Reflectivity-based evaluation of the coalescence of two condensing drops and shape evolution of the coalesced drop Shripad J. Gokhale, 1 Sunando DasGupta, 2 Joel L. Plawsky, 1, * and Peter C. Wayner, Jr. 1,† 1 The Isermann Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, USA 2 Department of Chemical Engineering, Indian Institute of Technology, Kharagpur, PIN 721302, India (Received 14 May 2004; revised manuscript received 25 August 2004; published 30 November 2004) Image analyzing interferometry is used to study the details of the evolving shapes and coalescence of two condensing drops of 2-propanol on a quartz surface. The measured thickness profiles give fundamental insights into the transport processes within the drops before and after coalescence and the evolution of the coalesced drop from asymmetric to symmetric shape. The results indicate that the constant value of the adsorbed film thickness between the drops and profiles of the local thickness, slope angle, curvature, and curvature gradient govern the pressure fields in the coalescing drops. The shape evolution after coalescence is found to be driven by the capillary forces within the drop. Using the experimental data, we find that the calculations of the average shear stress for the fluid flow between the drops, the decrease in the interfacial excess energy, and the positions of the center of mass of the drops explain the physics of the coalescence phenomenon. However, the flow field is found to be complex because the pressure field indicates that there are complicated flows within the drop. DOI: 10.1103/PhysRevE.70.051610 PACS number(s): 68.03.Cd, 47.55.Dz, 68.37.-d, 68.03.Fg I. INTRODUCTION The coalescence of drops is fundamental to the under- standing of a wide range of applications such as ink jet print- ing, emulsion formation, oil recovery, polymer blending, phase change heat transfer in dropwise condensation, etc. Previous studies of this subject have mainly analyzed the dynamics and external flow fields during coalescence [1–3], draining of the thin film between the drops and the role of intermolecular interactions [4–9], and the kinetics of relax- ation of the drop [1,2,10]. Andrieu et al. [1] experimentally observed the coalescence of water drops on a silane-modified glass surface and explained the observed relaxation time of the drops using a model based on the phase change near the contact line region. Menchaca-Rocha et al. [2] analyzed the effect of surface tension on the coalescence of mercury drops and compared their results with numerical calculations based on the Navier-Stokes equation. The effects of London–van der Waals forces, electrostatic interactions, and surface forces on the thinning of the film between the coalescing drops and on the coalescence time have been studied by Li [5], Deshikan and Papadopoulos [6], and Ivanov et al. [8]. Herein, we study experimentally the effects of the thickness, slope angle, curvature, apparent contact angle, and pressure fields in the contact line region, during low rates of conden- sation, on the shape evolution of condensing and coalescing drops due to capillary flow. In the experimental system [Fig. 1(a)], two drops of a partially wetting fluid (2-propanol) grow on a quartz surface during condensation and coalesce when they touch. A sche- matic of a drop is sketched in Fig. 1(b). In a 1957 seminal paper, Derjaguin and Zorin [11] demonstrated that a thin adsorbed flat film of n-propyl alcohol became unstable at the saturation point at a film thickness of approximately 5.5 nm. Above this thickness, they viewed “microdewdrops” on an adsorbed layer. Therefore, the adsorption isotherm near the saturation point is very complex for a polar fluid [11]. The important process of dropwise condensation occurs in this region of the adsorption isotherm. The macroscopic observa- tions of the condensing drops and the associated adsorbed *FAX: 518-276-4030. Electronic mail: plawsky@rpi.edu † FAX: 518-276-4030. Electronic mail: wayner@rpi.edu FIG. 1. (a) Schematic drawing of the experimental setup. (b) Schematic drawing of the cross section of a drop.  is the film thickness along the profile of the drop, and  0 is the thickness of the flat adsorbed film adjacent to the drop. PHYSICAL REVIEW E 70, 051610 (2004) 1539-3755/2004/70(5)/051610(12)/$22.50 ©2004 The American Physical Society 70 051610-1