and the theoretically predicted shape for various values of the Young’s angle. Investigating the spreading of a droplet on a completely wetting surface, the Voinov-Tanner-Cox law [@voinov1976; @tanner1979; @cox1986] ($\theta \propto {\text{Ca}}^{1/3}$) can be observed. Late time scaling follows $r \propto t^{1/2}$, suggesting spreading is limited by inertia. These observations are made without any fitting parameters except the slip length.

Theory
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Body force reformulation of uncompensated Young’s stress
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The traditional form of the Generalized Navier Boundary Condition (GNBC) used in, for example, Arbitrary Lagrangian-Eulerian simulations [@gerbeau2009], looks like: $$\beta {\left( \vec{u} - \vec{u}_{w} \right)} \cdot \tau
+ \mu {\left( \nabla \vec{u} + \nabla \vec{u}^{T} \right)} \hat{n}_{w} \cdot \tau
+ \sigma {\left( \cos{\theta} - \cos{\theta_{0}} \right)} \hat{t}_{w} \cdot \tau \delta_{{\text{cl}}}
=
  0
\label{eqn:gnbc}$$ Here the first two terms on the left hand side represent the Navier slip boundary condition [@navier1823], and the third term represents the unbalanced Young’s stress. $\beta$ is the slip coefficient, $\vec{u}$ is velocity, $\vec{u}_{w}$ is the velocity of the wall, $\tau$ is any vector tangent to the wall, $\mu$ is the dynamic viscosity, $\hat{n}_{w}$ is the normal of the wall pointing outward, $\sigma$ is the surface tension coefficient, $\theta$ is the dynamic contact angle, $\theta_{0}$ 