D Arcy s equation

The column may be packed or it may be an open tube but in this example, a packed column will be specifically considered. The column is considered to have a length (L) and inlet and outlet pressures and inlet and outlet velocities of (Pi), (Po) (ui) and (uo), respectively. The pressure and velocity at a distance (x) from the front of the column is (Px) and (ux), respectively. According to D Arcy s equation for fluid flow through a packed bed, at any point in the column. 

Assuming the laminar flow across the filter, the rate of filtration (dVj/dt can be expressed as a function of pressure drop AP by the modified D Arcy s equation as (Belter et al., p. 22, 1988),... 

For random mat non-woven reinforcements, permeability is isotropic in-plane while, for other textile structures, the permeability will be different in different directions, depending upon the nature of the textile structure (number and size of tows, warp and weft densities etc.). This differential permeability will result in complex flow patterns in the tool, making flow prediction even more important, although the use of D Arcy s equation then becomes an over-simplification. 

In this approach no assumption is made about pore structure or particle size or shape. The model is also more advanced than that described above, in that flow at higher Reynolds numbers is taken into account, which allows taking Ccire of fluid circulation within the pores between the particles. Dissipation resulting from hysteresis-induced meniscus expansion or contraction is cdso incorporated. All of this leads to cui extension of d Arcy s law (sec. I.6.4f). The resulting equations contain a number of physical constants, the interpretation of which in terms of the microscopic geometry of the medium is not direct. Nevertheless, theories such as this one provide useful scale laws. 

Gillespie (8) on the other hand developed an equation of the Lucas-Washburn type without specific reference to an explicit pore model on the basis of D Arcy s law (6). Assuming that AP was constant Gillespie derived the following equation for two dimensional radial spreading of a liquid drop... 

To obtain AGg, we first computed the value of AGip from Watt and D Arcy s data (] ) by means of graphical integration of Equation 5. The results are plotted in Figure 4. 

In the present study we try to obtain the isotherm equation in the form of a sum of the three terms Langmuir s, Henry s and multilayer adsorption, because it is the most convenient and is easily physically interpreted but, using more a realistic assumption. Namely, we take the partition functions as in the case of the isotherm of d Arcy and Watt [20], but assume that the value of V for the multilayer adsorption appearing in the (5) is equal to the sum of the number of adsorbed water molecules on the Langmuir s and Henry s sites ... 

The formula proposed by D Arcy should be modified when applied to gaseous phase diffusion. Hence, the compressibility of gas must be taken into accounf by introducing the mean value of pressure to the equation— A P +P ), where P, is an atmospheric pressure, and P —pressure under which the gas is forced. Therefore the gradient of pressure along the sample thickness L will be P2 Py Substituting with the oxygen viscosity as 2.02-10 N s/m at temperature 20°C, we get the permeability coefficient from the following formula ... 

A similar approach to Halsey s was also devised by D Arcy and Watt by extending Langmuir s equation [i.e. equation (3)] but including an extra term to account for multilayer formation (assumed to occur at a constant adsorption energy independent of the surface heterogeneity), i.e. 

---