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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.
B = diffusion coefficient of the eluting particles in the longitudinal direction, resulting in dispersion [m 2 s −1] C = Resistance to mass transfer coefficient of the analyte between mobile and stationary phase [s] u = speed [m s −1] In open tubular capillaries, the A term will be zero as the lack of packing means channeling does not occur ...
In Hamiltonian mechanics, the Boltzmann equation is often written more generally as ^ [] = [], where L is the Liouville operator (there is an inconsistent definition between the Liouville operator as defined here and the one in the article linked) describing the evolution of a phase space volume and C is the collision operator.
Charge transfer coefficient, and symmetry factor (symbols α and β, respectively) are two related parameters used in description of the kinetics of electrochemical reactions. They appear in the Butler–Volmer equation and related expressions. The symmetry factor and the charge transfer coefficient are dimensionless. [1]
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.
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
where we now view f as a function of k. The use of ω(k) to describe the dispersion relation has become standard because both the phase velocity ω/k and the group velocity dω/dk have convenient representations via this function. The plane waves being considered can be described by
In mathematics and its applications, particularly to phase transitions in matter, a Stefan problem is a particular kind of boundary value problem for a system of partial differential equations (PDE), in which the boundary between the phases can move with time.