(It sounds to me like there is not an established way to link shear rate with 3-phase contact angle (or surface energy, which would be the more appropriate parameter here).
There are many articles about the relationship between the contact angle and the sliding speed on the surface.
I found many articles in the literature search, but there is no flow modeling on the hydrophobic surface in the FLUENTT program.
I am writing my e-mail address.
Please I would be very happy if you could help.

If you know the FLUENTT program well, we can work on an article together.