[kossda]

I have been asked to develop and validate a method to determine the mineral oil content of a water in oil emlsion. The GC method I developed posses all of the normal attributes of a sound analytical method (linear, precise, accurate, good recovery, robust, repeatable, etc.) but due to the nature of the required sample prep the number of samples that can be run per day is limited. This set me to look for a faster, easier method to determine the oil content.

The method I am focused on right now is a density based method that uses a densitometer to measure the density of the emulsion, and the known densities of the oil and water to determine the oil content. I believe I am on the right track, but I need some help. Here is the logic behind my assay.
First, assume no volume change upon emulsification (I believe there is, but can't prove it as yet)
Second, assume that we weigh 1 ml of the emulsion.
Then:
Let X= volume (in mL) of water
Assume the volume total is 1 mL, and that we use the weight of that 1 ml
Then 1-x= volume of oil

If we know the densities of each component, then:
d1(vol1) + d2(v2)=weight of 1 mL(y) since
g/mL(mL) + g/mL(mL)=gms
 Solving for x:
x=(y-d2)/(d1-d2)
I believe that this give a result that would indicate teh volume percent water in the emulsion, which can then be used to determine the volume percent oil (which is what I want to measure). Is this correct?

Next, is it possible to move directly to density alone to determine the composition? Is so, how would this be expressed? As volume percent, mole percent or weigh percent? I could see using the same equation, except that teh value of x would be teh fractions precentage of water, and 1-x the fractional percentage of oil. But I don't see what the units would be, and since the target oil content (lable claim) is expressed as volume percent, I need to ensure that my results carry the same units.
Can anyone help with this?

[mjc123]

Your formula is correct, assuming no volume change on mixing. As you have defined it, x is the volume fraction of water. The volume percent value would be 100*x.
If you wanted weight fraction, you would have to work out the ratio of water mass to total mass of the sample:
Wf = x*d1/{x*d1+(1-x)*d2}
I don't think you want to do mole fraction; you'd need to know accurately the MW of the oil.

However, your results will be inaccurate if, as you suspect, there is a volume change on mixing. That is easily shown - take, say, 100 mL water and 100 mL oil and emulsify them, and see whether the volume differs from 200 mL. If the difference is significant, your formula will be inaccurate. Then your best bet is to make a series of mixtures of known composition and determine their densities, to construct a calibration curve.

Next, is it possible to move directly to density alone to determine the composition?

What do you mean? Isn't that what you're doing?

[kossda]

Thanks for the reply. I needed someone else to confirm that my logic was sound.

To answer your last question, the equation I derived was based on the "special" case where the volume of the weighed emulsion was 1 mL. This means that the weight I obtained was density, for that special case. It also meant that the sum of the individual volume contributions (assuming no change in volume during emulsification) totaled 1. This allowed me to define the volume as x and 1-x, in order to solve the equation.
 The process of what I did was to weigh 1 mL of the emulsion, determine the density of the individual components, then solve for x. As defined in my first post, x was the volume of water in the emulsion. What I want to do is to go straight from measured densities, using a oscillating u tube densitometer, to get directly to the composition. This would ignore volumes and the units would be g/mL for all inputs.
It has been more than 40 years since I was took algebra, and truth be told, it was not my favorite class. My final question, which I hope you can address, is:
IF
all units in the equation are g/ml
And IF
I define x as the percent composition of water in the emulsion
Then IF
I solve for x, are the units in vol% or weight%?
Since the target inputs provided to me are expressed in terms of vol%, it is critical that I return vol% in my validated method. But if the units on all the variables are g/mL, don't they cancel? That would leave me with a unitless number, and a confused analyst!

[Borek]

the equation I derived was based on the "special" case where the volume of the weighed emulsion was 1 mL

The same logic would work for a generalized case with sum of volumes being V. In the final formulas V should cancel out, as density and concentrations are extensive properties.

(Not that I checked details of your derivation, just skimmed to be honest).

[mjc123]

Since the target inputs provided to me are expressed in terms of vol%, it is critical that I return vol% in my validated method. But if the units on all the variables are g/mL, don't they cancel? That would leave me with a unitless number, and a confused analyst!

As I said, x as you define it is the volume fraction of water - a dimensionless number between 0 and 1. if you want the vol %, multiply this number by 100.

In the final formulas V should cancel out, as density and concentrations are extensive properties.

Actually they are intensive properties, but your reasoning is correct.

[Borek]

In the final formulas V should cancel out, as density and concentrations are extensive properties.

Actually they are intensive properties, but your reasoning is correct.

Thanks for correcting. These names are rarely used in Polish (or at least they were rarely used 30 years ago) and while the meaning behind is intuitively obvious, I always have problem combining correct name with the correct idea.

[Furanone]

I have been asked to develop and validate a method to determine the mineral oil content of a water in oil emlsion. The GC method I developed posses all of the normal attributes of a sound analytical method (linear, precise, accurate, good recovery, robust, repeatable, etc.) but due to the nature of the required sample prep the number of samples that can be run per day is limited. This set me to look for a faster, easier method to determine the oil content.

The method I am focused on right now is a density based method that uses a densitometer to measure the density of the emulsion, and the known densities of the oil and water to determine the oil content. I believe I am on the right track, but I need some help. Here is the logic behind my assay.
First, assume no volume change upon emulsification (I believe there is, but can't prove it as yet)
Second, assume that we weigh 1 ml of the emulsion.
Then:
Let X= volume (in mL) of water
Assume the volume total is 1 mL, and that we use the weight of that 1 ml
Then 1-x= volume of oil

If we know the densities of each component, then:
d1(vol1) + d2(v2)=weight of 1 mL(y) since
g/mL(mL) + g/mL(mL)=gms
 Solving for x:
x=(y-d2)/(d1-d2)
I believe that this give a result that would indicate teh volume percent water in the emulsion, which can then be used to determine the volume percent oil (which is what I want to measure). Is this correct?

Next, is it possible to move directly to density alone to determine the composition? Is so, how would this be expressed? As volume percent, mole percent or weigh percent? I could see using the same equation, except that teh value of x would be teh fractions precentage of water, and 1-x the fractional percentage of oil. But I don't see what the units would be, and since the target oil content (lable claim) is expressed as volume percent, I need to ensure that my results carry the same units.
Can anyone help with this?

If you are flexible in changing to other analytical methods and not set on using the density method, might I suggest an even faster method to analyze your mineral oil content?

I use this commonly for analyzing fat contents of many food products with high sample throughput and surprisingly very good correlations with Soxhlet (or Mojonnier for milk products), and it requires very small sample sizes (ie ~200 ul). Pipette 200 ul of your emulsion and 200 ul of Bromonapthalene into Eppendorf Microcentrifuge tube then centrifuge at 5000 rpm for 10 minutes. The mineral oil (Refractive Index=1.46) will partition in the Bromonapthalene (Refractive Index=1.65) separating from the water phase.

By collecting a small drop of the hydrophobic phase and putting on Abbe Refractometer and reading the refractive index, you can easily quantify the Mineral Oil since you will get a reproducible standard curve from running standard mixes from 200 ul Bromonapthalene + 0 ul mineral oil (RI=1.65) up to 200 ul Bromonapthalene + 200 ul Mineral Oil (ie. 0-100% Mineral Oil Content). Each sample should take under 30 seconds! The only thing you may have to play around with is the ratio of bromonapthalene to emulsion sample since if you find emulsion will not break you will need to add more bromonapthalene and this gets more expensive and also sensitivity of analysis goes down.