Effects of internal circulation and particle mobility during nanofluid droplet evaporation

Abstract

The effect of internal circulation on evaporation of fluid droplets containing nano-sized particles is analytically investigated, where internal circulation is caused by viscous effects at the liquid-gas interface in the convective environment. The competing time scales of liquid diffusion, convection, and particle diffusion are first analyzed as influenced by gas phase velocity, relative viscosities of gas and liquid phases, and the droplet size. The results reveal the importance of internal recirculation for droplets of practical sizes. To demonstrate the role of internal circulation plays on particle distribution and shell formation during the evaporation process, a symmetric Hill vortex and strong circulation are assumed for solving a one-dimensional governing equation, which to yield (i) the particle redistribution during the evaporation process, (ii) the time and the size upon shell formation (i.e., the end of the first-stage evaporation/drying) due to inclusion of particles at the droplet surface, and (iii) internal particle distribution that forecast possible morphologies of particle aggregates once the drying process is complete. These results are found to be dependent upon (a) the relative time scales of liquid diffusion and particle mobility (the effect of Lewis number, ), and (b) the relative importance or evaporation rate ( ) and particle mobility (the effect of Peclet number, ). Comparisons with previous results without internal circulation are made, as related to the time for shell formation and possible morphologies. Such comparisons reveal some distinctly different, and surprising, phenomena during and at the end of the first-stage evaporation.

In situ Raman composition profiling in drying droplets

“…Regarding the component distribution in the droplet and the influence of the acoustic levitator, the acoustic levitators employed in the literature generate a droplet rotation about both vertical and horizontal axis [24,36]. Because the spatial distribution of the droplet components is dependent on the flowfield inside the liquid phase, the presence of a centrifugal force could have an impact on the distribution of the solutes [24,37,38]. In those cases, the frequency employed in the acoustic levitator was in the order of 100 kHz.…”

Water evaporation from solute-containing aerosol droplets: Effects of internal concentration and diffusivity profiles and onset of crust formation

“…Therefore, analytical and numerical modeling methods must be used to better understand the details of the evaporation mechanism that is relevant for sedimenting droplets. Although modeling of free droplets does not face complexities due to substrate–droplet interactions that control the droplet shape at the solid/liquid/air interface 35,36 and Marangoni flow, 37,38 which occur in the case of sessile droplets, other factors such as evaporation-induced concentration gradients inside the droplet 39 and the possibility of crust formation on the droplet surface, 40 which are consequences of the increasing solute surface concentration during evaporation, 41 cause difficulties even in the modeling of free droplets in the presence of solutes. In addition, physical and chemical properties of the drying droplets, such as the internal viscosity, 42,43 the diffusivity of solvent and solutes in the liquid phase, 43 and the activity coefficient of the solvent, 44 are dependent on the local concentration of solutes (and, consequently, on both position and time), which makes the problem rather complex.…”

“…There are a few studies that address concentration gradients inside a solute-containing drying droplet 39,46–48 and propose analytical and numerical methods for modeling the evaporation process before 47–50 and after 40,49,51 crust formation. Handscomb et al 52 proposed a numerical model consisting of a set of advection–diffusion equations coupled to ordinary differential equations describing the particle size and temperature to simulate the drying of droplets that contain solid particles prior to crust formation.…”

Evaporative characteristics of sessile nanofluid droplet on micro‐structured heated surface

“…Experiments were recently carried out for the effects of multi‐sized and multi‐species nanoparticles on the evaporating sessile droplets with deposit morphology controlled by the particle‐particle interactions coupling with the particle‐dependent droplet dynamics . Numerical model and analytical investigation were also developed for predicting the evaporation behavior of liquid droplets containing nano‐sized insoluble particles with first analysis on the competing time scales of liquid diffusion, convection, and particle diffusion as a function of gas phase velocity, relative viscosities of gas and liquid, and the droplet size. Inspired by Marangoni flow generated inside the evaporating droplet, temperature gradient enforcement is common in evaporation manipulation .…”