In this paper, Eq 12 gives the height-averaged radial velocity, by which the radial velocity over times at a certain radius in the droplet can be calculated and is increasing numerically. However, this calculation doesn't match the physical understanding that the radial velocity should decrease over time. Then I traced back into the reference paper "contact line deposits in an evaporating drop" by Deegan, 2000, from which the Eq 12 is derived. However, in Deegan's paper, only an integration form (Eq 2) accounting for the height-averaged radial velocity is provided. So now I wondered how was Eq 12 was derived, and is it correct?
https://www.researchgate.net/publication/7901174_Analysis_of_the_microfluid_flow_in_an_evaporating_sessile_droplet
Article Analysis of the Microfluid Flow in an Evaporating Sessile Droplet
I need to use this analytical solution to compare with the experimental data of radial velocity of the evaporating droplet on which I am studying, so have to make sure that the analytical expression is correct.
I have had a quick read of the paper by Hu and Larson, you do not need equation (12) as it is replaced with equation (22). The derivation of equation (12) is likely to follow a similar derivation to equation (22).
If you can follow the derivation in Hu and Larson to equation (22), you will have a good understanding of the material. If you still need assistance I will see if I can get some time next week to upload the full derivation with explanations.
Good luck
Hi, James, thank you so much for reading the paper. I haven't got a time to read through the paper since last update, now preparing some droplet evaporation set-up. I will find a time to read the paper through after some time later. Then see if I can discuss with you. Thanks, wish everything going well with you.
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