Viscous shear torque

Tangential viscous traction produces torque equal to its moment integrated over the solid surface.

For a circular cylinder translating parallel to a nearby wall at zero Reynolds number, leading lubrication shear and pressure recovery make the zero-torque condition force zero angular velocity.

For a cylinder falling parallel to a wall through a minimum gap $ϵa/2$, the parabolic lubrication gap has length scale $a\sqrt{ϵ}$. The leading tangential drag scales as $\mu U/\sqrt{ϵ}$, while the leading rotational resistance scales as $\mu \Omega a/\sqrt{ϵ}$.

A nearly confined cylinder in Couette flow is driven by the unequal lubrication resistances of its two gaps. If their minimum widths are proportional to $1+\lambda$ and $1-\lambda$, force balance weights the relative wall velocities by the inverse square roots of those widths.