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Calculator for viscosity mixing based on the Lederer  Roegiers equation
#5141416
06/23/19 05:34 AM

Joined: Dec 2010
Posts: 4,778
Gokhan
OP

OP
Joined: Dec 2010
Posts: 4,778 
I just realized that the Widman viscositymixing calculator and similar calculators on the Internet are totally useless. They are very inaccurate. After some brief reading, it looks like the Lederer  Roegiers equation works well. The only caveat is that there is an adjustable parameter alpha that accounts for the intermolecular cohesion energy, which ideally needs to be determined empirically. Here is the article I read: Viscosityblending equations Boris Zhmud, Ph.D., Assoc.Prof., MRSC Sveacon Consulting, Stockholm, Sweden LubeTech, No: 93, Page 1 http://www.lubemedia.com/wpcontent/uploads/2017/11/LubeTech093ViscosityBlendingEquations.pdfI created a spreadsheet that you can plug in your values to calculate the blend viscosity: Here is the link for the calculator. Enjoy! Gokhan's viscositymixing calculator based on the Lederer  Roegiers equation
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5141493
06/23/19 08:17 AM

Joined: Dec 2010
Posts: 4,778
Gokhan
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OP
Joined: Dec 2010
Posts: 4,778 
Some clarification on alpha: alpha = 1.0 for mixing similar oils. Typical alpha values for mixing some different oil types are listed in the image as well as the spreadsheet. Clarification on dynamic vs. kinematic viscosity: You need to use the dynamic viscosity. However, if the density values are not available, you can use the kinematic viscosity with reduced accuracy. dynamic viscosity (DV) = density * kinematic viscosity (KV) Density varies as a function of the temperature. You can use this table to estimate it for different temperatures (the exact rate of change with temperature varies with the oil): T (°C) density(T)/density(15.6 °C)
15.6 1.000
20 0.997
30 0.990
40 0.983
50 0.976
60 0.969
70 0.962
80 0.955
90 0.948
100 0.941
110 0.934
120 0.926
130 0.919
140 0.912
150 0.905
160 0.898
170 0.891
180 0.883
190 0.876
200 0.869
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5141533
06/23/19 08:55 AM

Joined: Feb 2019
Posts: 93
Tjbouwhu

Joined: Feb 2019
Posts: 93 
Thank you, I have a fuel diluting GDI....this would be helpful for blending in some 0W30!
Tom



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5141619
06/23/19 10:46 AM

Joined: Oct 2005
Posts: 5,320
JAG

Joined: Oct 2005
Posts: 5,320 
Cool, thanks. That might account for the strange behavior of a mix of a relatively viscous polymer ester and paraffinic base oils in which the mix viscosity is much less than the simple calculators predict. Do you now need to update your spreadsheet that shows the HTFS viscosity or is it close enough?



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: JAG]
#5142034
06/23/19 06:04 PM

Joined: Dec 2010
Posts: 4,778
Gokhan
OP

OP
Joined: Dec 2010
Posts: 4,778 
Cool, thanks. That might account for the strange behavior of a mix of a relatively viscous polymer ester and paraffinic base oils in which the mix viscosity is much less than the simple calculators predict. Do you now need to update your spreadsheet that shows the HTFS viscosity or is it close enough? You're welcome! The calculation for the HTFS viscosity for a single oil doesn't use the viscositymixing calculator. I was asked to calculate the HTHS viscosity of two oils mixed/blended together and I wrote this calculator so that I can use it in that calculation: https://www.bobistheoilguy.com/foru...eraturefullshearviscosity#Post5141467
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5142112
06/23/19 07:11 PM

Joined: Dec 2010
Posts: 4,778
Gokhan
OP

OP
Joined: Dec 2010
Posts: 4,778 
In addition to the DV calculator, which can be used at any temperature, I have now included calculators for KV40 and KV100 as well. Nevertheless, there seems to be very little error in using the DV calculator for KV mixing. So, if you don't bother, use the DV calculator (first calculator) for KV mixing as well. If you're worried about the accuracy, use the KV40 and KV100 calculators (second and third calculators) with the respective KV values. Gokhan's DV and KV viscositymixing calculators based on the Lederer  Roegiers equation
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5149034
07/01/19 08:58 PM

