Determination of Diffusion Coefficient in Droplet Evaporation Experiment Using Response Surface Method
- 98 Downloads
Evaporation of a liquid droplet resting on a heated substrate is a complex free-surface advection-diffusion problem, in which the main driving force of the evaporation is the vapor concentration gradient across the droplet surface. Given the uncertainty associated with the diffusion coefficient of the vapor in the atmosphere during space evaporation experiments due to the environmental conditions, a simple and accurate determination of its value is of paramount importance for a better understanding of the evaporation process. Here we present a novel approach combining numerical simulations and experimental results to address this issue. Specifically, we construct a continuous function of output using a Kriging-based response surface method, which allows to use the numerical results as a black-box with a limited number of inputs and outputs. Relevant values of the diffusion coefficient can then be determined by solving an inverse problem which is based on accessible experimental data and the proposed response surface. In addition, on the basis of our numerical simulation results, we revisit a widely used formula for the prediction of the evaporation rate in the literature and propose a refined expression for the droplets evaporating on a heated substrate.
KeywordsDroplet evaporation Diffusion coefficient Response surface Marangoni flow Microgravity
This work was financially supported by the National Natural Science Foundation of China (Grant No. 11532015), the Strategic Pioneer Program on Space Science, Chinese Academy of Sciences (Grant No. XDA 04020202-02) and by the CNES (Centre National d’Etudes Spatiales). X. Chen has benefited from financial support from the Guangxi’s Key Laboratory Foundation of Manufacturing Systems and Advanced Manufacturing Technology (Grant No. 17-259-05-002Z) and China Postdoctoral Science Foundation (2018M633113).
- Krige, D.G.: A statistical approach to some basic mine valuations problems on the Witwatersrand. J. Chem. Metall. Mining Soc. South Africa 52, 119–139 (1951)Google Scholar
- Maxwell, J.C.: The Scientific Papers of James Clerk Maxwell. Collected Scientific Papers (Cambridge, Cambridge University Press) 11, 625 (1890)Google Scholar