How does the viscosity (besides density) of a fluid affects sinking

Question

If water, air of whatever fluid had a different viscosity, but the same density, would things fall/sink differently?

Answer 1

Yes they would fall differently.

For example, according to Stokes' Law the drag force is proportional to dynamic viscosity and the terminal velocity of a falling sphere is:

$$\frac{2(\rho_s -\rho_f)}{9\mu}gR^2$$

where $\rho_s$ and $\rho_f$ are the densities of the sphere, $\mu$ is the dynamic viscosity, $g$ is the acceleration due to gravity, and $R$ is the radius of the sphere.

Answer 2

The dynamics in case of relative motion will be different: e.g., the acceleration and terminal velocity when falling/sinking. But the equilibrium will be unaffected (e.g., floating and waterline). This is because viscosity is at the origin of a frictional force.