Preparation for Nov. 12th, Taylor wedge problem and its elastic analouge
Tarjei will present the following on Nov. 12, but I would encourage everyone to also follow the same derivation :)
Everyone should have read the article that will be part of the discussion, with particular emphasis of the physical consequences.
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Consider some very viscous liquid placed on a solid substrate being scrapped by another solid plate very slowly at a given angle. This will create a flow in the viscous fluid around the corner, and one can solve for the velocity field, the normal and the tangential stresses on the scrapper by treating it as a Stokes flow. More interestingly, if the angle between the solid substrate and the scrapper is small, one can obtain the same normal and tangential stress by considering the thin film flow instead of the Stokes flow:
- Demonstrate the derivation of the velocity field, the normal and tangential stresses on the scrapper using the Stokes flow. This is essentially the Taylor’s paper “on scrapping viscous fluid from a plane surface” attached to the email. You might also find “An introduction to fluid dynamics, G. K. Batchelor pp 224-226”https://doi.org/10.1017/CBO9780511800955 helpful.
- Derive the normal and tangential stress on the scrapper using thin film flow. You might find “Elementary fluid mechanics, D.J. Acheson, pp 248-249” helpful.
- Read the paper https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/flexible-scraping-of-viscous-fluids/C479D5BD0BBD1348459385097F0C55DCDiscuss and discuss the consequences of the scrapper being flexible.