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In an optical fiber, the material dispersion coefficient, M(λ), characterizes the amount of pulse broadening by material dispersion per unit length of fiber and per unit of spectral width. It is usually expressed in picoseconds per ( nanometre · kilometre ).
Dispersion can be differentiated from diffusion in that it is caused by non-ideal flow patterns [1] (i.e. deviations from plug flow) and is a macroscopic phenomenon, whereas diffusion is caused by random molecular motions (i.e. Brownian motion) and is a microscopic phenomenon.
is the Diffusion coefficient [2] and is the Source term. [3] A portion of the two dimensional grid used for Discretization is shown below: Graph of 2 dimensional plot. In addition to the east (E) and west (W) neighbors, a general grid node P, now also has north (N) and south (S) neighbors.
where ϕ(r, t) is the density of the diffusing material at location r and time t and D(ϕ, r) is the collective diffusion coefficient for density ϕ at location r; and ∇ represents the vector differential operator del. If the diffusion coefficient depends on the density then the equation is nonlinear, otherwise it is linear.
A. R. Forouhi and I. Bloomer deduced dispersion equations for the refractive index, n, and extinction coefficient, k, which were published in 1986 [1] and 1988. [2] The 1986 publication relates to amorphous materials, while the 1988 publication relates to crystalline.
The higher the diffusivity (of one substance with respect to another), the faster they diffuse into each other. Typically, a compound's diffusion coefficient is ~10,000× as great in air as in water. Carbon dioxide in air has a diffusion coefficient of 16 mm 2 /s, and in water its diffusion coefficient is 0.0016 mm 2 /s. [1] [2]
Mass transfer coefficients can be estimated from many different theoretical equations, correlations, and analogies that are functions of material properties, intensive properties and flow regime (laminar or turbulent flow). Selection of the most applicable model is dependent on the materials and the system, or environment, being studied.
For a stationary medium , in which the diffusion coefficients, which are not necessarily equal, can vary with the three spatial coordinates, the more general gradient based diffusion equation states, = + + Considering a point source, the boundary conditions are < < where such that =, where is the source strength (total amount of released).