Joined: Dec 2010
Posts: 4,778
Gokhan
OP

OP
Joined: Dec 2010
Posts: 4,778 
Here are the equations for viscosity mixing/blending.
___________________________________________________
Arrhenius equation:
n = n1^x1 * n2^x2
___________________________________________________
Lederer  Roegiers equation:
n = n1^x1_effective * n2^x2_effective
with
x1_effective = x1 / (x1 + x2 * alpha) x2_effective = x2 * alpha / (x1 + x2 * alpha)
___________________________________________________
These are the descriptions of the variables:
^ represents exponentiation: a^b = a raised to the power of b.
n = dynamic viscosity of the mix/blend n1 = dynamic viscosity of oil 1 n2 = dynamic viscosity of oil 2
Note that the dynamic viscosities should be measured at the same temperature for both oils and the mix/blend.
x1 = fraction of oil 1 (between 0 and 1) x2 = fraction of oil 2 (between 0 and 1)
Note that x1 + x2 = 1.
alpha = coefficient to account for the relative intermolecular cohesion energy of oil 2 with respect to oil 1
alpha = 1 if oil 1 and oil 2 have similar molecular structures; otherwise, alpha < 1 or alpha > 1 depending on how oil 2 differs from oil 1. If alpha = 1 (oil 1 and oil 2 have similar molecular structures), Lederer  Roegiers equation reduces to the Arrhenius equation.
x1_effective = effective fraction of oil 1 correcting for the difference in the intermolecular cohesion energy of the two oils x2_effective = effective fraction of oil 2 correcting for the difference in the intermolecular cohesion energy of the two oils
Note that x1_effective + x2_effective = 1.
Example:
If you have a 50/50 blend of an oil with a viscosity 16.0 cP with an oil with a viscosity of 8.0 cP, then the resulting viscosity of the mix/blend is:
16.0^0.5 * 8.0^0.5 = square root(16.0 * 8.0) = 11.3 cP
In other words for a 50/50 mix/blend of similar oils, the viscosity of the mix/blend is the geometric average of the two viscosities (11.3 cP), not the arithmetic average of the two viscosities (12.0 cP).
Finally note that while these equations are for the dynamic viscosities in cP units, they can also be used with good accuracy for the kinematic viscosities in cSt units. (dynamic viscosity = kinematic viscosity * density, with the density measured at the same temperature as the viscosity.)
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5156292
07/10/19 01:26 AM

Joined: Dec 2009
Posts: 28,128
Garak

Joined: Dec 2009
Posts: 28,128 
I just realized that the Widman viscositymixing calculator and similar calculators on the Internet are totally useless. They are very inaccurate. Are you going to go back and correct all the posts you made that were premised on them being nigh on the level of physical constants? On a constructive note, an equation renderer might be of value here.
Plain, simple Garak.
2008 Infiniti G37  Shell ROTELLA T6 MultiVehicle 5w30, Wix 57356 1984 F150 4.9L  Quaker State GB 10w30, Wix 51515



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Garak]
#5156784
07/10/19 01:43 PM

Joined: Jun 2003
Posts: 2,024
edhackett

Joined: Jun 2003
Posts: 2,024 
I just realized that the Widman viscositymixing calculator and similar calculators on the Internet are totally useless. They are very inaccurate. Are you going to go back and correct all the posts you made that were premised on them being nigh on the level of physical constants? On a constructive note, an equation renderer might be of value here. As an analytical chemist(retired) Gokhan's equation raised a lot of red flags as to potential inaccuracies. He's taking a formula that is specifically for a binary mixture and applying it to a mixture of two multi component mixtures, which is definitely not a binary mixture. The equations obtain their accuracy by empirically deriving alpha for each binary mixture at a single mixing ratio. Gokhan is guessing alpha. The accuracy of the Widman calculator and Gokhan's equation can be easily and economically tested. All we need to do is compare the results of the two methodologies to measured values. To that end, I contacted Blackstone and they will do viscosity cSt @100C for $10 each. I'm willing to buy 57 oils and pay for 12 analysis. That should give us a reasonable idea how things fall out of the equations. My plan would be to do mixes of oils of at least two SAE grades apart and of differing base stock mixtures. The mixes would be be biased toward differing brands, wide viscosity differences, and ratios other than 1:1, but would include mixes of the same brand line and mixes of similar oils from different brands. Gokan would supply data from the methodology proposed in this thread, Garak could supply the Widman calculations, and I will provide the measured values. Is everyone game? Ed
Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5156828
07/10/19 02:59 PM

