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Calculator for viscosity mixing based on the Lederer - Roegiers equation #5141416 06/23/19 05:34 AM
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Gokhan Offline OP
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I just realized that the Widman viscosity-mixing 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:

Viscosity-blending equations
Boris Zhmud, Ph.D., Assoc.Prof., MRSC
Sveacon Consulting, Stockholm, Sweden
Lube-Tech, No: 93, Page 1
http://www.lube-media.com/wp-content/uploads/2017/11/Lube-Tech093-ViscosityBlendingEquations.pdf

I created a spreadsheet that you can plug in your values to calculate the blend viscosity:

[Linked Image]

Here is the link for the calculator. Enjoy!

Gokhan's viscosity-mixing calculator based on the Lederer - Roegiers equation


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 70 mpg on gas, ~ 5,000 mi
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Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5141493 06/23/19 08:17 AM
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Gokhan Offline OP
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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):

Code
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

[Linked Image]


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Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5141533 06/23/19 08:55 AM
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Thank you, I have a fuel diluting GDI....this would be helpful for blending in some 0W-30!


Tom
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5141619 06/23/19 10:46 AM
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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
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Gokhan Offline OP
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Originally Posted by JAG
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 viscosity-mixing 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...erature-full-shear-viscosity#Post5141467


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 70 mpg on gas, ~ 5,000 mi
TGMO 0W-16 SN/RC Japan
OEM spin-on oil filter Japan
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5142112 06/23/19 07:11 PM
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Gokhan Offline OP
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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 viscosity-mixing calculators based on the Lederer - Roegiers equation

[Linked Image]


2020 Toyota Prius Prime XLE plug-in hybrid, 2ZR-FXE engine, ~ 70 mpg on gas, ~ 5,000 mi
TGMO 0W-16 SN/RC Japan
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Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5149034 07/01/19 08:58 PM
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Gokhan Offline OP
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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.)


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Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5156292 07/10/19 01:26 AM
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Garak Offline
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Originally Posted by Gokhan
I just realized that the Widman viscosity-mixing 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 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Garak] #5156784 07/10/19 01:43 PM
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edhackett Online Content
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Originally Posted by Garak
Originally Posted by Gokhan
I just realized that the Widman viscosity-mixing 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 5-7 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
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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
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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 base-oil types or viscosities, you can use the table to guess a better alpha but it will only be a rough guess.


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Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: edhackett] #5157337 07/11/19 03:08 AM
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Garak Offline
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Originally Posted by edhackett
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 Multi-Vehicle 5w-30, Wix 57356
1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
Re: Calculator for viscosity mixing based on the Lederer - Roegiers equation [Re: Gokhan] #5171273 07/26/19 11:05 AM
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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?! grin

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
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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
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Set it to drip, go on a camping trip, then come back. wink


Plain, simple Garak.

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1984 F-150 4.9L - Quaker State GB 10w-30, Wix 51515
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