Interplay of transport mechanisms during the evaporation of a pinned sessile water droplet

Droplet evaporation has been intensively investigated in past decades owing to its emerging applications in diverse fields of science and technology. Yet the role of transport mechanisms has been the subject of a heated debate, especially the presence of Marangoni flow in water droplets. This work aims to draw a clear picture of the switching transport mechanisms inside a drying pinned sessile water droplet in both the presence and absence of thermocapillarity by developing a comprehensive model that accounts for all pertinent physics in both phases as well as interfacial phenomena at the interface. The model reveals a hitherto unexplored mixed radial and buoyant flow by shedding light on the transition from buoyancy induced Rayleigh flow to the radial flow causing the coffee ring effect. Predictions of the model excellently match previous experimental results across varying substrate temperatures only in the absence of Marangoni flow. When thermocapillarity is accounted for, strong surface flows shape the liquid velocity field during most of the droplet lifetime and the model starts to overestimate evaporation rates with increasing substrate temperature.

Figure 1

Problem domain based on axisymmetry. Droplet is placed onto a two-stage substrate, which is assumed sufficiently thermally conductive such that walls of the substrate possess the same temperature, $T_w$. The substrate is surrounded by an environmental chamber, whose walls have a constant far field temperature, $T_{\infty }$. The gas adjacent to outer walls is assumed to have a constant far field vapor concentration, $c_{\infty }$, while, at the walls of the substrate with temperature control, the gradient of vapor concentration is assumed zero. $\varphi$ is the polar angle measured from the apex with respect to the center of curvature (CoC) of the droplet.

Figure 2

Temperature field and streamlines in the entire computational domain for (a) isothermal ($T_w=25.4$ ${}^{\circ }\mathrm{C}$) and (b) heated ($T_w=65.4$ ${}^{\circ }\mathrm{C}$) substrates.

Figure 3

Velocity magnitude field (left images) inside the droplet with superimposed total energy flux streamlines and temperature field (right images) inside the droplet with superimposed velocity streamlines and in the near droplet gas region with superimposed normalized velocity vectors in the (a) presence and (b) absence of thermocapillarity. Substrate temperature is $65.4^{\circ }\mathrm{C}$. White lines indicate the liquid-vapor interface. The value of the corresponding contact angle is specified on each plot. Note that velocity magnitude scale bars in (a) and (b) are common for the corresponding plots, whereas individual temperature scale bars are utilized for each plot.

Figure 4

Distributions of interfacial temperature and energy transfer rate per polar angle (a) with and (b) without thermocapillarity at selected contact angles. Substrate temperature is $65.4^{\circ }\mathrm{C}$. Angular position starts at the apex and terminates at the contact line.

Figure 5

Velocity magnitude field in the near droplet gas region in the presence and absence of thermocapillarity at the contact angles of (a) ${68}^{\circ }$, (b) ${36}^{\circ }$, and (c) $4^{\circ }$. Substrate temperature is $65.4^{\circ }\mathrm{C}$.