A Simple Method for Calculation of the Permeability Coefficient of Porous Media

Abstract

orous media, such as paper andpaperboard, contain small openspaces, voids and pores, distributedthroughout solid matrices [6].Adsorption and absorption of liquidsthrough these pores have repercussionswith respect to the barrier propertiesand to the ultimate strength of thesheet [7-9].Moreover,the pores have aneffect on the interaction between print-ing inks and paper [10-12].Paper is laminated,surface sized orextruded with a variety of film formersand plastics to lower its permeability tomoisture,water vapor,water and othersolvents,and paper is internally sized toprevent excessive spreading of inks [13-15].In addition,in many converting op-erations,where liquids are forced into thesheet by the action of a nip,the porousstructure of the base sheet is important.Thus,the characterization of the porousproperty,i.e.,permeability,is of major im-portance for predicting the barrier andprinting properties of paper products.PERMEABILITY AND POROSITYPermeability is the most importantphysical property of a porous medi-um, while the porosity is its mostimportant geometrical property. Thepermeability describes the conductivi-ty of a porous medium with respect tofluid flow,whereas porosity is a meas-ure of the fluid storage capacity of aporous material. Permeabilitydescribes how easily a fluid is able tomove through the porous material.Thus, it is related to the connected-ness of the void spaces and to thepore size of the paper. It is calculatedusing a formula widely known asDarcy’s Law [1].For quality control, units of meas-urement may be irrelevant, but for sci-entific research it is essential to be ableto express results in absolute units [3].Permeability measurements expressedin units of airflow or time cannot becompared directly with pore dimen-sions.For this reason,there is a need forcalculating permeability results in ap-propriate units,which is area or squareof length.As such,it can be interpretedin terms of an effective capillary crosssectional area or diameter [16].DARCY’S LAWCurrent equations describing fluidtransport in porous media are basedon semi-empirical equations derivedin the 19th century by Darcy [1] forsingle- phase flow and in the 20th cen-tury for multi-phase flow.These equa-tions describe the average behavior ofa mixture of a porous medium andone or more fluids. Darcy’s lawdescribes the kinetics of fluid flowthrough porous media in terms of thedriving force and the permeability ofthe medium.Darcy’s Law ( 1 )Where:Q = flow rate (m