Diagram of Couette Viscometer
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copyright 2002 J.M.McBride
The laminar flow of a liquid in the space between coaxial cylinders is known as "Couette Flow" in honor of Maurice Frédéric Alfred Couette, Professor of Physics at the end of the 19th Century at the French provincial university of Angers.
Couette, born in Tours in 1848, published only seven papers, all of them between 1888 and 1900. He condensed his doctoral thesis on liquid viscosity into a 78-page paper "Études sur le Frottement des Liquides" (Annales de Chimie et de Physique, 21, 433-510, 1890).
The first chapter of his thesis (pp. 438-468 of the paper) describes the first successful viscometer based on shearing a liquid between coaxial cylinders. Since the complex device was made of metal, he could not easily have observed the reversibility of this flow by eye, but he gives an extensive mathematical description of the flow, so perhaps the reversibility would not have surprised him.
I do not know who first noted the reversibility visually.
Diagram of Couette Viscometer
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