Liquid Mixtures at Infinite Dilution
 

 

 

Cris Hussar and Margot Herrman   |   Ceng 402

   

Derivation of Matlab Program

Density:

Densities were found from the CRC Handbook of Thermophysical and Thermochemical Data and were assumed to be independent of temperature. For liquid mixtures of infinite dilution, the density of the solution was approximated as the density of the solvent.

Viscosity:

Viscosities were calculated using the Lewis and Squires liquid viscosity-temperature correlation. For a general idea of the effect of temperature on liquid viscosity, click this link. Lewis Squires Chart. The Lewis and Squires chart can be expressed in equation form as:

Temperatures can be expressed in either Celsius or Kelvin. Using this equation, errors range from ~5-15% of experimentally determined values. This equation is not applicable at temperatures significantly above the normal boiling point. Just as with density, the contribution of the solute viscosity was assumed to be negligible.

Diffusivity:

Diffusivities were calculated using the Tyn and Calus method.

The determination of surface tensions Tb can be difficult to obtain, thus correlations are used to approximate the surface tension ratio using critical properties. Considering the low power to which the ratio is raised, the surface tension ratio estimate should be fairly reasonable. The molar volume at the normal boiling point was estimated using the Tyn and Calus method:

Example:

In order to validate the effectiveness of this program, we calculated the Schmidt numbers of an ethanol/water solution and compared it to the value found in the CRC Handbook of Chemistry and Physics.

Start301 output:

-----------------------------------------------------------------------

Enter the name of compound # 1: ethanol
Enter the name of compound # 2: water

Here are your compounds' formulae and names:
No. Formula Name
----------------------------------------
1 C2H5OH ethanol
2 H2O water

>> lschmidt2(298, 1, 16)

Sc =

726.7642

This value of 726.7642 compares well with the CRC value of 1097. This calculated value comes closer than past ceng402 attempts to calculated Schmidt numbers for liquids of infinite dilution.

 

 

Matlab Code for Liquids

function lschmidt2 = lschmidt2(T, Tdeg, solvent, index)

% Calculates the dimensionless Schmidt number for liquid mixtures at
% infinite dilution. For liquid mixtures, the Schmidt numbers can reach up to 40000.

% The densities used for Schmidt number calculations are the densities of the
% solvent at T=298.15K. Densities were assumed to be independent of
% temperature. Densities were found from the CRC handbook of thermophysical and
% thermochemical data.

% Viscosities were calculated using the Lewis and Squires liquid
% viscosity-temperature correlation. Given a value of viscosity at
% a chosen temperature, viscosity values can be estimated at other
% temperatures.

% Diffusivities were calculated using using Tyn and Calus method. The Tyn
% and Calus method has certain restrictions:
% 1) The method cannot be used for diffusion in viscous solvents
% 2) If the solute is water, a dimer value of molar volume and surface
% tension should be used.
% 3) If the solute is an organic acid and the solvent is not water,
% methanol, or butanol, the acid should be considered a dimer, with twice
% the expected value of molar volume.
% 4) For non-polar solute diffusing into monohydroxy alcohols, the values
% of Vb and Pb should be multiplied by a factor equal to 8*mu where mu is
% the solvent viscosity.

% Argument List:
%T [=] temperature in the units of Tdeg
%Tdeg [=] chosen temperature scale
% 1 - 'kelvin'
% 2 - 'celsius'
% 3 - 'rankine'
% 4 - 'farenheit'

%solvent[=] association parameter of solvent liquid species as follows
% 1 - 'water'
% 2- '1-butene'
% 3- '1,2-dichloroethane'
% 4- '1-hexene'
% 5- '1-pentene'
% 6- 'acetone'
% 7- 'benzene'
% 8- 'carbon dioxide'
% 9- 'carbon disulfide'
% 10- 'carbon tetrachloride'
% 11- 'chloroform'
% 12- 'cyclohexane'
% 13- 'dichloromethane'
% 14- 'diethyl ether'
% 15- 'ethane'
% 16- 'ethanol'
% 17- 'methanol'
% 18- 'methyl chloride'
% 19- 'n-hexane'
% 20- 'n-octane'
% 21- 'n-pentane'
% 22- 'nitrous oxide'
% 23- 'o-xylene'
% 24- 'phenol'
% 25- 'propane'
% 26- 'propylene'
% 27- 'styrene'
% 28- 'toluene'

