## December 05, 2007

### How to Calculate Viscosity of Liquid Mixture?

Have you ever faced a problem of calculating the Viscosity of a Muixture?
Most of us feel that there is no approx formula for calculating Viscosity of mixture of liquids.

Now here is a useful co-relation. Thanks to Milt, It is his effort which can be very useful for many of us.

Calculating the viscosity of a blended liquid consisting of two or more liquids having different viscosities is a three step procedure. The first step involves calculation of the Viscosity Blending Index (VBI) of each component of the blend using the following equation (known as a Refutas equation):

(1) VBI = 14.534 × ln[ln(v + 0.8)] + 10.975

where v is the viscosity in centistokes and ln is the natural logarithm (Loge).

The second step involves using this blending equation:

(2) VBI-blend = [wA × VBIA] + [wB × VBIB] + ... + [wX × VBIX]

where w is the weight fraction (i.e., % ÷ 100) of each component of the blend. In using the above blending equation, it is necessary that all viscosities are determined at the same temperature, for example, 100 °C.

The third and final step is to determine the viscosity of the blend by using the invert of equation (1):

(3) v = (ee(VBI - 10.975) ÷ 14.534) − 0.8

where VBI is the Viscosity Blending Index of the blend and e is the transcendental number 2.71828, also known as Euler's number.

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#### 28 comments:

Anonymous said...

How does equation 1 change if I want "v" to be in centipoise? Thanks

-Justin

Anonymous said...

Also, what is the weight fraction? Is it the same as the mass fraction? thanks
-Justin

profmaster said...

Yes Justin,
Wt Fraction is Mass Fraction basically. You should use this equn in Cst & then convert to centipoise as they are two different units.

If we convert this equation in centi poise, it will not be usable for all general purpose due to different densities.

Anonymous said...

I would like to know if the modified REFUTAS equation can be used in order to predict the v@100°C of oil bases containing viscosity index improvers in order to make me sure that the finshed product meets the SAE requirements.

I already use the REFUTAS for calculation @40°C using VI improvers and it works pretty well (using also correction coefficients for VI improvers determined by experiments) but at 100°C it doesn't work at all.

Can you suggest me a good text book for the modification of the equation for calculation @100°C?

Can I modify the equation using correction coefficients based on experimental determination in order to make it reliable for calculation @100°C?

Looking forward to hear from you soon.

Best regards

Antonio Lofu

profmaster said...

Yes in that case you should go for correction coefficients experimentally determined at 100°C.

VI improvers may behave differently than a conventional solution mix. Therefore, it is better to determine those coefficients practically.

Anonymous said...

I've tried to apply the correction coefficients but the coefficients, differently from the behaviour @40°C, depend on the amount of VII used and on the nature of the base (if mineral or hydrocracked) so it's a little bit difficult the prevision.

Do you have more tricks to reveal?

Antonello Lofù

Anonymous said...

I'm still waiting for your reply

profmaster said...

I could not understand your comment. Can you re-phrase & elaborate more.

Anonymous said...

I'm sorry I forgot to write my name

I'm Antonello lofù and I need you can reply to my post about v@100 in the presence of VII

Antonello Lofù

profmaster said...

As I wrote earlier I could not understand your last question. Can U pls elaborate it with ref to equations given in the post. This will help me in answering.

Anonymous said...

The question is:

correction coefficients fail at 100°C because they seems to depend strongly on the amount of OCP used (I made this observation changing the value of correction coefficients in order to obtain the experimental viscosity value at different VII amount).
This change also changing the nature of the base (if strongly hydrotreated or less hydrotreated)

So their use seems to be completely useless.

Is it right? Or is there a modified REFUTAS equation I can use to solve this problem?

Sincerely yours.

Antonello Lofù

Anonymous said...

You are right..

I told you that unfortunately the correction coefficients don't work in the presence of VII at 100°C becuase their value change using different amounts of VI improver (as determined by changing the coefficients untill to get the experimental viscosity value)making useless any prevision.

Moreover the coefficients change also changing the nature of the base (if moderately or severely hydrotreated)...

So I would like to know if there is an accurate model like a modified Refutas equation which can take in account all this evidence in order to make an accurate prevision of viscosity @100°C.

Looking forward from hearing to you soon,

I send you my best regards

Antonello Lofù

profmaster said...

Have you tried sutherlands correction formula for temperature. If not what is the value of coefficients based on sutherland formula & based on your experiments.

Use base temp as 30 or 40°C at which your coeff were matching. Correct these coeff for 100°C using sutherlands formula and compare with test results.

Also have you considered your VII as another blending liquid or not.
Probably this may help. Let me know your results.

Anonymous said...

how we calculate viscosity for eahc liquid.ex: for ethnanol how we calculate viscosity at different temperatures?

Anonymous said...

how to convert the final viscosity value from centistokes to centipoise?

profmaster said...

Centipoise / Density = Centistoke

Oli said...

Is there a similar equation for rotational (dynamic) viscosities? Or is that a lot more complicated? I'm only looking for an approximate answer.

Anonymous said...

I too am trying to calculate the theoretical viscosity at known temperatures using this formula. I have base oil, viscosity index improvers and additives. The formula above does not account for the latter two per ASTM method. Can anyone show me a formula that can?

Anonymous said...

I need to calculate the viscosity for a liquid mixture consisting of benzene, propylene and propane. First, we need to find the VBN for each component, right? But then, the problem I facing is that I cannot get the VBN value for propylene and propane. This is because when I substitute the kinematic viscosity (in cSt) into the first equation, it shows math error .
So, is there any other method to calculate the viscosity for the liquid mixture?
Thanks

Shirley

profmaster said...

Shirley
Please check if you are using figures for liquid or Gas.
I doubt you may be having figures for propylene & propane in gas form.

Anonymous said...

How to calculate viscosity of reaction mass (pharmacueticals).pls help

Anonymous said...

how to find the viscosity of a liquid-gas mixture??? very urgent please help!!!! thank you

profmaster said...

What do you mean by gas liquid mixture? Is it Gas & liquid in a container or Gas dissolved in liquid or gas reacted with liquid?

How do you define it?

Thuy Hoang said...

Dear profmaster!
I have used this equation to calculate but the calculated results compared with experiments is not the same.
Example 1:
Base oils 1: 73.5g - Viscosity at 40 ° C = 85.45 cSt
2: 25.5g - Viscosity at 40 ° C = 30.20 cSt
Additives 3: 1.0g - Viscosity at 40 ° C = 65.00 cSt
The result: 63.78 cSt
Measurement results: 68.10 cSt
Example 2:
Base oils 1: 72.6g - Viscosity at 40 ° C = 85.45 cSt
2: 16.0g - Viscosity at 40 ° C = 492.14 cSt
Additives 3: 3.9g - Viscosity at 40 ° C = 4100.00 cSt
4: 1.5g - Viscosity at 40 ° C = 650.00 cSt
5: 6.0g - Viscosity at 40 ° C = 12000.00 cSt
The result: 157.31 cSt
Measurement results: 175.74 cSt
Can you explain more help? You have a better calculation please help me! Thank!
Nguyen Hoang.

Anonymous said...

regarding the 'ee' in the final step, is it euler's number squared? Thanks.

Ladislao Oyola said...

equation (3) comes from equation (1). e is for anti-ln.

Anonymous said...

So, for water-methanol mixture i've got the resulting -5,076 cSt. What's wrong? this method is applicable in this case , btw ?

Ahmed said...

How we calculate weight fraction of the oil

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