Neglect hydrostatic pressure variation in the air. The usual boundary condition in a liquid at the interface
between this liquid and a gas is the so-called shear-free condition. This assumes that the shear force on the liquid by the gas is negligible. The interfacial shear stress in the honey is μ dw/dx. So, the boundary condition at the interface is μ dw/dx = 0 at x = δ.