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Abstract Supercritical Impregnation methods are becoming popular in the development of food packaging materials. Bulk functional improvements of cellulose substrates using this method may be influenced by interfacial interactions between the impregnated solutes and cellulose. Hence, an interfacial adsorption kinetics study of solute molecules onto the substrate can provide insight on bulk property development, leading to an optimized packaging material with improved functionality. Paper substrates were impregnated with two food-grade waxes: Alkyl Ketene Dimer (AKD) and Carnauba Wax (CW). Hydrophobic development was monitored over a 3-week period. A quartz crystal microbalance (QCM-D) was used to determine interfacial characteristics and behavior of each wax with cellulose, and adsorption kinetics were quantified to compare the mass transfer processes of each wax at the interface. AKD significantly contributed to the substrate’s hydrophobic development over time. CW generated mildly hydrophobic substrates only when heated. AKD strongly adhered to the cellulose fibers at the interface, and demonstrated a 3-stage kinetic adsorption process, tentatively assigned (i) diffusion through the solvent; (ii) diffusion through the substrate; and (iii) attachment onto the fibers. CW readily washed off the cellulose surface, demonstrating only the first adsorption process. The different chemical structures also impacted these behaviors, as did concentration and temperature. Graphical Abstract 

ABSTRACT Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop a simple semi-analytical method to calculate the shape of the spirals launched by an eccentric planet. We assume that the planet emits wavelets during its orbit, and the wave fronts of these propagating wavelets form the spirals. The resulting spiral shape from this simple method agrees with numerical simulations exceptionally well. The spirals excited by an eccentric planet can detach from the planet, bifurcate, or even cross each other, which are all reproduced by this simple method. The spiral’s bifurcation point corresponds to the wavelet that is emitted when the planet’s radial speed reaches the disc’s sound speed. Multiple spirals can be excited by an eccentric planet (more than five spirals when e ≳ 0.2). The pitch angle and pattern speed are different between different spirals and can vary significantly across one spiral. The spiral wakes launched by high-mass eccentric planets steepen to spiral shocks and the crossing of spiral shocks leads to distorted or broken spirals. With the same mass, a more eccentric planet launches weaker spirals and induces a shallower gap over a long period of time. The observed unusually large/small pitch angles of some spirals, the irregular multiple spirals, and the different pattern speeds between different spirals may suggest the existence of eccentric perturbers in protoplanetary discs.