Experiments giving the mass efflux of a Poiseuille flow over a naturally permeable block are reported. The efflux is greatly enhanced over the value it would have if the block were impermeable, indicating the presence of a boundary layer in the block. The velocity presumably changes across this layer from its (statistically average) Darcy value to some slip value immediately outside the permeable block. A simple theory based on replacing the effect of the boundary layer with a slip velocity proportional to the exterior velocity gradient is proposed and shown to be in reasonable agreement with experimental results.

Boundary conditions at a naturally permeable wall

A calculation is given of the viscous force, exerted by a flowing fluid on a dense swarm of particles. The model underlying these calculations is that of a spherical particle embedded in a porous mass. The flow through this porous mass is decribed by a modification of Darcy's equation. Such a modification was necessary in order to obtain consistent boundary conditions. A relation between permeability and particle size and density is obtained. Our results are compared with an experimental relation due to Carman.

A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles

Theory of Infiltration

/pdf/time-lag-and-soil-permeability-in-ground-water-observations-35rhd2nms5.pdf

Time lag and soil permeability in ground-water observations

1 Basic Wood-Moisture Relationships.- 1.1 Introduction.- 1.2 Saturated Vapor Pressure.- 1.3 Relative Humidity.- 1.3.1 Use of the Psychrometric Chart.- 1.3.2 Measurement of Relative Humidity.- 1.3.3 Control of Relative Humidity.- 1.4 Equilibrium Moisture Content and the Sorption Isotherm.- 1.5 The Effect of Changes in Pressure and Temperature on Relative Humidity.- 1.6 Specific Gravity and Density.- 1.7 Specific Gravity of the Cell Wall and Porosity of Wood.- 1.8 Swelling and Shrinkage of the Cell Wall.- 1.9 Swelling and Shrinkage of Wood.- 2 Wood Structure and Chemical Composition.- 2.1 Introduction.- 2.2 The Cell Wall.- 2.3 Structure of Softwoods.- 2.4 Types of Pit Pairs.- 2.5 Softwood Pitting.- 2.6 Microscopic Studies of Flow in Softwoods.- 2.7 Structure of Hardwoods.- 2.8 Hardwood Pitting.- 2.9 Microscopic Studies of Flow in Hardwoods.- 2.10 Chemical Composition of Normal Wood.- 2.10.1 Cellulose.- 2.10.2 Hemicelluloses.- 2.10.2.1 Introduction.- 2.10.2.2 Softwood Hemicelluloses.- 2.10.2.3 Hardwood Hemicelluloses.- 2.10.3 Lignins.- 2.11 Chemical Composition of Reaction Wood.- 2.11.1 Introduction.- 2.11.2 Compression Wood.- 2.11.3 Tension Wood.- 2.12 Topochemistry of Wood.- 3 Permeability.- 3.1 Introduction.- 3.2 Darcy's Law.- 3.3 Kinds of Flow.- 3.4 Specific Permeability.- 3.5 Poiseuille's Law of Viscous Flow.- 3.6 Turbulent Flow.- 3.7 Nonlinear Flow Due to Kinetic-Energy Losses at the Entrance of a Short Capillary.- 3.8 Knudsen Diffusion or Slip Flow.- 3.9 Corrections for Short Capillaries.- 3.10 Permeability Models Applicable to Wood.- 3.10.1 Simple Parallel Capillary Model.- 3.10.2 Petty Model for Conductances in Series.- 3.10.3 Comstock Model for Softwoods.- 3.10.4 Characterization of Wood Structure from Permeability Measurements.- 3.11 Measurement of Liquid Permeability.- 3.12 Measurement of Gas Permeability.- 3.13 The Effect of Drying on Wood Permeability.- 3.14 Treatments to Increase Permeability.- 3.15 The Effect of Moisture Content on Permeability.- 3.16 The Influence of Specimen Length on Permeability.- 3.17 Permeability of the Cell Wall.- 3.18 Zones of Widely Differing Permeabilities in Wood.- 3.19 General Permeability Variation with Species.- 4 Capillary and Water Potential.- 4.1 Surface Tension.- 4.2 Capillary Tension and Pressure.- 4.3 Mercury Porosimetry.- 4.4 Influence of Capillary Forces on the Pressure Impregnation of Woods with Liquids.- 4.5 Collapse in Wood.- 4.6 Pit Aspiration.- 4.7 The Relationship Between Water Potential and Moisture Movement.- 4.8 Notes on Water Potential. Equilibrium Moisture Content, and Fiber Saturation Point of Wood.- 5 Thermal Conductivity.- 5.1 Fourier's Law.- 5.2 Empirical Equations for Thermal Conductivity.- 5.3 Conductivity Model.- 5.4 Resistance and Resistivity Conductance and Conductivity.- 5.5 Derivation of Theoretical Transverse Conductivity Equation.- 5.6 Derivation of Theoretical Longitudinal Conductivity Equation.- 5.7 R and U Values Convection and Radiation.- 5.8 Application to Electrical Resistivity Calculations.- 5.9 Application to Dielectric Constant Calculations.- 6 Steady-State Moisture Movement.- 6.1 Fick's First Law Under Isothermal Conditions.- 6.2 Bound-Water Diffusion Coefficient of Cell-Wall Substance.- 6.3 The Combined Effect of Moisture Content and Temperature on the Diffusion Coefficient of Cell-Wall Substance.- 6.4 Water-Vapor Diffusion Coefficient of Air in the Lumens.- 6.5 The Transverse Moisture Diffusion Model.- 6.6 The Importance of Pit Pairs in Water-Vapor Diffusion.- 6.7 Longitudinal Moisture Diffusion Model.- 6.8 Nonisothermal Moisture Movement.- 6.9 Measurement of Diffusion Coefficients by Steady-State Method.- 7 Unsteady-State Transport.- 7.1 Derivation of Unsteady-State Equations for Heat and Moisture Flow.- 7.2 Derivation of Unsteady-State Equations for Gaseous Flow in Parallel-Sided Bodies.- 7.3 Graphical and Analytical Solutions of Diffusion-Differential Equations with Constant Coefficients.- 7.3.1 Solutions of Equations for Parallel-Sided Bodies.- 7.3.2 Solutions of Equations for Cylinders.- 7.3.3 Simultaneous Diffusion in Different Flow Directions.- 7.3.4 Significance of Flow in Different Directions.- 7.3.5 Special Considerations Relating to the Heating of Wood.- 7.4 Relative Values of Diffusion Coefficients.- 7.5 Retention.- 7.6 Unsteady-State Transport of Liquids.- 7.6.1 Parallel-Sided Bodies, Permeability Assumed Constant with Length.- 7.6.2 Parallel-Sided Bodies with Permeability Decreasing with Length (Bramhall Model).- 7.6.3 Cylindrical Specimens.- 7.6.4 Square and Rectangular Specimens.- 7.7 Unsteady-State Transport of Moisture Under Noniso-thermal Conditions.- 7.8 Heat Transfer Through Massive Walls.- References.- Symbols and Abbreviations.

M Muskat

Papers

The flow of homogeneous fluids through porous media: analogies with other physical problems