Influence of inertia on liquid absorption into paper coating structures

We elucidate in this paper the influence of inertia of the imbibing liquid with special attention to the printing of paper. This is used to explain th e observed differences between the absorption properties of fluids into lar ge and small pores in paper coating structures. Without invoking arbitrary changes of the assumed constants in Lucas-Washbum (Washburn 1921) it has be en hitherto impossible to describe the retarded imbibition seen when absorb ing into highly porous structures containing large pores, for example in ma tt papers or coatings derived from very steep particle size distribution pi gments. We verify the differential effect between coarse and fine pores in a networ k model by the computational network simulator Pore-Cor where, uniquely, Bo sanquet's equation (Bosanquet 1923), which describes both inertial and visc ous capillarity, was incorporated together with mass balance calculations a t each feature entry on a timestep of 1 ns. We apply the findings to compre ssed coating pigment samples of different porosities determined independent ly by mercury porosimetry. This is used to demonstrate the sensitivity of a bsorption rate and potential for separation of fluid(s) into differential p ore sizes based on viscosity, fluid density and pore size distribution dete rmined by the proportion of fine pores present up to a size equal to a Bosa nquet-defined optimum. In a network, like a porous paper coating layer, it is proposed that for low viscosity wetting fluids the smaller features cont inue to fill sequentially according to this inertial preference to the init ial exclusion of larger pores. The proportion of excluded pore volume after imbibition is a function of the available fluid volume which, to define th is regime, must be less than the total available pore volume of the sample.