Journal of Colloid and Interface Science 325 (2008) 440–446 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.elsevier.com/locate/jcis Sessile droplet spread into porous substrates—Determination of capillary pressure using a continuum approach Homayun K. Navaz a,∗ , Bojan Markicevic a , Ali R. Zand a , Yuri Sikorski a , Ewen Chan a , Matthew Sanders a , Terrence G. D’Onofrio b a Kettering University, Department of Mechanical Engineering, 1700 3rd Avenue, Flint, MI 48504, USA b Department of the Army, Edgewood Chemical Biological Center (ECBC), Aberdeen Proving Ground, MD 21010, USA article info abstract Article history: Received 26 February 2008 Accepted 18 April 2008 Available online 21 May 2008 Keywords: Chemical warfare agents Depth penetration Permeation Non-dimensional curves The problem of primary and secondary spread of sessile droplets into a porous substrate was formulated and solved numerically. A continuum approach for liquid- and gas-phases was utilized. The governing equations were discretized by finite difference method and solutions for both phases are obtained by marching in time using the fourth-order Runge–Kutta integration algorithm. This type of spread is a purely momentum-driven process that is caused by gradients both in capillary pressure and in saturation. A methodology was developed for finding the capillary pressure function for sessile droplets, which has not been described before. This approach was based on experimental data for a liquid/porous medium pair, and using universal, non-dimensional curves. Similar solutions were generated by the continuum approach and validated using experimental results. The model shows qualitative and quantitative agreement with experimental data. Although the focus of this work was to understand the interaction of chemical warfare agents with porous media, the approaches are universal and can be applied to determining the spread of any liquid into a porous material.  2008 Elsevier Inc. All rights reserved. 1. Introduction There are a variety of engineering applications in which the spread of the fluid phase within a porous medium occurs, ranging from oil recovery and other natural formation flows to compos- ites, printing, polymer filling, and fuel cells. One of the problems of interest is to predict the spread of sessile droplets into a porous substrate that can occur when a liquid is disseminated into the environment. Specific examples include pesticide spray and an at- tack from chemical warfare agents. Understanding the interaction of a liquid with a porous material is critical for determining the fate of toxic chemicals and has environmental, defense, and home- land security implications. The studies documented here have ap- plication to form an important fundamental basis for detection, protection, decontamination, and remediation following a chemical spill or attack. Although the focus of this work was to understand the interaction of chemical warfare agents with porous media, the approaches are universal and can be applied to determining the spread of any liquid into a porous material. Several chemical and physical processes determine the ulti- mate fate of a droplet, including the spread and penetration into a porous substrate, evaporation, and chemical reactions. The co- * Corresponding author. Fax: +1 (810) 762 7860. E-mail address: hnavaz@kettering.edu (H.K. Navaz). existence of all these phenomena complicates the prediction of the environmental fate of the droplet [1–3]. The droplet fate may further be influenced by droplet deposition velocity [4] during its impact onto the surface of a porous material. Following deposition onto a porous surface, the droplet spread is momentum-driven by the capillary and hydrostatic pressures. For volatile liquids, evap- oration occurs both from the surface of the droplet outside the porous medium, and from inside the pores where liquid phase re- sides. Some liquids may go through a solidification process that will eventually make less liquid phase available to the pores [5–7]. In addition, chemical reactions in either the vapor or liquid phases may exist that can contribute to the fate of droplets [8,9]. Spread dynamics is influenced by the porous medium thickness, where two- and three-dimensional flows occur. For thin porous media, the liquid flows in a radial direction and can be modeled by the method of ‘common-lines’ [10–12]. In these solutions, there are only two parameters that need to be determined experimentally. In thick porous media, the flow becomes three-dimensional, although a cylindrical symmetry has been assumed in the past [13]. This solution was compared with the experimental results of Denesuk et al. [14] and a good agreement was found. Holman et al. [15] had shown that the surface spread is a function of the permeability of the porous material; the droplet penetration dynamics can be dominated by the surface spread. In all these solutions, the wetted volume was assumed to be fully saturated (s = 1), with a clear in- 0021-9797/$ – see front matter  2008 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2008.04.078