Abstract
A fouling process is often preceded by an induction period in which no significant fouling is observed. In this paper, a simple lumped parameter model based on fractional surface coverage θ has been developed to correlate experimental data in the induction period. The model assumes that active foulant species stick to the surface and gradually cover it, the rate of change of surface coverage d θ/d t being proportional to the fractional free surface (1 − θ). It is further assumed that the foulant already on the surface acts as a seed, attracting more foulant in a micro-growth manner such that the growth rate is first order in θ with a rate constant k 1. Adopting the concept of removal mechanism similar to that used in adsorption science, the removal rate of the coverage is set to be proportional to the coverage with a rate constant of k 2. The three assumptions are combined to obtain the relationship d θ/d t = k 1 θ(1 − θ) − k 2 θ. The fouling layer grows on the covered surface and the fouling rate can be expressed as θR f′ where R f′ can be any established fouling rate expression. Experimental data, including data obtained during induction periods have been successfully correlated for systems including crude oil fouling, water scaling and whey protein fouling. The physical meanings of the model parameters are discussed. The model supports experimental observations in which shorter induction periods are found with higher surface temperatures. The effects of the surface material and the flow velocity are also analysed.
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