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TimeDomain CVD, Inc. |
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Fluid Flow Made Simple: Ignore (almost) EverythingMass transport can occur due to motion of the bulk fluid or gas, whether or not concentration gradients exist: that is, through motion of the fluid containing the stuff of interest. Anyone who has ever watched a smoker exhale or a leaf fall in a breeze knows this can be a very complex field! However, in many cases of interest for chemical vapor deposition flows are fairly simple (necessarily, as otherwise the machines could never be made to work!). How do we tell what sort of flow we're dealing with? |
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The first clue is the Reynolds number.
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When Re is small (less than about 10), flows are typically very smooth: the "streamlines" (paths of imaginary test particles in the fluid) lie in neighboring layers or laminae, giving rise to the description of this "laminar" flow. |
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As Re grows large flows become more complex: first recirculations and vortices appear (in which the local velocity is opposed to the global average) and then the flow becomes turbulent: time-varying and unpredictable with variations at many length scales.
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Thus the first step in understanding flows is to find a reasonable value of Re. |
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To figure out the physical significance of this obscure combination of parameters, it is first useful to introduce the kinematic viscosity: the viscosity divided by the density:
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Note that the kinematic viscosity has the dimensions of a diffusion coefficient:
It is interesting to note that it is also numerically of the same order as binary diffusion coefficients for gases: i.e. around 0.1 to 1 cm2/sec. |
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If we treat it as a diffusion coefficient, then we can calculate a diffusion length, using the residence time L/U: |
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We then find that the Reynolds number is the square of the ratio of the system size to the diffusion length for momentum: Re is the Peclet number for momentum. |
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| We can now see that small Re corresponds to diffusion lengths comparable to system size: just as before, gradients (in this case in velocity ) are small, and the system behaves as a single unit. When Re is very large (flows with Re > 10,000 or even > 1,000,000 are common in the real world, though fortunately not in CVD reactors) diffusion of momentum only proceeds locally within very tiny cells, and huge gradients are possible: i.e. recirculating and turbulent flows. |
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