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Unformatted text preview: 0.4 nm Displacement distance 1 pm Molecular Velocity 10 3 m/s 8/22/2006 ME509: Fluid Mechanics 4 The Smallest Length Scale of a Continuum (Deen, Analysis of Transport Phenomena, 1998) Average over sufficient number of molecules Point quantities, , u , T Random process theory N ~ 10 4 molecules L ~ 70 nm (gases at STP) L ~ 8 nm (liquids) Point Value Macroscopic Value Averaging Volume ~ L 3 2 / 1 N x 8/22/2006 ME509: Fluid Mechanics 5 The Smallest Length Scale of a Continuum (Deen, Analysis of Transport Phenomena, 1998) Length scale of molecular interactions (transport properties, , , D ) Gases: mean free path ~ 100 nm Liquids: molecular diameter ~ 0.3 nm Average over ~ 10 3 interaction length scales L ~ 1 m (gases) L ~ 3 nm (liquids) Taking the max of these two types of quantities L ~ 1 m (gases) L ~ 10 nm (liquids) 8/22/2006 ME509: Fluid Mechanics 6 Gad-el-Hak, 1999...
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