A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets

This paper investigates the coupled relationship between solid-phase temperature fields and droplet evaporation, focusing on the effects of substrate thermal conduction properties on droplet evaporation behavior. A mathematical model is developed to analyze the impacts of substrate thermal conductiv...

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Main Authors: Longfei Xu, Xuefeng Xu
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Applied Sciences
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Online Access:https://www.mdpi.com/2076-3417/15/11/6083
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author Longfei Xu
Xuefeng Xu
author_facet Longfei Xu
Xuefeng Xu
author_sort Longfei Xu
collection DOAJ
description This paper investigates the coupled relationship between solid-phase temperature fields and droplet evaporation, focusing on the effects of substrate thermal conduction properties on droplet evaporation behavior. A mathematical model is developed to analyze the impacts of substrate thermal conductivity, thickness, and lower-surface temperature on evaporation rate, surface temperature, and evaporation flux. A dimensionless relative evaporation rate (HCs) is introduced to characterize the influence of substrate thermal conduction. Results show that increasing substrate thermal conductivity enhances droplet surface temperature and evaporation flux, thereby monotonically increasing evaporation rate until it approaches the rate of the evaporative cooling model. Conversely, increasing substrate thickness lengthens the heat transfer path, reducing heat conducted to the solid–liquid interface and decreasing evaporation rate. Changes in substrate lower-surface temperature significantly affect evaporation rate, but HCs remains nearly unaffected. The concept of equivalent substrates is proposed and verified through dimensionless analysis and simulations. It is found that different combinations of substrate thickness and thermal conductivity exhibit consistent effects on droplet evaporation, with minimal relative errors in evaporation rate and total heat transfer at the solid–liquid interface. This confirms the existence of the equivalent substrate phenomenon. Additionally, the effects of droplet properties, such as contact angle and evaporative cooling coefficient (<i>Ec</i>), on the equivalent substrate phenomenon are explored, revealing negligible impacts. These findings provide theoretical guidance for optimizing droplet evaporation processes in practical applications, such as micro/nanoscale thermal management systems.
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spelling doaj-art-00182c72bb2941bf9d398ce74716e02a2025-08-20T02:33:01ZengMDPI AGApplied Sciences2076-34172025-05-011511608310.3390/app15116083A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile DropletsLongfei Xu0Xuefeng Xu1School of Technology, Beijing Forestry University, Beijing 100083, ChinaSchool of Technology, Beijing Forestry University, Beijing 100083, ChinaThis paper investigates the coupled relationship between solid-phase temperature fields and droplet evaporation, focusing on the effects of substrate thermal conduction properties on droplet evaporation behavior. A mathematical model is developed to analyze the impacts of substrate thermal conductivity, thickness, and lower-surface temperature on evaporation rate, surface temperature, and evaporation flux. A dimensionless relative evaporation rate (HCs) is introduced to characterize the influence of substrate thermal conduction. Results show that increasing substrate thermal conductivity enhances droplet surface temperature and evaporation flux, thereby monotonically increasing evaporation rate until it approaches the rate of the evaporative cooling model. Conversely, increasing substrate thickness lengthens the heat transfer path, reducing heat conducted to the solid–liquid interface and decreasing evaporation rate. Changes in substrate lower-surface temperature significantly affect evaporation rate, but HCs remains nearly unaffected. The concept of equivalent substrates is proposed and verified through dimensionless analysis and simulations. It is found that different combinations of substrate thickness and thermal conductivity exhibit consistent effects on droplet evaporation, with minimal relative errors in evaporation rate and total heat transfer at the solid–liquid interface. This confirms the existence of the equivalent substrate phenomenon. Additionally, the effects of droplet properties, such as contact angle and evaporative cooling coefficient (<i>Ec</i>), on the equivalent substrate phenomenon are explored, revealing negligible impacts. These findings provide theoretical guidance for optimizing droplet evaporation processes in practical applications, such as micro/nanoscale thermal management systems.https://www.mdpi.com/2076-3417/15/11/6083liquid evaporationheat conductionevaporative coolingsolid phase
spellingShingle Longfei Xu
Xuefeng Xu
A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
Applied Sciences
liquid evaporation
heat conduction
evaporative cooling
solid phase
title A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
title_full A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
title_fullStr A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
title_full_unstemmed A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
title_short A Computational Investigation of the “Equivalent Substrates” in the Evaporation of Sessile Droplets
title_sort computational investigation of the equivalent substrates in the evaporation of sessile droplets
topic liquid evaporation
heat conduction
evaporative cooling
solid phase
url https://www.mdpi.com/2076-3417/15/11/6083
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