Seminar on Differential Equations and Dynamical Systems by G. S. Jones

By G. S. Jones

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12) Considering the second stagnation point near 6=n, at 6=6 2 say, where 6 2=n+c 2. e. for I{»O. e. 15) 54 as £, and £2 are small this becomes, s - '" a 1. e. 16) '" sin(!! ) 2 )+f2n [ 2kot(!! 5), but when the sampler is orientated at an angle ~ to the flow the distance between the stagnation points is a constant plus a term of 0('1'). In extending the empirical model to include sampling at any orientation Vincent(1987) assumed that s varied with 'I' in the same way as when facing the flow and this is clearly not correct.

1) it can be seen that in Vincents empirical formulae the correction term is positive but from the theoretical model it is negative. 18. In these cases the size of the inlet is significant relative to the diameter of the sampler body and therefore the assumption made in the mathematical model that 5«a is not valid. 1). e. In this case the inlet is 52 small and so the experimental results can be compared with the theoretical model where the inlet is modelled as a line sink. 6), it is seen that the second term in the expansion is not significant relative to the first and therefore s/a=~(~/n), agreeing with Vincents experimental result.

A study of non-spherical particles was also made by Cox (1965, 1970, 1971). Fuchs (1964) described the motion of ellipsoidal particles moving through a viscous fluid under the influence of an external force acting through its centre. In this case, for low particle Reynolds numbers, it has been found that the torque about the particles centre is zero and therefore it will not rotate about its centre. Also, experiments have shown that the resistance offered by a fluid is given by Stokes law, even for particles of non-spherical shape, if the numerical coefficient is adjusted according to the particle shape.

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