Joined: Jun 2002
Posts: 21,011
MolaKule
Global Moderator

Global Moderator
Joined: Jun 2002
Posts: 21,011 
Sounds like a plan, but I think we need to stipulate that the equations and constants discussed in
posts #5141416 and #5149034 be frozen until the Blackstone results have materialized.
Dr. Larry Fleinhardt: "You know, that term "dark matter" has always perplexed me. It fallaciously implies that the 95% of our universe that cannot be observed is some amorphous, eventless emptiness." Amita Ramanujan: "I'm sorry?" Dr. Larry Fleinhardt: "I guess it's all too human. Instead of admitting to the present limits of our knowledge, we just declare things to be unknowable." NUMB3RS



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5157024
07/10/19 06:45 PM

Joined: Dec 2010
Posts: 4,778
Gokhan
OP

OP
Joined: Dec 2010
Posts: 4,778 
Clarification:
alpha is an adjustable empirical constant that you can only determine by mixing/blending two oils and then actually measuring the viscosity of the mix/blend. You then adjust alpha until the theory agrees with the experiment. Once you know alpha for the two oils you are mixing/blending, you can use it to calculate the viscosity of the mix/blend for different fractions of oil 1 and oil 2.
If you don't know alpha empirically, you can assume that alpha = 1 (as the Widman mixing/blending calculator does but it also does some strange things I don't understand) and go from there. This assumes that oil 1 and oil 2 have similar base oils with viscosities in the same order of magnitude. For two oils with greatly differing baseoil types or viscosities, you can use the table to guess a better alpha but it will only be a rough guess.
2020 Toyota Prius Prime XLE plugin hybrid, 2ZRFXE engine, ~ 70 mpg on gas, ~ 5,000 mi TGMO 0W16 SN/RC Japan OEM spinon oil filter Japan



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: edhackett]
#5157337
07/11/19 03:08 AM

Joined: Dec 2009
Posts: 28,128
Garak

Joined: Dec 2009
Posts: 28,128 
Gokan would supply data from the methodology proposed in this thread, Garak could supply the Widman calculations, and I will provide the measured values. Is everyone game? I'm on board!
Plain, simple Garak.
2008 Infiniti G37  Shell ROTELLA T6 MultiVehicle 5w30, Wix 57356 1984 F150 4.9L  Quaker State GB 10w30, Wix 51515



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5171273
07/26/19 11:05 AM

Joined: Jun 2003
Posts: 2,024
edhackett

Joined: Jun 2003
Posts: 2,024 
I have oils and a plan. The order for sample bottles apparently fell though the cracks at Blackstone. I called this morning and bottles are now on the way. I'll be doing the mixing using Class A graduated cylinders. What? You don't have Class A measuring equipment in your bar kit?! Ed
Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: Gokhan]
#5190771
08/18/19 09:55 PM

Joined: Jun 2003
Posts: 2,024
edhackett

Joined: Jun 2003
Posts: 2,024 
Blackstone has had the samples for a week. No data yet. I'm leaving for a camping trip on Wednesday. If I don't get the data by Tuesday night, I won't get it posted until the following Tuesday.
I'm looking forward to getting the results of this experiment. It took close to three hours to do the mixing as getting a precision that I was comfortable with took long drain times from the cylinder. If you want an oil that will cling like crazy, Redline 50WT Race Oil is the cat's pajamas!
Ed
Never attribute to engineers that into which politicians, lawyers, accountants, and marketeers have poked their fingers.



Re: Calculator for viscosity mixing based on the Lederer  Roegiers equation
[Re: edhackett]
#5193390
08/21/19 09:49 PM

Joined: Dec 2009
Posts: 28,128
Garak

Joined: Dec 2009
Posts: 28,128 
Set it to drip, go on a camping trip, then come back.
Plain, simple Garak.
2008 Infiniti G37  Shell ROTELLA T6 MultiVehicle 5w30, Wix 57356 1984 F150 4.9L  Quaker State GB 10w30, Wix 51515



