Algal detachment in response to flushing

Definition

The rate of accidental detachment of fixed biomass is calculated at each section as follows:

\(\frac{\partial B}{\partial t} (x,t) = - \frac{1}{\delta }\left ( \frac{\tau_{0}(x,t) - \tau_{0,cr}(x)}{\tau_{ref}(x)} - s_B \right )^\eta B(x,t)\) , if\(\frac{\tau_{0}(x,t) - \tau_{0,cr}(x)}{\tau_{ref}(x)} > s_B\)

\({\frac{\partial B}{\partial t} = 0}\) , otherwise

With: - \({B(x,t)}\) : the fixed biomass in kg m^-1 - \({\tau _ 0(x,t)}\) : the wall shear stress in N m^-2 - \({\tau_{0,cr}(x)}\) : the critical shear value which integrates the memory effect of the algae in their resistance capacity. - \({\tau_{ref}(x)}\) : the reference shear value - \({s_B}\) : the sensitivity threshold which takes into account the fluctuations prior to the flushing - \({\delta}\) : a time constant in seconds - \({\eta}\) : a dimensionless exponent

Characteristics

• Law identifier: 201
• Number of classes involved: 1
• Number of parameters: 5

Classes involved: -# \({B}\)

Parameters as a function of chainage: -# \({\tau_{0,cr}}\) -# \({\tau_{ref}}\)

Parameters possibly as a function of time -# \({s_B}\) -# \({\delta}\) -# \({\eta}\)