pingu_98/cara
1
0
Fork 0
Code Issues Pull requests Projects Releases Packages Wiki Activity Actions

updates to concentration chapter

Browse source
This commit is contained in:
CERN\Andrejh 2022-06-21 07:29:56 +02:00
parent 67b1c623c7
commit 5c72cd1fa3
1 changed files with 6 additions and 7 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

13
cara/docs/full_diameter_dependence.rst
View file

@ -68,19 +68,18 @@ Note that this result is not integrated over the diameters at this stage, thus t
Note that the diameter-dependence is kept at this stage. Since other parameters downstream in code are also diameter-dependent, the Monte-Carlo integration over the aerosol sizes is computed at the level of the dose :math:`\mathrm{vD^{total}}`.
In case one would like to have intermediate results for emission rate, perform the Monte-Carlo integration of :math:`E_{c, j}^{\mathrm{total}}` and compute :math:`\mathrm{vR^{total}} =\mathrm{vl_{in}} \cdot E_{c, j}^{\mathrm{total}} \cdot \mathrm{BR_k}`
Concentration - C(t, D)
=======================
Long-range approach
===================
*******************
Concentration - :math:`C(t, D)`
***********************
Starting with the long-range concentration of virus, that depends on the **emission rate**, the concentration of viruses in aerosols of a given size :math:`D` is:
Starting with the long-range concentration of virus-laden aerosols of a given size **D**, that is based on the mass balance equation between the emission and removal rates, is given by:
:math:`C(t, D)=\frac{\mathrm{vR}(D) \cdot N_{\mathrm{inf}}}{\lambda_{\mathrm{vRR}}(D) \cdot V_r}-\left (\frac{\mathrm{vR}(D) \cdot N_{\mathrm{inf}}}{\lambda_{\mathrm{vRR}}(D) \cdot V_r}-C_0(D) \right )e^{-\lambda_{\mathrm{vRR}}(D)t}` ,
where :math:`\mathrm{vR}(D)` **(emission rate)** and :math:`\lambda_{\mathrm{vRR}}` **(viral removal rate)** depend on the particle diameter :math:`D`.
Since the emission rate is dependent on diameter-independent variables (:math:`\mathrm{vl_{in}}` and :math:`\mathrm{BR_k}`) that should not be included when calculating the integral, the concentration method was written to be normalized by the emission rate.
where **emission rate vR(D)** and **viral removal rate** :math:`\lambda_{\mathrm{vRR}}` (:meth: `infectious_virus_removal_rate`) are diameter-dependent.
Since the emission rate is, in turn, dependent on other diameter-independent variables (:math:`\mathrm{vl}_\mathrm{in}` and :math:`\mathrm{BR}_k``) that should not be included when calculating the integral, the concentration method was written to be normalized by the emission rate.
In other words, we can split the concentration in two different formulations: