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Particle Deposition Mechanisms: Impaction
Inertia Impactions
Near the stagnation point of an in-viscid flow the fluid velocity field is given by
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(1)
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where b is a non-dimensional constant. For a particle under Stokes drag moving on the stagnation streamline, the equation of motion is given by
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(2)
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Using (1) in (2) and restating the resulting equation in a non-dimensional form, it follows that
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(3)
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where the Stokes number is defined as
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(4)
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and
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(5)
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For the linear constant coefficient equation given by (3), the solution is given as
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(6)
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where  are the
solutions to the characteristic equation given by
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(7)
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That is,
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(8)
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It is observed that for
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(9)
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the roots are real and negative. This will lead to
vanishing of  . Additional
details were provided by Friedlander (2000).
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