In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.
Hydrogeology is the area of geology that deals with the distribution and movement of groundwater in the soil and rocks of the Earth's crust. The terms groundwater hydrology, geohydrology, and hydrogeology are often used interchangeably, though hydrogeology is the most commonly used.
Soil liquefaction occurs when a cohesionless saturated or partially saturated soil substantially loses strength and stiffness in response to an applied stress such as shaking during an earthquake or other sudden change in stress condition, in which material that is ordinarily a solid behaves like a liquid. In soil mechanics, the term "liquefied" was first used by Allen Hazen in reference to the 1918 failure of the Calaveras Dam in California. He described the mechanism of flow liquefaction of the embankment dam as:
If the pressure of the water in the pores is great enough to carry all the load, it will have the effect of holding the particles apart and of producing a condition that is practically equivalent to that of quicksand... the initial movement of some part of the material might result in accumulating pressure, first on one point, and then on another, successively, as the early points of concentration were liquefied.
Permeability in fluid mechanics, materials science and Earth sciences is a measure of the ability of a porous material to allow fluids to pass through it.
Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference via the hydraulic conductivity. In fact, the Darcy's law is a special case of the Stokes equation for the momentum flux, in turn deriving from the momentum Navier-Stokes equation.
Poromechanics is a branch of physics and specifically continuum mechanics and acoustics that studies the behaviour of fluid-saturated porous media. A porous medium or a porous material is a solid referred to as matrix permeated by an interconnected network of pores (voids) filled with a fluid. Usually both solid matrix and the pore network, or pore space, are assumed to be continuous, so as to form two interpenetrating continua such as in a sponge. Natural substances including rocks, soils, biological tissues including heart and cancellous bone, and man-made materials such as foams and ceramics can be considered as porous media. Porous media whose solid matrix is elastic and the fluid is viscous are called poroelastic. A poroelastic medium is characterised by its porosity, permeability as well as the properties of its constituents. The distribution of pores across multiple scales as well as the pressure of the fluid with which they are filled give rise to distinct elastic behaviour of the bulk.
Poroelasticity is a field in materials science and mechanics that studies the interaction between fluid flow, pressure and bulk solid deformation within a linear porous medium and it is an extension of elasticity and porous medium flow. The deformation of the medium influences the flow of the fluid and vice versa. The theory was proposed by Maurice Anthony Biot as a theoretical extension of soil consolidation models developed to calculate the settlement of structures placed on fluid-saturated porous soils. The theory of poroelasticity has been widely applied in geomechanics, hydrology, biomechanics, tissue mechanics, cell mechanics, and micromechanics.
Applied mechanics is the branch of science concerned with the motion of any substance that can be experienced or perceived by humans without the help of instruments. In short, when mechanics concepts surpass being theoretical and are applied and executed, general mechanics becomes applied mechanics. It is this stark difference that makes applied mechanics an essential understanding for practical everyday life. It has numerous applications in a wide variety of fields and disciplines, including but not limited to structural engineering, astronomy, oceanography, meteorology, hydraulics, mechanical engineering, aerospace engineering, nanotechnology, structural design, earthquake engineering, fluid dynamics, planetary sciences, and other life sciences. Connecting research between numerous disciplines, applied mechanics plays an important role in both science and engineering.
Tortuosity is widely used as a critical parameter to predict transport properties of porous media, such as rocks and soils. But unlike other standard microstructural properties, the concept of tortuosity is vague with multiple definitions and various evaluation methods introduced in different contexts. Hydraulic, electrical, diffusional, and thermal tortuosities are defined to describe different transport processes in porous media, while geometrical tortuosity is introduced to characterize the morphological property of porous microstructures.
The void ratio of a mixture of solids and fluids, or of a porous composite material such as concrete, is the ratio of the volume of the voids filled by the fluids to the volume of all the solids. It is a dimensionless quantity in materials science and in soil science, and is closely related to the porosity, the ratio of the volume of voids to the total volume, as follows:
In petroleum engineering, the Leverett J-function is a dimensionless function of water saturation describing the capillary pressure,
In the theory of composite materials, the representative elementary volume (REV) is the smallest volume over which a measurement can be made that will yield a value representative of the whole. In the case of periodic materials, one simply chooses a periodic unit cell, but in random media, the situation is much more complicated. For volumes smaller than the RVE, a representative property cannot be defined and the continuum description of the material involves Statistical Volume Element (SVE) and random fields. The property of interest can include mechanical properties such as elastic moduli, hydrogeological properties, electromagnetic properties, thermal properties, and other averaged quantities that are used to describe physical systems.
Terzaghi's Principle states that when stress is applied to a porous material, it is opposed by the fluid pressure filling the pores in the material.
The Kozeny–Carman equation is a relation used in the field of fluid dynamics to calculate the pressure drop of a fluid flowing through a packed bed of solids. It is named after Josef Kozeny and Philip C. Carman. The equation is only valid for creeping flow, i.e. in the slowest limit of laminar flow. The equation was derived by Kozeny (1927) and Carman from a starting point of (a) modelling fluid flow in a packed bed as laminar fluid flow in a collection of curving passages/tubes crossing the packed bed and (b) Poiseuille's law describing laminar fluid flow in straight, circular section pipes.
Porosity or void fraction is a measure of the void spaces in a material, and is a fraction of the volume of voids over the total volume, between 0 and 1, or as a percentage between 0% and 100%. Strictly speaking, some tests measure the "accessible void", the total amount of void space accessible from the surface.
Nuclear magnetic resonance (NMR) in porous materials covers the application of using NMR as a tool to study the structure of porous media and various processes occurring in them. This technique allows the determination of characteristics such as the porosity and pore size distribution, the permeability, the water saturation, the wettability, etc.
In fluid mechanics, fluid flow through porous media is the manner in which fluids behave when flowing through a porous medium, for example sponge or wood, or when filtering water using sand or another porous material. As commonly observed, some fluid flows through the media while some mass of the fluid is stored in the pores present in the media.
Morris Muskat was an American petroleum engineer. Muskat refined Darcy's equation for single phase flow, and this change made it suitable for the petroleum industry. Based on experimental results worked out by his colleagues, Muskat and Milan W. Meres also generalized Darcy's law to cover multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized flow equation provides the analytical foundation for reservoir engineering that exists to this day.
Pore structure is a common term employed to characterize the porosity, pore size, pore size distribution, and pore morphology of a porous medium. Pores are the openings in the surfaces impermeable porous matrix which gases, liquids, or even foreign microscopic particles can inhabit them. The pore structure and fluid flow in porous media are intimately related.
Kambiz Vafai is a mechanical engineer, inventor, academic and author. He has taken on the roles of Distinguished Professor of Mechanical Engineering and the Director of Bourns College of Engineering Online Master-of-Science in Engineering Program at the University of California, Riverside.
