Different stratifications of micro-clumping tested in our hydrodynamic atmosphere models. Left: the black solid, dashed, and dotted lines represent clumping stratifications that increase outward, while the cyan line depicts clumping that decreases outward. The brown solid, dashed, and dotted lines represent constant clumping throughout the atmosphere. The grey dashed vertical line indicates the velocity at the critical radius which is roughly v_crit ≈ 75 km s⁻¹ for all the models tested here. Right: the predicted mass-loss rate as a function of the clumping value at the critical point.