"The time needed to set up a gradient: detailed calculations"

Date:
1970-1971
Reference:
PP/CRI/H/4/25
Catalogue details

Licence: In copyright

Credit: "The time needed to set up a gradient: detailed calculations". Source: Wellcome Collection.

    4/133
    where and thereafter 0® J? = JQ) at - = °, c = Co at X = o CeOatXsL „ :£ ■A We have expressed time in a convenient dimensionless form by putting C d -ï b= ,ri * ¿ 2 ; In the first instance let us assume that the initial concentration is everywhere zero (i.e. f(x)rò). Then at any given time the maximum ' Ç U. <Us> value of AC, the difference between the concentration and its final value, is at the midpointjc » because of the symmetry of the problem. For this special case^e_vakie of AC i s given by: AC - - 2 _CÒ\ - sin exp (-n 2 7T 2 T) , i-—- n ¿ (3) — _D-I ~ If we only consider cases in which AC is small, we need take no more than the first two terms, so that _AC = - [ exp(-n^T) - I exp (-9t¿T) ... ] (4) and usually the first term alone will suffice. In ligure 1 we plot the value of )against T (for the middle point). A C — For example, if (^rf) is taken as 1%, then _T has the value of 0.42. C CY v , XZZ-S^) We have also computed the whole course of the concentration curve for certain selected values of T, using formula (2). Linear Gradient with Initial Constant Background A smaller value of T (for a chosen value of ) can be obtained if
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