The role of viscosity in capillary type diluters
The dynamic dilution is always obtained by controlling the two flows (gas to be diluted and diluent gas), the union of which (diluted gas) is characterized by holding all the components present in the gas to be diluted, but with low concentrations because of the dilution ratio (the ratio between the flow of gas to be diluted and the flow of diluted gas). This applies when the diluent gas is a neutral gas.
In capillary based diluters, the control of the two amounts (diluted and diluting gas) is entrusted to the laws that govern the physics of fluids (law of Hagen-Poiseuille) and depends on: the size of the capillaries (R and L), the pressure difference between inlet and discharge of the capillary (DP), the viscosity of the mixture that passes through the capillary tube (η).
In all dynamic diluters one or more of a characteristic of the gas affects the dilution and must therefore be taken into account when it is considerably different for the gas to be diluted with respect to the diluent gas : depending on the technique used for dilution, the physical characteristics to be taken into account depending on the composition of the gases used. Changing the gas mixture composition, a factor GCF (Gas Correction Factor) must be calculated basing on various parameters that may be found on some technical tables. In some cases, the same composition leads to different GCF, depending on the flow controller manufacturer.
When it’s required to compensate for viscosities difference :
- when the diluent gas is different from the gas balance of the mixture to be diluted (eg.: in nitrogen balanced mixture to be diluted with synthetic air) or when the concentration of the active components exceeds a few percent (eg .: 15 vol.% CO2 in nitrogen or 25 vol.% O2 in nitrogen), the effect of the difference in viscosity should be considered and compensated.
- Viscosity compensation is not required when the mixture to be diluted using, as gas “balance” the same component which constitutes the diluent gas and the “active” components of the mixture to be diluted are in a concentration less than a few volume percent.
By applying the Hagen-Poiseuille equation in the dilution ratio formula (Kdil. = flow of the gas to be diluted / output diluted flow,) it is noted that in a equal capillaries type diluter the effect of viscosity is perfectly compensated by the above expression of the flow through one capillary .
Calculation procedure
The calculation and experimental verification of viscosity values corresponding to the different fluids compounds has committed, after Poiseuille, a large number of researchers: the calculation of flows and pressure drops in the ducts (large and small) is required in many technical fields and in medicine. A large number of tables and empirical calculation procedures is available in literature.
Here it is described and automated a calculation empirically developed by Reichenberg, which is one of the most accurate. The description below is provided only for completeness.
Data from the problem (for each component of the mixture) :
– i = components number in the mixture
– yi = molar fraction of ith component (near to Vol% content)
– T = Reference temperature (generally 20°C = 293°K)
– P = Reference pressure (generally 1013 hPa)
Data from the tables (related to individual component) :
– ηi = viscosity of ith pure component (at defined temperature)
– μi = dipole moment [debrys]
– Tci = critical temperature of ith component
– Pci = critical pressure of ith component
– Mi = molar weight of ith component
Calculated parameters :
– Tri = T / Tci
– Pri = P / Pci
– μRi = dipole moment nondimensioned = 52.46 μi^2 x Pc / Tc^2
– FRi = [Tri^3.5 + (10 μRi)^7] / { Tri^3.5 [ 1 + (10 μRi)^7] }
– Ui = { [ 1 + 0.36 Tri (Tri – 1)]^1/6 x FRi } / Tri^1/2
– Trij = T / (Tci x Tcj)^1/2
– μRij = (μRi x μRj)^1/2
– FRij = [Trij^3.5 + (10 μRij)^7] / { Trij^3.5 [ 1 + (10 μRij)^7] }
– Uij = { [ 1 + 0.36 Trij (Trij – 1)]^1/6 x FRij } / Trij^1/2
– Ci = Mi^1/4 / (ηi x Ui)^1/2
Final formulas :
Excel sheet for the automatic calculation
The spreadsheet below described may be downloaded by clicking the green button :
The use of the spreadsheet is very simple: for each compo-nent of the mixture you insert the chemical formula in the boxes of the left and the corresponding concentration on the same line in the column that identifies the wanted measuring unit
In the red box at the bottom, it’s immediately readable the value of viscosity of the mixture calculated in two ways: the calculation according Reichenberg is definitely more accu-rate than the calculation according to Carr (much simplified).
The list of components that can be considered in the mixture is quite substantial. The addition of more components requires some small changes in the control functions of the cells mentioned above.
Anyone interested in adding some chemical compound, can request them to roberto@beta-strumentazione.it , possibly providing the parameters indicated in the table of components.