Diffusivities with dcalc

First, we use dcalc to determine the diffusivity of CO₂ in N₂ so we can check the program against data given in Table 16.2-2 of BS&L^**. Here is a listing of the program:

function D = dcalc (p,T,index)

% Chapman-Enskog formula for mass diffusivity coefficient for binary mixtures
%
% function D = dcalc(p,T,index)
%
% Argument List:
%   p     [=] pressure in kPa
%   T     [=] temperature in the units of Tdeg
%   index [=] index of 2 compounds in cnms whose Dab is to be found
%              (If this argument is omitted, Dab will be found for the first 2)
% Returns:
%   D [=] mass diffusivity in units of m2/s
%
% Ex:  >> clear
%      >> start402
%      >> d = dcalc(0.0099, 298, [1 2])
%      d =
%         1.8961e-05                                Created 3/21/95-2 Jim Lee

global mw lenjones

 lj = checklj;

T=at(T);
if nargin==2
  index=[1 2];
end

sig = 0.5*(lj(index(1),1)+lj(index(2),1));
epDk = sqrt(lj(index(1),2)*lj(index(2),2));
ktDe = T/epDk;
[mu k omega_D] = omegacalc(ktDe);

D = 1.8583e-7 * sqrt(T^3*(1/mw(index(1))+1/mw(index(2)))) / (p*sig^2*omega_D) * 101.325;

% This file was created by m2html.

Here is the estimation of the diffusivity of CO₂-N₂ at 273.2K after the data for CO2, O2, N2 and Ne have been set by use of start301:

>>dcalc(101,273.2,[1 3])
ans =          <-- Note units: m2/s
   1.3005e-05  <-- given as 1.44e-5 in BS&L
>>dcalc(101,298.2,[1 3])  <-- Here it is at 298.2K
ans =
   1.5265e-05  <-- given as 1.65e-5 in BS&L

At both temperatures the predicted values were about 10% lower than the experimental values.

** Bird, Stewart and Lightfoot, Transport Phenomena, Wiley, 1960.