Linear driving force approximation to a radial diffusive model

Transient volume-averaged and spatial intraparticle contaminant concentrati on in a dissolved phase of spherical immobile aggregates is examined using the linear driving force (LDF) model a special case of a generalized concen tration profile (GCP) approximation. Particular cases are solved when a mas s Fur occurs between the surrounding bulk concentration and intraparticle c oncentration. Four different forms for the time-variant surrounding bulk co ncentration are considered: linear, exponential, sinusoidal (oscillatory) a nd step function. Both pointwise and volume-averaged intraparticle concentr ations computed by the LDF model match the numerical and analytical (when a vailable) solutions almost perfectly, when the surrounding bulk concentrati on is assumed to be changing linearly or exponentially. For the other two c ases, however only volume-averaged concentrations across the immobile spher ical particle and the temporal concentrations at the outer boundary of the particle computed from the LDF approximation match the numerical model resu lts reasonably well.