%index [=] index of compounds from start301

% Returns:
%Sc [=] Schmidt

global mw lrho critP critV TbpK critT

if nargin==3
index = [1 2];
end

j=index(1); %j will always be the solvent
k=index(2);

% Conversion of given T to Kelvin
if Tdeg==2
T=(T+273.15);
end
if Tdeg==3
T=(T*.55556);
end
if Tdeg==4
T=(T+459.67)*.55556;
end

% Calculation of liquid viscosity
% -------------------------------------------------------------------
if solvent==1 %water
mu=liqmucalc(T, 1);
end
if solvent==2 %1-butene
muk = 0.17; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==3 %dichloroethane
muk = 0.83; % muk at Tk
Tk = 20+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==4 %1-hexene
muk = 0.25; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==5 %1-pentene
muk = 0.24; % muk at Tk
Tk = 273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==6 %acetone
muk = 0.32; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==7 %benzene
muk = 0.61; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==8 %carbon dioxide
muk = 0.06; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==9 %carbon disulfide
muk = 0.36; % muk at Tk
Tk = 20+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==10 %carbon tetrachloride
muk = 0.86; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==11 %chloroform
muk = 0.52; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==12 %cyclohexane
muk = 0.88; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==13 %dichloromethane
muk = 0.41; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==14 %diethyl ether
muk = 0.23; % muk at Tk
Tk = 20+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==15 %ethane
muk = 0.032; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==16 %ethanol
muk = 1.04; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==17 %methanol
muk = 0.55; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==18 %methyl chloride
muk = 0.18; % muk at Tk
Tk = 20+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==19 %n-hexane
muk = 0.30; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==20 %n-octane
muk = 0.51; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==21 %n-pentane
muk = 0.225; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==22 %nitrous oxide
muk = 0.35; % muk at Tk
Tk = -160+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==23 %o-xylene
muk = 0.76; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==24 %phenol
muk = 3.25; % muk at Tk
Tk = 50+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==25 %propane
muk = 0.091; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==26 %propylene
muk = 0.081; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==27 %styrene
muk = 0.71; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end
if solvent==28 %Toluene
muk = 0.55; % muk at Tk
Tk = 25+273.15;
mu = (muk^-.2661+(T-Tk)/233)^(-1/.2661);
end

if mu > 25
fprintf('This Schmidt number calculated will be inaccurate')
end

%---------------------------------------------------------------------

% Calculation of liquid Diffusivity using Tyn and Calus method

Tbrsolvent = TbpK(j)/critT(j);
Tbrsolute = TbpK(k)/critT(k);
alphasolvent = 0.9076*(1+(Tbrsolvent*log(critP(j)*.01/1.013)/(1-Tbrsolvent)));
alphasolute = 0.9076*(1+(Tbrsolute*log(critP(k)*.01/1.013)/(1-Tbrsolute)));
sigmasolvent = (critP(j)*.01)^(2/3)*(critT(j))^(1/3)*(.132*alphasolvent-.278)*(1-Tbrsolvent)^(11/9);
sigmasolute = (critP(k)*.01)^(2/3)*(critT(k))^(1/3)*(.132*alphasolute-.278)*(1-Tbrsolute)^(11/9);

% Estimating molar volumes at normal boiling temperature
Vsolvent = 0.285*(critV(j)*100^3)^1.048;
Vsolute = 0.285*(critV(k)*100^3)^1.048;

% Diffusivities
DAB = 8.93*10^-8*Vsolvent^.267/(Vsolute)^.433*T/mu*(sigmasolvent/sigmasolute)^.15;

DAB = DAB/(100^2) % changing units to m^2/s

rho = lrho(j);

mu = mu*10^-3; % changing units from cP to kg/ (m s)

Sc = mu/(DAB*rho)

 

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