##Definition of the Robin boundary condition

The Robin boundary condition or mixed boundary condition is defined as follows :

$$ \boldsymbol{u}_{t} = u_{S} - \lambda \frac{\partial{\boldsymbol{u}_{t}}}{\partial \boldsymbol{n}}$$
	with $\boldsymbol{u}_{t}$ the tangential velocity at the boundary,  $u_{S}$ the prescribe substrate velocity, $\lambda$ the slip length and $\boldsymbol{n}$ the inward normal to the surface.
        
##Patch

The patch containing the addition of the **Robin boundary condition** in the list of pre-defined expressions (Dirichelet, Neumann) can be found [here](https://drive.google.com/open?id=1M6XbBgFFntZI8GWFe86w_NZUFoR454ry).

To apply the patch :

~~~bash
cd $BASILISK
darcs apply "patchname"
make clean
make
~~~

##Usage

The Robin boundary condition takes the prescribed velocity and the slip length as inputs. For example, consider a moving plate with slip at the bottom of the domain :

~~~literatec
u.t[bottom] = robin(U_plate,lambda)
u.n[bottom] = dirichlet(0);
~~~

##**Warning**
*Currently working on this issue.*

We define the homogeneous counterpart of the Robin boundary condition as $\boldsymbol{u}$ is solution of the [*Poisson problem*](http://basilisk.fr/src/poisson.h#homogeneous-boundary-conditions). The value of the slip length $\lambda$ of the robin homogeneous boundary condition, found in the file [common.h](http://basilisk.fr/src/common.h), has to be changed **manually**.

For example, for $\lambda = 0.1$ :

~~~literatec
u.t[bottom] = robin(U_plate,0.1)
~~~

Go to the robin_homogeneous line in the [common.h](http://basilisk.fr/src/common.h) file :

~~~bash
cd $BASILISK
vi +/robin_homogeneous common.h
~~~

Modify the value of ($\lambda$) so that it's equal to 0.1 :

~~~literatec
@define robin_homogeneous() ( ((2.*(0.1)-Delta)/(2.*(0.1)+Delta))*val(_s,0,0,0) )
~~~