Formulation of a mathematical model to predict solar water disinfection

A mathematical model was formulated that will facilitate the prediction of solar disinfection by analyzing the effect of sunlight exposure (x1) and the load of bacterial contamination (x2), as predictor variables, on the efficiency of solar disinfection (y). Aliquots of 0.1 ml containing average numbers of E. coli, ranging between 1 and 5×103 cells/ml raw water, were introduced into each of the 96 wells of polystyrene microtitre plates. Plates, with the lid on, were exposed to sunlight for varying exposures ranging between 1.04×103 and 8.40×103 kJ m2. Double strength nutrient broth was then added. After 48 h incubation wells containing visible contamination were considered as containing one cell or more that survived the exposure. Data showed that disinfection is dependent both on the load of bacterial contamination and sunlight exposure. This relationship is characterized by curves having shoulders followed by a steep decline and then tailing off in an asymptotic fashion. The shoulder size increased with the increase of the contamination load, however, the slope remains the same. Statistical analysis indicates a positive correlation among the variables (R2 = 0.893); the mathematical model, y=1(1ekx1) x2, represents the relationship, with k being the solar inactivation constant. The exposure required to produce a given decontamination level can be predicted using the equation: x1=1/k ln[1(1y)1/x2]e(mu)/(rho)·m/A, where (mu)is the linear attenuation coefficient (m1), (rho)is the density, m is the mass and A is the area of the exposed part of the sample. The predictor variables (x1, x2) strongly influence the efficiency of solar disinfection, which can be predicted using the suggested mathematical model. The present data provides a means to predict the efficiency of solar disinfection as an approach to improve the quality of drinking water mainly in developing countries with adequate sunshine all year-round.