Degree of removal, Chick’s law, Watson’s law, Dose-response curve.

**Basis of disinfection**

The term percentage removal of actual micro-organisms is used in environmental engineering. In microbiological terms log10 removal or inactivation (decimal removal) is used to define the disinfection yield; normally a reduction of between 99 and 99.99% of the total number of bacteria is wanted, which corresponds to a log disinfection of 2–4. However, these terms do not give exact values of the number of micro-organisms left; they only indicate by how much numbers are reduced from the starting concentration.

*Example*

*The normal concentration of bacteria is 107/ml and a reduction of 99.9% is required. Find the concen-tration of bacteria present after disinfection.*

*Solution*

concentration of bacteria after infection = 107(1 − 0.999)

*Example*

*The starting concentration of bacteria is 107/ml. A log disinfection of 3 is wanted. Calculate the new concentration of bacteria.*

*Solution*

*Let the starting concentration be N1 and the end con-centration N*2*; log(disinfection) *=* 3.*

log(disinfection) = log*(N*1/*N*2*)*

= log*N*1 − log*N*2log *N*2= log *N1*−log(disinfection)

=7 – 3

=4

*N*2=104/ml

Inactivation of micro-organisms in a disinfection plant depends on the time that the micro-organism are exposed to the disinfectant. This is described by Chick’s law:

d*n* / d*t *= *kN*

where:

d*n*/d*t*= necessary time to inactivate *n* micro-organisms

*k *=time constant depending on disinfectant,type of micro-organism and water quality

*N *=number of live micro-organisms* t *=time.

This differential equation can be integrated within limits to give the following equation:

*N*1=* N*0e−*kt*

where:

*N*0=number of micro-organisms at the start

*N*1=number of micro-organisms after time* t*.

Based on the results of Chick’s law, Watson’s law can be developed:

where:

Λ = coefficient of specific toxicity

*C *=concentration of disinfectant

*n *=exponent (normally around 1)

*t *=time after start-up.

This means that the relation between the number of active and inactive micro-organisms is a product of the concentration of the disinfectant and the exposure time.

Based on Watsons’s law a dose-response relation may be established for specific types of micro-organism. This gives the proportion of micro-organisms inactivated by fixed doses of disinfectant over various time periods. Exact dose-response relationships are difficult to determine in practice for several reasons. It is often difficult to isolate new pathogens and the response to a certain dose depends, amongst other factors, on the immune status of the organism, environmental conditions and population density.

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