Sizing paper against capillary suction

Paper without treatment is blotting paper: a network of pores a few microns across, lined with the most wettable surface industry knows. Drop water on it and the water is inside before you look up. Sizing agents exist to flip that behaviour while changing nothing else — to keep a sheet of hydrogen-bonded hydrophilic fibre from behaving like a sponge, using fractions of a percent of hydrophobe.

Why paper drinks

The physics is the Lucas–Washburn law: the distance a liquid penetrates a capillary grows with the square root of time, and the driving capillary pressure scales with surface tension times the cosine of the contact angle divided by pore radius. Small pores suck harder, which is why fine paper wicks faster than coarse board. The sign of the cosine is the switch: wetting contact angles drive spontaneous uptake, and a clean cellulose surface is fully wetting. Everything a sizing program does is aimed at one variable — the contact angle at the fibre wall. Push it past ninety degrees and the capillary pressure reverses: the pore now resists entry, and only pressure-driven penetration remains.

Three ways to place a hydrophobe

Rosin is the original and was bio-based before the category existed: abietane resin acids from pine, a rigid hydrophobic skeleton carrying a single carboxyl handle. Saponified to a soap and precipitated onto fibres with alum at acidic pH — or fortified with maleic anhydride and emulsified cationically — the hydrophobes settle against the fibre wall with their skeletons outward. AKD, alkyl ketene dimer, is built from long-chain fatty acids: its strained ketene group reacts with cellulose hydroxyls as the sheet dries, anchoring the molecule covalently with the alkyl chains pointing away from the fibre. That covalent cure under neutral-to-alkaline conditions is also why AKD displaced acid rosin in fine paper — it allowed calcium carbonate filler and alkaline, permanent sheets. ASA, alkenyl succinic anhydride, cures fastest of the three, esterifying cellulose within the wet end; conventional ASA is built from fossil olefins plus maleic anhydride, and the renewable route swaps the olefin for maleated vegetable oil. Rosin and fatty-acid AKD are thus the case where renewable carbon is the default, not the retrofit.

What sizing cannot do

A sized pore repels only spontaneous wetting. Under pressure — a printing nip, a coating head — liquid is forced in regardless of contact angle, which is why sizing performance is specified by static absorption tests and still fails at the press. Surfactants arriving with other wet-end additives defeat it the same way, by dropping local surface tension. And every hydrophobic patch on the fibre is an area stolen from hydrogen bonding: oversizing measurably weakens the sheet, so the sizer and the strength program fight over the same surface. The historical bill was larger: alum-rosin sizing left the sheet acidic, and acid hydrolysis of cellulose is what crumbled the books of the nineteenth and twentieth centuries. The limiting quantity of the craft is the contact angle — and the bonded area you are willing to spend to raise it.