The flux of fluid relative to the solid matrix is given by the vector $\mathbf{w}$ . Since viscosity is not explicitly modeled in a biphasic material, the tangential component of $\mathbf{w}$ on a boundary surface may not be prescribed. Only the normal component of the relative fluid flux, $w_{n}=\mathbf{w}\cdot\mathbf{n}$ , represents a natural boundary condition. To prescribe a value for $w_{n}$ on a surface, use:

<surface_load type="fluidflux" surface="surf1">
  <flux lc="1">1.0</flux>
  <linear>0</linear>
  <mixture>1</mixture>
</fluidflux>

When linear is set to zero (default) it means that the flux matches the prescribed value even if the surface on which it is applied changes in area as it deforms. Therefore, the net volumetric flow rate across the surface changes with changes in area. This type of boundary condition is useful if the fluid flux is known in the current configuration.

When linear is set to non-zero it means that the prescribed flux produces a volumetric flow rate based on the undeformed surface area in the reference configuration. Therefore, the flux in the current configuration does not match the prescribed value. This type of boundary condition is useful if the net volumetric flow rate across the surface is known. For example: Let $Q$ be the known volumetric flow rate, let $A_{\mathrm{0}}$ be the surface area in the reference configuration (a constant). Using “linear” means that the user prescribes $Q$ /$A_{\mathrm{0}}$ as the flux boundary condition. (However, regardless of the type, the fluid flux saved in the output file has a normal component equal to $Q$ /$A$ , where $A=$ area in current configuration.)

Prescribing $w_{n}$ on a free surface works only if the nodal displacements of the corresponding faces are also prescribed. If the nodal displacements are not known a priori, the proper boundary condition calls for prescribing the normal component of the mixture velocity, $v_{n}=\left(\mathbf{v}^{s}+\mathbf{w}\right)\cdot\mathbf{n}$ . To prescribe the value of $v_{n}$ on a surface, use

<surface_load type="fluidflux" surface="surf1">
  <flux lc="1">1.0</flux>
  <linear>0</linear>
  <mixture>1</mixture>
</surface_load>