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 :

  1.  A_i : drift class modified by the law
  2.  B_i : fix class modified by the law
  3.  B_j : the parameter class of the law

Parameters :

  1.  s_B : sensitivity treshold
  2.  \delta : time constant
  3.  \eta : adimensional exponent