of a thin sessile liquid droplet: Comparison between experiment and theory [J].
Dunn, G. J. ;
Wilson, S. K. ;
Duffy, B. R. ;
David, S. ;
Sefiane, K. .
COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, 2008, 323 (1-3) :50-55
[6]   The strong influence of substrate conductivity on droplet evaporation [J].
Dunn, G. J. ;
Wilson, S. K. ;
Duffy, B. R. ;
David, S. ;
Sefiane, K. .
JOURNAL OF FLUID MECHANICS, 2009, 623 :329-351
[7]   Experimental study of the evaporation of a sessile drop on a heat wall. Wetting influence [J].
Grandas, L ;
Reynard, C ;
Santini, R ;
Tadrist, L .
INTERNATIONAL JOURNAL OF THERMAL SCIENCES, 2005, 44 (02) :137-146
[8]   Evaporating drops of alkane mixtures [J].
Guena, G. ;
Poulard, C. ;
Cazabat, A. M. .
COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, 2007, 298 (1-2) :2-11
[9]   The leading edge of evaporating droplets [J].
Guena, G. ;
Poulard, C. ;
Cazabat, A. M. .
JOURNAL OF COLLOID AND INTERFACE SCIENCE, 2007, 312 (01) :164-171
[10]   Evaporation of sessile liquid droplets [J].
Guena, G. ;
Poulard, C. ;
Voue, M. ;
De Coninck, J. ;
Cazabat, A. M. .
COLLOIDS AND SURFACES A-PHYSICOCHEMICAL AND ENGINEERING ASPECTS, 2006, 291 (1-3) :191-196
123