We develop a dust efflux model of radiation pressure acting on dust grains which successfully reproduces the relation between stellar mass, dust opacity and star formation rate observed in local star-forming galaxies. The dust content of local star-forming galaxies is set by the competition between the physical processes of dust production and dust loss in our model. The dust loss rate is proportional to the dust opacity and star formation rate. Observations of the relation between stellar mass and star formation rate at several epochs imply that the majority of local star-forming galaxies are best characterized as having continuous star formation histories. Dust loss is a consequence of sustained interaction of dust with the radiation field generated by continuous star formation. Dust efflux driven by radiation pressure rather than dust destruction offers a more consistent physical interpretation of the dust loss mechanism. By comparing our model results with the observed relation between stellar mass, dust extinction and star formation rate in local star-forming galaxies, we are able to constrain the time-scale and magnitude of dust loss. The time-scale of dust loss is long and therefore dust is effluxed in a 'slow flow'. Dust loss is modest in low-mass galaxies but massive galaxies may lose up to 70-80 per cent of their dust over their lifetime. Our slow flow model shows that mass-loss driven by dust opacity and star formation may be an important physical process for understanding normal star-forming galaxy evolution.