Thermal effects of substrate on Marangoni flow in droplet evaporation: Response surface and sensitivity analysis

Abstract

a b s t r a c tIn this paper, the evaporation of sessile droplets resting on a substrate with different thermal properties is numerically investigated. Computations are based on a transient axisymmetric numerical model. Special attention is paid to evaluate thermal effects of substrate on the structure of bulk fluid flow in the course of evaporation. Numerical results reveal that Marangoni convection induced by nonuniform distribution of temperature along the interface exhibits three distinctly different behaviours: inward flow, multicellular flow and outward flow, consequently resulting in different particle depositions. It is highlighted that three factors (i.e. relative thermal conductivity, relative substrate thickness and relative substrate temperature) strongly affect the flow pattern. In order to further investigate the coupling effects of different influential factors, a Kriging-based response surface method is introduced. We model the flow behaviour as a function of continuous influential factors using a limited number of computations corresponding to discrete values of the inputs. The sensitivities of the Marangoni flow are also analysed using Sobol' index to study the coupling mechanisms of influential factors. The proposed method can be used to forecast the flow patterns for any input parameter without additional sophisticated computer simulation, and allows to confidently estimate an unknown environmental parameter.

Thermocapillary flow transition in an evaporating liquid layer in a heated cylindrical cell

“…Finally, instead of using the energy balance and mass conservation conditions at the free surface, as in, e.g., [35], we adopt a phenomenological approach in which the heat flux and mass conservation across the interface are given by global heat and mass transfer coefficients. As such, the heat transfer in the gas phase and the cooling effect due to evaporation can be described respectively by an equivalent Biot number [31,32,36,37].…”

Determination of Diffusion Coefficient in Droplet Evaporation Experiment Using Response Surface Method

“…Using uncertainty quantification analysis can help us numerically predict the change of concerned variables and estimate the unknown input. Here, we simply outline the methodology of the response surface method; more details about its principle and numerical procedure can be found in Chen et al (2017b). In short, this analysis includes the following three steps: -First, we select some discrete points of inputs (diffusion coefficient and substrate temperature) and calculate the corresponding evaporation rates via numerical simulation.…”

“…Very recently, Chen et al (2017a) obtained simple scaling laws for the evaporation rate that scales linearly with the drop radius but follows a power-law with the substrate temperature. Combining numerical simulations with response surface method, Chen et al (2017b) further investigated the thermal effects of the substrate on the Marangoni flow and clearly identified three characteristic bulk flow structures. These recent studies called for an improved empirical relation of Hu and Larson (2002) for the prediction of the evaporation rate.…”

Droplets and Sprays

“…In a number of papers, including the most recent ones [38,39,40], the problem of heating and evaporation of droplets was solved based on direct numerical solution of transport equations in the vicinity of individual droplets. This approach, however, cannot be applied in CFD codes and will not be considered in this chapter.…”