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 the observed differences between the absorption properties of fluids into large and small pores in paper coating structures. Without invoking arbitrary changes of the assumed constants in Lucas-Washburn (Washburn 1921) it has been hitherto impossible to describe the retarded imbibition seen when absorbing into highly porous structures containing large pores, for example in matt papers or coatings derived from very steep particle size distribution pigments. We verify the differential effect between coarse and fine pores in a network model by the computational network simulator Pore-Cor where, uniquely, Bosanquet's equation (Bosanquet 1923), which describes both inertial and viscous capillarity, was incorporated together with mass balance calculations at each feature entry on a timestep of 1 ns. We apply the findings to compressed coating pigment samples of different porosities determined independently by mercury porosimetry. This is used to demonstrate the sensitivity of absorption rate and potential for separation of fluid(s) into differential pore sizes based on viscosity, fluid density and pore size distribution determined by the proportion of fine pores present up to a size equal to a Bosanquet-defined optimum. In a network, like a porous paper coating layer, it is proposed that for low viscosity wetting fluids the smaller features continue to fill sequentially according to this inertial preference to the initial exclusion of larger pores. The proportion of excluded pore volume after imbibition is a function of the available fluid volume which, to define this regime, must be less than the total available pore volume of the sample.