the shear rate calculation for tunning fork

[01766451297]

For in-line viscosity measurement in chemical process, there is a kind of Vibration viscometers which use Tuning fork Vibration Method. How can i calculate the shear rate between two sensor plates of this tunning fork? Will the shear rate be influenced by the driven frequency of this tunning fork?

 

[Compositepro]

Your best approach is to consult the manufacturer of your instrument. However, I can tell you that there is no simple answer to your question. Oscillatory viscometers do not have a constant or uniform shear rates. Shear rate is related, but not equal to, the velocity that the fork moves. That velocity goes from zero to max each cycle and varies with location on the fork. The instrument actually measures damping or energy loss. It must be calibrated to be able to calculate a viscosity. There are several assumptions about the liquid properties involved in the calculation.

 

[01766451297]

Thanks alot for your answer.
But if the tunning fork is oscilating at the resonance frequency,then there is only one shear rate. It's not possible to get more shear rates to measure the viscosity,right?
So normally, this kind of instrument can not be used for voscosity measurement of non-newton fluid?

 

[jmw]

Firstly, the apparent shear rate may vary from one fluid to another.
For many Behavioural applications (viscosity at the operating temperature) the shear rate is not a concern since more often than not it is repeatability that is important and there are two conditions of measurement: when the product is on-spec abd where repeatability is important and when it is off-spec when all that is important is to know that the fluid quality is off-spec.
However, for quality or analytical measurements the fact that the fluid is shear sensitive only means that you may have to calibrate the sensor against your laboratory standard. There are many successful, very succesful process measurements of viscosity for some highly non-newtonian fluids. One of the keys to successful measurement is to control the variables. For example, use a pump and flow the fluid at a constant flowrate (and constant shear) past the sensor.
The manufacturers of controlled shear process viscometers would like you to think that you cannot use a tuning fork viscometer on a non-Newtonian fluid but in reality most fluids that have process viscometers used are non-newtonian with the exception of hydrocarbons (and the more viscous they are the less Newtonian they are).
Examples of success for the tuning fork include chalk slurries (cement industry) which has had viscosity modifiers added, muds, methyl methacrylate, bitumens, asphalts, vinyl coatings and so on.
Perhaps if you want to tell us about your application and the conditions, more specific advice can be given.


JMW

http://www.ViscoAnalyser.com

 

[jmw]

PS you can ask the manufacturer (Emerson Mowbrey/Solartron?) but you will not get a definitive answer. (If you do get an answer, post it here!)

JMW

http://www.ViscoAnalyser.com

 

[Compositepro]

Tuning forks are good for maintaining constant frequency, but frequency is not shear rate. Until you are clear on that concept you will not get an answer to your original question. As I wrote earlier, shear rate will go from zero to maximum twice in each period of the oscillation. Amplitude of the vibration goes from zero to maximum from the base to the tip of the tuning fork. At zero amplitude there is zero shear (no movement).

I'd did not truely understand what shear rate was until years after I graduated from university (sad). If you have fluid between two plates one inch apart and you move one plate to shear the fluid one inch in one second, then the shear rate is one reciprocal second (one inch divided by one inch per second). This means that a line that was initially drawn straight between these plates would be at a 45 degree angle (1:1 slope) after one second. At a shear rate of 100 reciprocal seconds, that same line would have a slope of 100:1 after one second.

I apologize if anyone finds this discussion way too basic but my experience is that there are a lot of engineers out there who talk about shear rates but don't have a good understanding of what it is. And solving most engineering problems is just a matter of reducing it to basic principles and not getting confused with irrelevant details.

 

[jmw]

As a displacement type sensor the tuning fork resonant frequency changes with the density of the fluid which will also contribute to a change in the shear rate.
Is it significant? who knows, having recognised that there is not a constant shear rate nor even one that can be quantified in any meaningful way, it would have been pointless to investigate it further, especially as it does not preclude it from being used as a process instrument for non-Newtonian fluids.

