  The photoevaporation of protoplanetary discs by nearby massive stars present
in their birth cluster plays a vital role in their evolution. Previous
modelling assumes that the disc behaves like a classical Keplerian accretion
disc out to a radius where the photoevaporative outflow is launched. There is
then an abrupt change in the angular velocity profile, and the outflow is
modelled by forcing the fluid parcels to conserve their specific angular
momenta. Instead, we model externally photoevaporating discs using the slim
disc formalism. The slim disc approach self consistently includes the advection
of radial and angular momentum as well as angular momentum redistribution by
internal viscous torques. Our resulting models produce a smooth transition from
a rotationally supported Keplerian disc to a photoevaporative driven outflow,
where this transition typically occurs over ~4-5 scale heights. The penetration
of UV photons predominately sets the radius of the transition and the
viscosity's strength plays a minor role. By studying the entrainment of dust
particles in the outflow, we find a rapid change in the dust size and surface
density distribution in the transition region due to the steep gas density
gradients present. This rapid change in the dust properties leaves a
potentially observable signature in the continuum spectral index of the disc at
mm wavelengths. Using the slim disc formalism in future evolutionary
calculations will reveal how both the gas and dust evolves in their outer
regions and the observable imprints of the external photoevaporation process.
