  In lab-scale Faraday experiments, meniscus waves respond harmonically to
small-amplitude forcing without threshold, hence potentially cloaking the
instability onset of parametric waves. Their suppression can be achieved by
resorting to a contact line pinned at the container brim with static contact
angle $\theta_s=90^{\circ}$ (brimful condition). However, tunable meniscus
waves are desired in some applications as those of liquid-based biosensors,
where they can be controlled adjusting the shape of the static meniscus by
slightly under/over-filling the vessel ($\theta_s\ne90^{\circ}$) while keeping
the contact line fixed at the brim. Here, we refer to this wetting condition as
nearly-brimful. Although classic inviscid theories based on Floquet analysis
have been reformulated for the case of a pinned contact line (Kidambi 2013),
accounting for (i) viscous dissipation and (ii) static contact angle effects,
including meniscus waves, makes such analyses practically intractable and a
comprehensive theoretical framework is still lacking. Aiming at filling this
gap, in this work we formalize a weakly nonlinear analysis via multiple
timescale method capable to predict the impact of (i) and (ii) on the
instability onset of viscous sub-harmonic standing waves in both brimful and
nearly-brimful circular-cylinders. Notwithstanding that the form of the
resulting amplitude equation is in fact analogous to that obtained by symmetry
arguments (Douady 1990), the normal form coefficients are here computed
numerically from first principles, thus allowing us to rationalize and
systematically quantify the modifications on the Faraday tongues and on the
associated bifurcation diagrams induced by the interaction of meniscus and
sub-harmonic parametric waves.
