2,376 research outputs found
Statistical model for collisions and recollisions of inertial particles in mixing flows
Finding a quantitative description of the rate of collisions between small
particles suspended in mixing flows is a long-standing problem. Here we
investigate the validity of a parameterisation of the collision rate for
identical particles subject to Stokes force, based on results for relative
velocities of heavy particles that were recently obtained within a statistical
model for the dynamics of turbulent aerosols. This model represents the
turbulent velocity fluctuations by Gaussian random functions. We find that the
parameterisation gives quantitatively good results in the limit where the \lq
ghost-particle approximation' applies. The collision rate is a sum of two
contributions due to \lq caustics' and to \lq clustering'. Within the
statistical model we compare the relative importance of these two collision
mechanisms. The caustic formation rate is high when the particle inertia
becomes large, and we find that caustics dominate the collision rate as soon as
they form frequently. We compare the magnitude of the caustic contribution to
the collision rate to the formation rate of caustics.Comment: 9 pages, 4 figures, final version as publishe
Advective collisions
Small particles advected in a fluid can collide (and therefore aggregate) due
to the stretching or shearing of fluid elements. This effect is usually
discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1,
16-30, (1956)]. We show that in complex or random flows the Saffman-Turner
theory for the collision rate describes only an initial transient (which we
evaluate exactly). We obtain precise expressions for the steady-state collision
rate for flows with small Kubo number, including the influence of fractal
clustering on the collision rate for compressible flows. For incompressible
turbulent flows, where the Kubo number is of order unity, the Saffman-Turner
theory is an upper bound.Comment: 4 pages, 1 figur
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