  Pulsar glitches provide a unique way to study neutron star microphysics
because short post-glitch dynamics are directly linked to strong frictional
processes on small scales. To illustrate this connection between macroscopic
observables and microphysics, we review calculations of vortex interactions
focusing on Kelvin wave excitations and determine the corresponding mutual
friction strength for realistic microscopic parameters in the inner crust.
These density-dependent crustal coupling profiles are combined with a
simplified treatment of the core coupling and implemented in a three-component
neutron star model to construct a predictive framework for glitch rises. As a
result of the density-dependent dynamics, we find the superfluid to transfer
angular momentum to different parts of the crust and the core on different
timescales. This can cause the spin frequency change to become non-monotonic in
time, allowing for a maximum value much larger than the measured glitch size,
as well as a delay in the recovery. The exact shape of the calculated glitch
rise is strongly dependent on the relative strength between the crust and core
mutual friction, providing the means to probe not only the crustal superfluid
but also the deeper neutron star interior. To demonstrate the potential of this
approach, we compare our predictive model with the first pulse-to-pulse
observations recorded during the December 2016 glitch of the Vela pulsar. Our
analysis suggests that the glitch rise behavior is relatively insensitive to
the crustal mutual friction strength as long as $\mathcal{B} \gtrsim 10^{-3}$,
while being strongly dependent on the core coupling strength, which we find to
be in the range $3 \times 10^{-5} \lesssim \mathcal{B}_{\rm core} \lesssim
10^{-4}$.
