  A mathematically challenging model of dynamic wetting as a process of
interface formation has been, for the first time, fully incorporated into a
numerical code based on the finite element method and applied, as a test case,
to the problem of capillary rise. The motivation for this work comes from the
fact that, as discovered experimentally more than a decade ago, the key
variable in dynamic wetting flows -the dynamic contact angle - depends not just
on the velocity of the three-phase contact line but on the entire flow
field/geometry. Hence, to describe this effect, it becomes necessary to use the
mathematical model that has this dependence as its integral part. A new
physical effect, termed the `hydrodynamic resist to dynamic wetting', is
discovered where the influence of the capillary's radius on the dynamic contact
angle, and hence on the global flow, is computed. The capabilities of the
numerical framework are then demonstrated by comparing the results to
experiments on the unsteady capillary rise, where excellent agreement is
obtained. Practical recommendations on the spatial resolution required by the
numerical scheme for a given set of non-dimensional similarity parameters are
provided, and a comparison to asymptotic results available in limiting cases
confirms that the code is converging to the correct solution. The appendix
gives a user-friendl step-by-step guide specifying the entire implementation
and allowing the reader to easily reproduce all presented results, including
the benchmark calculations.
