Our recent equilibrium dialysis studies showed that proteins are able to interact preferentially with acrylamide (Punyiczki et al. (1993) Biophys. Chem. 47, 9-19). The presence of considerable amounts of acrylamide--albeit weakly bound--in the protein volume, coupled with the failure of a simple gating model of quenching to rationalise viscosity dependence of the quenching of tryptophan (Trp) fluorescence in Ribonuclease T1 (RNase T1) has prompted us to explore a new model, the two-phase model for quenching. According to this model, the dynamic quenching is accomplished by quencher molecules already in the protein phase at the moment of excitation. Some of the molecules may, at this moment, form an encounter complex with the fluorophore and thus be responsible for the observed static contribution. We use the rate equation derived from our model to study the viscosity dependence of acrylamide quenching of Trp fluorescence in RNase T1. The model allows us to separate co-solvent effects: the chemical effect on the protein and on the distribution of quencher molecules between the bulk and the protein phases and, further, the viscosity effect due to coupling between the bulk viscosity and the local friction affecting intramolecular fluctuations of the protein matrix. We express local friction in terms of bulk viscosity, eta, and a coupling constant kappa (friction = eta kappa). Addition of glycerol up to 65% is characterised by a kappa of 0.50. The viscosity dependence of the apparent bimolecular quenching constant is a combination of two compensating effects: changes in chemical activity and changes in patterns of structural fluctuations.