Wicking and Evaporation of Liquids in Porous Wicks: A Simple Analytical Approach to Optimization of Wick Design Saman Beyhaghi Laboratory for Flow and Transport Studies in Porous Media, Dept. of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211 Sandrine Geoffroy Universit e de Toulouse; UPS, INSA; LMDC (Laboratoire Mat eriaux et Durabilit e des Constructions); 135, avenue de Rangueil; F-31077 Toulouse Cedex 04, France Marc Prat Universit e de Toulouse, INPT, UPS, IMFT, Avenue Camille Soula 31400, Toulouse, France, and CNRS, IMFT 31400, Toulouse, France Krishna M. Pillai Laboratory for Flow and Transport Studies in Porous Media, Dept. of Mechanical Engineering, University of Wisconsin-Milwaukee, Milwaukee, WI 53211 DOI 10.1002/aic.14353 Published online February 12, 2014 in Wiley Online Library (wileyonlinelibrary.com) Wicking and evaporation of volatile liquids in porous, cylindrical wicks is investigated where the goal is to model, using simple analytical expressions, the effects of variation in geometrical parameters of a wick, such as porosity, height and bead-size, on the wicking and evaporation processes, and find optimum design conditions. An analytical sharp-front flow model involving the single-phase Darcy’s law is combined with analytical expressions for the capillary suction pressure and wick permeability to yield a novel analytical approach for optimizing wick parameters. First, the optimum bead- radius and porosity maximizing the wicking flow-rate are estimated. Later, after combining the wicking model with evaporation from the wick-top, the allowable ranges of bead-radius, height and porosity for ensuring full saturation of the wick are calculated. The analytical results are demonstrated using some highly volatile alkanes in a polycarbonate sintered wick. V C 2014 American Institute of Chemical Engineers AIChE J, 60: 1930–1940, 2014 Keywords: wick design, porous media, wicking, imbibition, evaporation, Darcy’s law, bead radius, porosity, optimiza- tion, sintered wick Introduction Wicking is the spontaneous transport of a liquid through a porous medium as a result of capillary suction taking place at liquid-gas interfaces at the surface or within the porous medium. Wick action is present in many engineering applica- tions, such as heat pipes and capillary pumped loops, 1,2 propel- lant management devices (PMD) used in spacecraft tanks, 3 as well as in other systems made of porous sheets. 4 This is also an important phenomenon in relation with salt weathering issues in building physics, e.g., Puyate and Lawrence. 5 In almost all these examples, wicking takes place in conjunction with evapo- ration at the liquid-gas menisci present in the system. Several wick-based systems are designed by consumer prod- ucts companies to disperse vapors of volatile perfume or insect- repellent liquids in a room. These systems, which motivate this study, also work due to the combined action of wicking and evaporation. As sketched in Figure 1a, the wick top in such a system is usually exposed to the air so that the volatile liquid can slowly diffuse from the liquid-air interface present on top of the wick into the room air. Note that the top surface of the wick could be in level with, higher than, or lower than the sur- rounding casing. The evaporation phenomenon is generally improved by using local heaters placed around the wick top region so as to increase the saturation vapor pressure. As the other systems mentioned previously, this type of system poses interesting engineering and scientific questions. In particular, we are interested in the questions concerning the design and optimization of the system. Questions such as the range of parameters allowing the system to operate with a fully liquid-saturated wick, or the parameters maximizing the wick action, are of interest in many systems. In this arti- cle, those questions are addressed for the particular system sketched in Figure 1a. It should be clear, however, that many of the results obtained in the course of the study of this particular type of systems are of broader interest. The wicks used in consumer products applications for dis- charging perfume or other volatile compounds in the air are generally made by sintering. Sintering is a common indus- trial process for making porous wicks. For example, wicks Correspondence concerning this article should be addressed to K. M. Pillai at Krishna@uwm.edu. V C 2014 American Institute of Chemical Engineers 1930 AIChE Journal May 2014 Vol. 60, No. 5