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The variance per unit length of the column is taken as the ratio of the column length to the column efficiency in theoretical plates. The van Deemter equation is a hyperbolic function that predicts that there is an optimum velocity at which there will be the minimum variance per unit column length and, thence, a maximum efficiency.
In 1943 Dr Olaf George Dixon of ICI applied for a patent of a new product for column distillation. [1] He used stainless steel mesh instead of sheet steel in the Lessing ring in order to improve the pressure drop of the packed column (in fact, they were called "wire gauze Lessing rings" in a 1949 publication [2]).
Random column packing is the practice of packing a distillation column with randomly fitting filtration material in order to optimize surface area over which reactants can interact while minimizing the complexity of construction of such columns. Random column packing is an alternative to structured column packing.
Proper column packing is important for maximum resolution: An over-packed column can collapse the pores in the beads, resulting in a loss of resolution. An under-packed column can reduce the relative surface area of the stationary phase accessible to smaller species, resulting in those species spending less time trapped in pores.
The dimension of the column space is called the rank of the matrix and is at most min(m, n). [1] A definition for matrices over a ring is also possible. The row space is defined similarly. The row space and the column space of a matrix A are sometimes denoted as C(A T) and C(A) respectively. [2] This article considers matrices of real numbers
Where HETP is the height equivalent theoretical plate, A is the eddy-diffusion parameter, B is the longitudinal diffusion coefficient of the eluting material in the longitudinal direction, C is the resistance to mass transfer coefficient of the analyte between mobile and stationary phase, and u is the linear velocity of the column flow.
A larger surface area allows more cycles, improving separation. This is the rationale for a Vigreux column or a packed fractionating column. Spinning band distillation achieves the same outcome by using a rotating band within the column to force the rising vapors and descending condensate into close contact, achieving equilibrium more quickly.
An a × b rectangle can be packed with 1 × n strips if and only if n divides a or n divides b. [15] [16] de Bruijn's theorem: A box can be packed with a harmonic brick a × a b × a b c if the box has dimensions a p × a b q × a b c r for some natural numbers p, q, r (i.e., the box is a multiple of the brick.) [15]