A theoretical analysis was given for the kinetics of an observable in general first-order reaction process (R→P) . It was assumed that reaction degree x≡ [P] / ( [R] + [P] ) obeyed a first-order reaction rate equation and that the observable o of sample during reaction was related with reaction degree through the mixing rule of a power-law type oν= (1-x) oνR+xoνP where oR and oP represent the values of observable, being proper to the reactant and the product respectively (oR<oP) . It was demonstrated for ν<1 that an observable-time curve could possess an inflection point at o*= (1-ν) 1/νoP with the maximum growth rate do/dt= (1-ν) 1/ν-1oPK1. These results coincide in the ν→0 limit with those obtained for a logarithmic (ln o) mixing rule.
Knowledge of survival behaviors of microorganisms on solid surfaces is important to assess and control the risk of cross contamination for food being processed on the surface. Here we report the survival behavior of Escherichia coli left on polypropylene coupons with or without nutritious soil subjected to drying at room temperature. When E. coli cells were left on the coupons with 0.85% saline solution, decrease in the viable cell number was observed in two stages, each of which followed the first order kinetics. The specific death rate was 0.21 h-1 initially and reduced to 0.11 h-1 after the water content reached 3.9 g-water/g-solid. When E. coli cells were left with Luria-Bertani broth, as a model soil, of different water contents, the viable cell number did not show a distinct decrease until the water content reached 3-4 g-water/g-solid. After the water content went down below the threshold, the specific death rate was roughly 0.1 h-1 though deviation was large especially at the final stage of drying. E. coli survived on the surface even after 2 days, and coexistence of nutrients enhanced the final level of viable cells.