Algual detachment in response to flushing with reference shear stress equal to the first time step
Definition
The rate of accidental detachment of fix algae \(b_i\) towards drift algae \(a_i\) is calculated in each section as follows :
\[\frac{\partial B_i}{\partial t}(x,t) = -S\frac{\partial A_i}{\partial t}(x,t) = -\frac{1}{\delta}\left ( \frac{\tau_{0}(x,t) - \tau_{0}(x,0)}{\tau_{0}(x,0)} - s_B \right )^\eta B_j(x,t) \] if\(\frac{\tau_{0}(x) - \tau_{0}(x,0)}{\tau_{0}(x,0)} > s_B\)
\(\frac{\partial A_i}{\partial t}(x,t) = \frac{\partial B_i}{\partial t}(x,t) = 0\) atherwise.
Where : - \(A_i(x,t)\) : drift algae (kg/m3) - \(B_i(x,t)\) : fix algae (kg/m) - \(B_j(x,t)\) : fix algae (\(i=j\) for standard applications). - \(S(x)\) : e cross sectional area (m2) - \(\tau(x,t)\) : shear stress (N m-2) - \(\tau_{0}(x,0)\) : shear stress at \(t=0\) - \(s_B\) : sensitivity treshold - \(\delta\) : time constant (s) - \(\eta\) : adimensional exponent
Specifications
- Law’s ID : 341
- Number of acting classes : 3
- Number of parameters : 3
Acting classes : -# \(A_i\) : drift class modified by the law -# \(B_i\) : fix class modified by the law -# \(B_j\) : the parameter class of the law
Parameters : -# \(s_B\) : sensitivity treshold -# \(\delta\) : time constant -# \(\eta\) : adimensional exponent