limits to be consistent with the pressure. It can be appreciated how the pressure integral converges to a constant value and the velocity integral approaches zero as resolution increases, showing a convergent solution for both the pressure and velocity.

Dynamic
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For the validation of the dynamic case, the starting point is again a 2D droplet in planar geometry. However, in this case, the equilibrium Young’s contact angle is set to $\theta_{0} = 0$, and the spreading behavior as a function of time is investigated.

![\[figure:contourTanner\] Interface of a droplet at different times at a resolution of $512 \times 256$.](fig9){width="60.00000%"}

Figure \[figure:contourTanner\] shows the interface ($\alpha = 0.5$) at various times for a box of $1.5 \si{\milli\m} \times 0.75 \si{\milli\m}$ and with a resolution of $512 \times 256$. As expected the droplet keeps spreading until the edge of the simulation box is reached and the simulation is stopped.

![\[figure:diameterTanner\] Radius of a droplet as a function of time.](fig10){width="60.00000%"}

Figure \[figure:diameterTanner\] shows how the droplet spreads by showing the radius of the droplet as a function of time for two different resolutions of $256
\times 128$ and $512 \times 256$. For lower resolutions the contact line was pulled apart and the 