Pressure drop for air flow through dry and moist paper has previously been expressed in terms of permeability as determined by Darcy’s law, an approximation now demonstrated to be substantially in error at through flow rates relevant to through drying. The more fundamental, non dimensional treatment using, the Reynolds number-friction factor model has never been applied for paper because of the need for characteristic dimension in Reynolds number. The use of various assumptions for this characteristic dimension in terms of permeability, specific surface, and llagen-Poiseuille equivalent capillary diameter are now shown to be in substantial disagreement with the pore structure of paper as examined by scanning electron microscopy.
A new characteristic dimension for flow through paper has been determined by application of fundamental principles of momentum transport. This characteristic dimension was determined for kraft paper over a wide range of basis weight, 25-250 g/m2 , and over the full range of moisture content from wet to dry. With this characteristic dimension, Reynolds number is rigorously the ratio of the inertial to the viscous contribution to momentum transport. With variation in .moisture content, the value of this characteristic dimension changes between two asymtotic limits which differ by a factor of about 2.5. The limits of these asymptotic regions correspond to known water-fiber relations. The values of the characteristic dimension agree with measurements by scanning electron microscopy.
A theoretical relationship between Reynolds number and friction factor is shown to fit a set of about 3000 measurements of pressure drop taken with about 150 sheets of kraft paper over a wide range of air through flow rate, paper moisture content and basis weight. This successful treatment, based on momentum transport theory, not only eliminates the need for the Darcy law permeability approximation, which leads to errors up to 600% for through flow rates used industrially in through drying, but also provides the basis for theoretical analysis’of heat and mass transport phenomena during through drying.