# A -superharmonic functions and supersolutions of degenerate by Heinonen J., Kilpelftine T.

By Heinonen J., Kilpelftine T.

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This theory was later shown by Bartok and Hason (1957), Forgacs and Mason (1959) and Goldsmith and Hason (1962) to also be applicable to discs and 43 cylinders. Bretherton (1962) proved that most bodies of revolution, except some extreme shapes, show periodic rotation with no lift, provided inertia terms are neglected. 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.

The entry efficiency was shown to have a large dependence on the wind speed, particle size, breathing rate and the orientation of the head with respect to the flow, but less dependence on whether the nose or mouth is used for inhaling or the facial details. This work on the human head characteristics was later extended by Vincent and Armbruster (1981), Armbruster and Breuer (1982) and Vincent and Hark (1982). Armbruster and Breuer extended the range of wind velocities and particle sizes used by Ogden and Birkett and also simulated inhalation.

Considering firstly the stagnation point near 6=n-~, at 6=6, say, where 6,=n-«" c, is small. e. 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.