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Vapour-liquid rebalancing behaviour of free water evaporation kinetics: experimental investigation and modelling


Drying and moisture evaporation are inextricably linked and major attention is focused on thermal conditions. But the non-thermal factors, especially the relative humidity and air distribution of wet air, also affects drying kinetics. Aiming to obtain the drying kinetic features of water evaporation under isothermal conditions, an experimental investigation was conducted using a variation of each single variable method. The experimental phenomena of non-thermal factors affecting evaporation kinetics under different isothermal process were presented. The results show that water evaporation rate is linear with vapor partial pressure difference under constant temperature condition, and nonlinear change in evaporation rate is caused by wet air flow hindering factors, i.e. the wall height above water surface. A vapour-liquid rebalancing behaviour hypothesis was concluded basing on the results, that water is dried by turning into saturated vapour then being transferred through convection and diffusion. The stronger capability to remove saturated water vapor from the liquid surface is associated with higher evaporation rate. A comprehensive evaporation kinetic model was obtained basing on experimental data and the prediction accuracy is verified by an out of sample experiment. The most probable physical reasons behind the thermal condition change caused parameter change rules were interpreted. This proposed vapor–liquid rebalancing hypothesis shows a consistent behavior with respect to drying theory.

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A :

Experimentally used evaporation area (mm2)

\({A}_{\#3}\) :

Experimentally used evaporation area marked as #3 (mm2)

\({A}_{mc}\) :

Coefficient of the evaporation area modification under the effect of the uneven characteristic of RLc

\(H{|}_{r}\) :

Wall resistance height under a constant evaporation radius (mm)

K :

Coefficient of evaporation mass transfer (kg/[m•s2])

K cd :

Coefficient of convection–diffusion evaporation mass transfer (kg/[m•s2])

K d :

Coefficient of pure diffusion evaporation mass transfer (kg/[m•s2])

K cd #3 :

Kcd obtained experimentally under the condition of A#3 (kg/[m•s2])

p sat :

Partial pressure of saturated water vapor (Pa)

p w, v :

Water vapor partial pressure of wet air (Pa)

\(\Delta p{|}_{T}\) :

Water vapor partial pressure difference for mass transfer at temperature T (Pa)

\(r{|}_{H}\) :

Evaporation radius under constant wall resistance height (mm)

R :

Evaporation rate (kg/[m2•s])

R Lc :

Local evaporation rate (kg/[m2•s])

R cd :

Convection–diffusion evaporation rate (kg/[m2•s])

R d :

Pure diffusion evaporation rate (kg/[m2•s])

R c :

Comprehensive evaporation rate (kg/[m2•s])

R cd #3 :

Rcd obtained experimentally under the condition of \({A}_{\#3}\) (kg/[m2•s])

T :

Experimentally controlled wet air temperature (°C)


Experimentally controlled wet air relative humidity

Lc :


r :


H :


c :


w :


v :


sat :


T :


cd :

Convection and diffusion

d :


mc :

Modification coefficient

i :

Serial component

G :

Components of PararGa


Relative humidity


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  1. Prommas R, Rattanadecho P, Cholaseuk D (2010) Energy and exergy analyses in drying process of porous media using hot air. Int Commun Heat Mass Transfer 37:372–378.

    Article  Google Scholar 

  2. Chen L, Subbiah J, Jones D, Zhao Y, Jung J (2021) Development of effective drying strategy with a combination of radio frequency (RF) and convective hot-air drying for inshell hazelnuts and enhancement of nut quality. Innov Food Sci Emerg Technol 67:1–9.

    Article  Google Scholar 

  3. Zhou C, Feng Y, Zhang L, Abu EA, Yagoub HW, Ma H, Sun Y, Xiaojie Yu (2021) Rehydration characteristics of vacuum freeze and hot air-dried garlic slices. LWT Food Sci Technol 143:1–8.

    Article  Google Scholar 

  4. Lihui Zhang Yu, Qiao CW, Liao Li, Shi D, An K, Jianzhong Hu, Wang J, Shi L (2020) Influence of high hydrostatic pressure pretreatment on properties of vacuum-freeze dried strawberry slices. Food Chem 331:1–9.

