1. n. 
A type of distortion of a wave train in which the velocity of the wave varies with frequency. Surface waves and electromagnetic body waves typically exhibit dispersion, whereas P-waves in most rocks show little change in velocity with frequency.
2. n. 
The phenomenon of a wave separating into its frequency constituents as it passes through a medium. Each frequency component travels at its phase velocity (vp), which is the product of the frequency (f) and wavelength (λ) of that component.
Angular dispersion results from anisotropy, which causes velocity to vary with direction.
Dispersion affects all types of waves, including light, electromagnetic, sound, elastic, gravity, and water waves.
3. n. 
The act of breaking up large particles into smaller ones and distributing them throughout a liquid or gaseous medium. For example, in water-base drilling mud, dispersion is the act of degrading clay materials, starches, carboxymethylcellulose, biopolymer, synthetic polymers, or oils into submicroscopic particles by applying mechanical energy, heat, or chemical means. In oil-mud emulsion terminology, dispersion is the act of forming a fine-grained emulsion of an aqueous phase into an oil. This is usually accomplished with by mechanical shearing or heating in the presence of surfactants. It also includes dispersing solids into an oil mud, such as barite or organophilic clays. Mud viscosity increases as more and more platelets are dispersed. No gel structure can form as long as mechanical shearing is in progress.
4. n. 
A colloidal system, such as a drilling fluid, that has been dispersed. More generally, the term applies to any two (or more) phase system in which one phase exists as small particles or droplets dispersed in the second phase.
5. n. 
Spatial separation of components within a fluid. This separation is often driven by diffusion, mixing, or differential flow. In an oil field, components might be separated because of heterogeneity of permeability, or simply because of different paths taken by the fluid through the pore structure. Hydrodynamic dispersion includes both of these mechanical effects and molecular diffusion. The components of an enhanced oil recovery formulation can also be dispersed within a porous rock via differential adsorption properties (chromatographic effects).