Gokhan
Thread starter
I have finally got to calculate the empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix.
My conclusions in summary:
(1) Lederer - Roegiers equation when used with the proper alpha value works!
(2) Arrhenius equation and the Widman mixing calculator do not work!
(3) alpha values ranged from 0.42 to 1.46 in Ed's samples, greatly deviating from the Arrhenius equation and Widman mixing calculator, which assume alpha = 1.
(4) You need to have at least one measured sample to calculate the alpha empirically, from which you can calculate the viscosity for different mix ratios for the same two oils.
If you want to calculate the alpha for a given sample directly without trial and error, here is the formula:
beta = [ln(n / n2)] / [ln (n1 / n2)]
alpha = [x1 * (1 - beta)] / [ (1 - x1) * beta]
Note the parentheses. n1, n2, and n are the viscosities of Oil 1, Oil 2, and Mix, respectively. x1 is the fraction of Oil 1. Once you know the alpha for a given sample, you can calculate the viscosity for different fractions of the same two oils using:
n = n1^x1_effective * n2^x2_effective
x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = 1 - x1_eff
Here are the average alpha values for Ed's samples, with the info in the parenthesis showing the approximate oil composition:
Code
Oil 1 Oil 2 alpha
M1 EP 0W-20 (~ PAO) M1 FS 0W-40 (~ GTL) 1.40
Castrol GTX UC 5W-30 (~ Gr II) Castrol GTX 20W-50 (~ Gr II) 0.86
M1 EP 0W-20 (~ PAO) Redline 50WT Race (~ PAO) 0.85
M1 FS 0W-40 (~ GTL) Redline 50WT (~ PAO) 0.42
Castrol GTX UC 5W-30 (~ Gr II) Rotella T5 10W-30 (~ Group II + GTL ?) 0.50
M1 EP 0W-20 (~PAO) Castrol GTX 20W-50 (~ Group II) 0.81
Redline 50WT Race (~ PAO) Valvoline SAE 30 ND (~ Group II) 1.46
Note that similar base oils result in alpha ~ 1 as expected but when you mix a PAO base oil even with a GTL base oil, alpha differs from 1 significantly.
Use these alpha values along with the spreadsheet provided in the original post for a lot more accurate estimates of the viscosity of the mix. Note that the order of the oils matters when you use a given alpha value -- do not exchange Oil 1 and Oil 2.
The actual empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix:
Code
Sample # alpha_empirical Name Average alpha_empirical
1 1.47 M1 EP 0W-20 - M1 FS 0W-40 1.40
2 1.41 M1 EP 0W-20 - M1 FS 0W-40
3 1.33 M1 EP 0W-20 - M1 FS 0W-40
4 0.86 GTX 5W-30 UC - GTX 20W-50 0.86
5 0.86 GTX 5W-30 UC - GTX 20W-50
6 0.79 M1 EP 0W-20 - Redline 50WT 0.85
7 0.88 M1 EP 0W-20 - Redline 50WT
8 0.89 M1 EP 0W-20 - Redline 50WT
9 0.39 M1 FS 0W-40 - Redline 50WT 0.42
10 0.45 M1 FS 0W-40 - Redline 50WT
11 0.50 GTX 5W-30 UC - Rotel. T5 10W-30 0.50
12 0.81 M1 EP 0W-20 - GTX 20W-50 0.81
13 1.46 Redline 50WT - Valvoline 30 ND 1.46
Last but not least, thank you very much, edhackett, for this great work! It's much appreciated!
My conclusions in summary:
(1) Lederer - Roegiers equation when used with the proper alpha value works!
(2) Arrhenius equation and the Widman mixing calculator do not work!
(3) alpha values ranged from 0.42 to 1.46 in Ed's samples, greatly deviating from the Arrhenius equation and Widman mixing calculator, which assume alpha = 1.
(4) You need to have at least one measured sample to calculate the alpha empirically, from which you can calculate the viscosity for different mix ratios for the same two oils.
If you want to calculate the alpha for a given sample directly without trial and error, here is the formula:
beta = [ln(n / n2)] / [ln (n1 / n2)]
alpha = [x1 * (1 - beta)] / [ (1 - x1) * beta]
Note the parentheses. n1, n2, and n are the viscosities of Oil 1, Oil 2, and Mix, respectively. x1 is the fraction of Oil 1. Once you know the alpha for a given sample, you can calculate the viscosity for different fractions of the same two oils using:
n = n1^x1_effective * n2^x2_effective
x1_effective = x1 / (x1 + x2 * alpha)
x2_effective = 1 - x1_eff
Here are the average alpha values for Ed's samples, with the info in the parenthesis showing the approximate oil composition:
Code
Oil 1 Oil 2 alpha
M1 EP 0W-20 (~ PAO) M1 FS 0W-40 (~ GTL) 1.40
Castrol GTX UC 5W-30 (~ Gr II) Castrol GTX 20W-50 (~ Gr II) 0.86
M1 EP 0W-20 (~ PAO) Redline 50WT Race (~ PAO) 0.85
M1 FS 0W-40 (~ GTL) Redline 50WT (~ PAO) 0.42
Castrol GTX UC 5W-30 (~ Gr II) Rotella T5 10W-30 (~ Group II + GTL ?) 0.50
M1 EP 0W-20 (~PAO) Castrol GTX 20W-50 (~ Group II) 0.81
Redline 50WT Race (~ PAO) Valvoline SAE 30 ND (~ Group II) 1.46
Note that similar base oils result in alpha ~ 1 as expected but when you mix a PAO base oil even with a GTL base oil, alpha differs from 1 significantly.
Use these alpha values along with the spreadsheet provided in the original post for a lot more accurate estimates of the viscosity of the mix. Note that the order of the oils matters when you use a given alpha value -- do not exchange Oil 1 and Oil 2.
The actual empirical alpha values using the Blackstone KV100 for Oil 1, Oil 2, and Mix:
Code
Sample # alpha_empirical Name Average alpha_empirical
1 1.47 M1 EP 0W-20 - M1 FS 0W-40 1.40
2 1.41 M1 EP 0W-20 - M1 FS 0W-40
3 1.33 M1 EP 0W-20 - M1 FS 0W-40
4 0.86 GTX 5W-30 UC - GTX 20W-50 0.86
5 0.86 GTX 5W-30 UC - GTX 20W-50
6 0.79 M1 EP 0W-20 - Redline 50WT 0.85
7 0.88 M1 EP 0W-20 - Redline 50WT
8 0.89 M1 EP 0W-20 - Redline 50WT
9 0.39 M1 FS 0W-40 - Redline 50WT 0.42
10 0.45 M1 FS 0W-40 - Redline 50WT
11 0.50 GTX 5W-30 UC - Rotel. T5 10W-30 0.50
12 0.81 M1 EP 0W-20 - GTX 20W-50 0.81
13 1.46 Redline 50WT - Valvoline 30 ND 1.46
Last but not least, thank you very much, edhackett, for this great work! It's much appreciated!