    Article  Google Scholar 

  5. Dolgun EC, Karaca G, Aktaş M (2020) Performance analysis of infrared film drying of grape pomace using energy and exergy methodology. Int Commun Heat Mass Transfer 118:1–12.

    Article  Google Scholar 

  6. Shen L, Gao M, Zhu Y, Liu C, Lei Wang Md, Kamruzzaman CL, Zheng X (2021) Microwave drying of germinated brown rice: Correlation of drying characteristics with the final quality. Innov Food Sci Emerg Technol 70:1–15.

    Article  Google Scholar 

  7. Li K, Zhang Y, Wang YF, El-Kolaly W, Gao M, Sun W, Li M (2021) Effects of drying variables on the characteristic of the hot air drying for gastrodia elata: Experiments and multi-variable model. Energy 222:1–14.

    Article  Google Scholar 

  8. Biz AP, Cardozo-Filho L, Zanoelo EF (2019) Drying dynamics of microalgae (Chlorella pyrenoidosa) dispersion droplets. Chem Eng Process 138:41–48.

    Article  Google Scholar 

  9. Manzoor A, Khan MA, Mujeebu MA, Shiekh RA (2021) Comparative study of microwave assisted and conventional osmotic dehydration of apple cubes at a constant temperature. J Agri Food Res 5:1–13.

    Article  Google Scholar 

  10. Mugodo K, Workneh TS (2021) The kinetics of thin-layer drying and modeling for mango slices and the influence of differing hot-air drying methods on quality. Heliyon 7:1–15.

    Article  Google Scholar 

  11. Dejchanchaiwong R, Arkasuwan A, Kumar A, Tekasakul P (2016) Mathematical modeling and performance investigation of mixed-mode and indirect solar dryers for natural rubber sheet drying. Energy Sustain Dev 34:44–53.

    Article  Google Scholar 

  12. Hao-Yu Ju, Shi-Hao Zhao AS, Mujumdar X-M, Gao Z-J, Zheng Z-A, Xiao H-W (2018) Energy efficient improvements in hot air drying by controlling relative humidity based on Weibull and Bi-Di models. Food Bioprod Process 3:20–29.

    Article  Google Scholar 

  13. Wanxiu Xu, Islam MN, Cao X, Tian J, Zhu G (2021) Effect of relative humidity on drying characteristics of microwave assisted hot air drying and qualities of dried finger citron slices. LWT Food Sci Technol 137:1–10.

    Article  Google Scholar 

  14. Ruberto S, Reutzsch J, Weigand B (2016) Experimental investigation of the evaporation rate of supercooled water droplets at constant temperature and varying relative humidity. Int Commun Heat Mass Transfer 77:190–194.

    Article  Google Scholar 

  15. Jie Qu, Escobar L, Li J, Rao Z, Ben Xu (2020) Experimental study of evaporation and crystallization of brine droplets under different temperatures and humidity levels. Int Commun Heat Mass Transfer 110:1–11.

    Article  Google Scholar 

  16. Air-Conditioning Engineers (2013) 2013 ASHRAE handbook: fundamentals. In: Owen MS (ed) Psychrometrics, SI edn. ASHRAE, Atlanta, p 2

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This work is supported by the National Key Research and Development Program of China (No.2018YFB0606104).

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All authors contributed to the study conception and design. Conceptualization, investigation, methodology, visualization and writing were performed by Liuan Yang. Material and experimental resources were performed by Shaowu Yin, Chuanping Liu and Peikun Zhang. Supervision, writing, review and editing were performed by Lige Tong, Li Wang and Yulong Ding. The first draft of the manuscript was written by Liuan Yang and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Lige Tong.

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Yang, L., Tong, L., Yin, S. et al. Vapour-liquid rebalancing behaviour of free water evaporation kinetics: experimental investigation and modelling. Heat Mass Transfer 59, 215–227 (2023).

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