A point sink superposition method for predicting droplet interaction effects during vapor-diffusion-driven dropwise condensation in humid air

Abstract

During dropwise condensation from the ambient environment, water vapor present in air must diffuse to the surface of each droplet. The spatial distribution of water vapor in the local surroundings of each individual droplet determines the total condensation rate. However, available models for dropwise condensation in humid air assume that such systems of droplets grow either as an equivalent film or that the growth of each droplet is completely isolated; the interactions between droplets are poorly described and, consequently, predictions of total condensation rates may mismatch experimental observations. This paper presents a reduced-order analytical method to calculate the condensation rate of each individual droplet within a group of droplets on a surface by resolving the vapor concentration field in the surrounding air. A point sink superposition method is used to account for the interaction between droplets without requiring solution of the diffusion equation for a full three-dimensional domain containing all of the droplets. For a simplified scenario containing two neighboring condensing droplets, the rates of growth are studied as a function of the inter-droplet distance and the relative droplet size. For representative systems of condensing droplets on a surface, the total condensation rates predicted by the reducedorder model match numerical simulations to within 15%. The results show that assuming droplets grow as an equivalent film or in a completely isolated manner can severely overpredict condensation rates.

A laser-driven optical atomizer: photothermal generation and transport of zeptoliter-droplets along a carbon nanotube deposited hollow optical fiber

“…However, since most gas molecules exist in a high concentration near the central axis, several nanodroplets are generated and are in contact with one another. 62,63 As shown in a cryo-SEM image, their contact coalesces into large microdroplets near the center. 63,64 Consequently, the diameter of the droplets decreased as its position moved radially outward where droplets had rarely coalesced.…”

Spatial Control of Condensation: The Past, the Present, and the Future

“…This has been done using the point sink superposition method (Figure 4c). [92,93] Based on the present literature, I believe that particularly three recurring themes are currently limiting the full utilization of spatial control. These are 1) their issues with robustness, 2) their fixed behavior, and 3) only spatial control of water is considered.…”

Predicting the growth of many droplets during vapor-diffusion-driven dropwise condensation experiments using the point sink superposition method

“…The point sink superposition method solves for the diffusion of vapor within the air domain surrounding the droplets during dropwise condensation. Our previous work [15] provides a complete description of the method which is briefly summarized here. The model assumes: (i) droplets can be treated as point sinks located at the droplet centers, (ii) the condensation process can be treated as quasi-steady state, (iii) there is negligible thermal resistance across the droplets (i.e., the temperature at the surface of the droplet is equal to the temperature of the substrate), (iv) the contact angle of the droplets is independent of droplet size, and (v) changes in vapor concentration at the surface of the droplets due to curvature are negligible.…”

“…At later times, droplets that have polygons with larger areas do not necessarily grow faster. We have previously shown that the condensation rate of pairs of droplets predicted by the PSSM is sensitive to the ratio of between the droplet sizes [15]. Large droplets can limit the vapor diffusion to small droplets in their surroundings For example, droplet h in Figure 9 (b) has a larger Voronoi polygon area than its neighbor droplet l , but grows at a smaller rate, because droplet l has a larger size and it is surrounded by smaller neighbors than droplet h .…”

“…To account for the complete set of interactions between all droplets on the substrate, communicated through the vapor concentration field, we recently developed a point source superposition method to describe droplet growth during dropwise condensation [15]. By assuming that each droplet can be treated as point sink for vapor, this method solves for the condensation rate of each droplet within a system of many droplets by superposing a modified version of Popov's solution [16] for the condensation of individual droplets; the point sink superposition method was demonstrated to be in reasonable agreement with complete numerical solutions of the vapor diffusion equation.…”