line force as a body or volume force, so it can be treated as a momentum source term in the Navier-Stokes equations. The first step is to find a relation, that rewrites the line force $\vec{F}_{\tau L}$ as surface force $\vec{F}_{\tau A}$ acting on the wall: $$\lim_{h \to 0} \int_{\Delta A_{w}} \vec{F}_{\tau A} {\left( \vec{x} \right)} d^{2} \vec{x}
=
  \int_{\Delta L} \vec{F}_{\tau L} {\left( \vec{x}_{L} \right)} d \vec{x}
\label{lineForce}$$ The points, $\vec{x}_{L}$, form the contact line or triple point, $\Delta L$ is the length of the line segment in a the small volume of integration $\Delta V$, and $\Delta A_{w}$ is the side of $\Delta V$ that is part of the wall, and in which the points $\vec{x}_{L}$ lay. An additional constraint for $\vec{F}_{\tau
A} {\left( x \right)}$ is that it is zero outside of the interface region: $$\vec{F}_{\tau A} {\left( x \right)}
=
  0
{\text{ for }}
  {\left|{
    \hat{n}_{2D} {\left( \vec{x}_{L} \right)}
    \cdot
    {\left( \vec{x} - \vec{x}_{L} \right)}
  }\right|}
\geq
  h$$ where $\hat{n}_{2D} {\left( \vec{x}_{L} \right)}$ is the normal to the contact line in the plane of the wall, and $\delta {\left[ \hat{n}_{2D} {\left( \vec{x}_{L} \right)} \cdot
{\left( \vec{x} - \vec{x}_{L} \right)} \right]}$ describes the plane $\Delta A_{w}$.

Consider 