We report an experimental analysis of the local entrainment velocity in the self-similar region of a turbulent jet. Particle tracking velocimetry is performed to determine the position of the convoluted, instantaneous turbulent/non-turbulent interface and to compute velocity and velocity derivatives in the proximity of the interface. We find that the local entrainment velocity is mostly governed by a viscous component and that its magnitude depends on the local shape of the interface. It is illustrated that local entrainment is faster for surface elements concave towards the turbulent region. A closer analysis of the plane spanned by mean and Gaussian curvature reveals that depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, namely, viscous diffusion for concave shapes and vortex stretching for convex shapes. Key quantities influencing viscous diffusion and vortex stretching in the entrainment process are identified. It is illustrated that the viscous advancement of the interface into the non-turbulent region mostly depends on the shape of the enstrophy profile normal to the interface. The inviscid contribution is intimately related to the alignment of vorticity with the eigenvectors of the rate of strain tensor. Finally, the analysis substantiates that the convolution of the instantaneous interface is driven by the advection of the underlying fluid together with a contribution from the local entrainment velocity, with the advection velocity being the governing part.