Relevance of diffusion through bacterial spore coats/membranes and the associated concentration boundary layers in the initial lag phase of inactivation: a case study for Bacillus subtilis with ozone and monochloramine

Math Biosci. 2006 Feb;199(2):175-87. doi: 10.1016/j.mbs.2005.10.001. Epub 2006 Jan 4.


Disinfectants are generally used to inactivate microorganisms in solutions. The process of inactivation involves the disinfectant in the liquid diffusing towards the bacteria sites and thereafter reacting with bacteria at rates determined by the respective reaction rates. Such processes have demonstrated an initial lag phase followed by an active depletion phase of bacteria. This paper attempts to study the importance of the combined effects of diffusion of the disinfectant through the outer membrane of the bacteria and transport through the associated concentration boundary layers (CBLs) during the initial lag phase. Mathematical equations are developed correlating the initial concentration of the disinfectant with time required for reaching a critical concentration (C*) at the inner side of the membrane of the cell based on diffusion of disinfectant through the outer membranes of the bacteria and the formation of concentration boundary layers on both sides of the membranes. Experimental data of the lag phases of inactivation already available in the literature for inactivation of Bacillus subtilis spores with ozone and monochloramine are tested with the equations. The results seem to be in good agreement with the theoretical equations indicating the importance of diffusion process across the outer cell membranes and the resulting CBL's during the lag phase of disinfection.

MeSH terms

  • Bacillus subtilis / drug effects*
  • Bacillus subtilis / metabolism*
  • Bacillus subtilis / physiology
  • Cell Membrane / metabolism
  • Chloramines / pharmacokinetics
  • Chloramines / pharmacology*
  • Disinfectants / pharmacokinetics
  • Disinfectants / pharmacology*
  • Disinfection / methods
  • Models, Biological*
  • Ozone / pharmacokinetics
  • Ozone / pharmacology*
  • Spores, Bacterial / drug effects
  • Spores, Bacterial / metabolism
  • Water Purification / methods


  • Chloramines
  • Disinfectants
  • Ozone
  • chloramine