The Weissenberg or rod-climbing effect - a viscoelastic fluid climbing up a rotating rod - is a classic non-Newtonian phenomenon driven by normal-stress-generated hoop stress, but its time-dependent behavior had not been analyzed theoretically (prior work treated only the steady equilibrium height). Using the Oldroyd-B constitutive model and nondimensionalized governing equations, this paper studies the transient interface height by matched asymptotic analysis. Neglecting surface tension and inertia to isolate the gravity-viscoelasticity coupling, the small-deformation equations reveal a boundary layer in time: the interface rises rapidly on a short time scale (captured with a stretched time variable, yielding the transient velocity field and interface profile) before relaxing to the known steady-state profile on a longer time scale. Reintroducing small but finite inertia, the authors analyze its interplay with viscoelasticity and propose a criterion for the conditions under which rod-climbing (rather than rod-descending) occurs. Under consideration at J. Fluid Mech.
The Weissenberg or rod-climbing effect - a viscoelastic fluid climbing up a rotating rod - is a classic non-Newtonian phenomenon driven by normal-stress-generated hoop stress, but its time-dependent …