The shear behaviour is consistent enough to give repeatable results.
This is partly because (for the 7827) the time period is very short compared to the calculation period so any cyclic effects average out.
Because the frequency is comparatively high the data cycle is anywhere from 1-2 seconds (not to be confused with the calculation cycle which is user adjustable from 0.5seconds and up.
For example the device flips between operating at the upper and lower 3dB frequencies and the frequency of each is determined by measuring the time required to count 1000 cycles (typical). So a calculation period depends on the time for two such cycles (viscosity is a function of the bandwidth or the difference in the upper and lower 3dB frequencies) plus the stabilisation time (the time taken for the sensor to stabilise at the operating frequency). Hence any variation in viscosity due to variation in shear rate caused by the sinusoidal motion of the tines is not evident in the final measurement and the viscosity measurement can be very stable indeed.

The only surprise with some non-Newtonian fluids is just what that "viscosity" will be.
With any process instrument, even rotational viscometers where because of the different compromises in design between a laboratory and a process instrument, getting agreement between the lab and process instruments isn't straightforward, what is required is to find out what the process instrument says and then adjust its calibration to match the laboratory measurement (just like any other instrument?).
Two main sources of shear are the sensor shear and flow shear. Hence keeping flow constant provides a for a relatively constant shear regime for the measurement. It just won't be the same shear that you get with the lab instrument. It will be somewhere else along the viscosity shear curve and you correct for that in the instrument calibration software.



JMW

http://www.ViscoAnalyser.com

 

[01766451297]

Thanks alot for your explanation.I just start my project and I will ask some manufactures to get more information. If i could get any useful information, I will post it here.

 

[Compositepro]

I forgot to add in my last post that I have nothing against vibratory viscometers, which may have been infered from what I was saying. In many process applications they may well be the best choice of instrument.

But, sometimes it is very useful to measure the true stress versus shear rate curve for materials. The original question was how do you calculate the true shear rate for a tuning-fork viscometer. The basic answer is you can't. But the instrument can make useful viscosity measurements if calibrated against standards that were developed using other types of instruments. A Brookfield cone and plate viscometer comes pretty close to measuring shear stress at known shear rates. The ratio is viscosity.

 

[jmw]

Absolutely.
There are some fluids which currently defy using vibrational instruments because of their more complex rheology but for a significant range of fluids, Newtonian and non-newtonian, the vibrational instrument is exceptionally good. It is very "accurate" (or repeatable) and very reliable.
With shear sensitive fluids, the best way to determine the real viscosity is to do as compositepro suggests: take a sample to the lab and measure the viscosity under lab conditions. By maintaining repeatable process conditions you can calibrate the process instrument against the lab.
However, for many process applications the viscosity is valuable control parameter but not so important as a quality factor; it doesn't matter what the true viscosity is as the success of the instrument is measured in terms of production reject rates. Mostly these are what can be referred to as "behavioural" measurements where you measure the viscosity at the process temperature and then adjust the viscosity by heating or adding viscosity modifiers, or solvents. Success is when you have minimised the use of materials but also minimised the reject levels. These are typically coating dipping, spraying and atomisation of fluids type of processes.
Analytical measurements are where viscosity is a quality factor of the fluid and often needed at a reference temperature. These are by far the more difficult applications but the problem is much more to do with temperature than it is to do with the shear dependent properties.


JMW

http://www.ViscoAnalyser.com

 

[jmw]

Sorry, for completeness I thought I should add that the frequency varies with the density in a tuning fork device which displaces the fluid. Viscosity dampens the vibration.
Thus as the viscosity increases the amplitude of the movement will reduce so that the peak shear rate will reduce as viscosity increases. Also, as the density changes the shear rate will change.
Plus, as Compositepro says, because it is a tuning fork the tips of the tines move furthest and the fastest so the shear will vary along the length of the tines.

Similar thoughts arise with the Sofraser viscometer which is a vibrating rod. However, most vibrating element viscometers use a rotational oscilation e.g. Nametre, Hydramotion, VAF etc.
They do no displace the fluid so they don't measure density and the frequency will simply be the resonant frequency of the sensor which does not change. The shear will be constant along the surface of the sensor in a direction paralel to the axis of rotation, if the sensor is cylindrical (VAF) but some rotational elements are spherical so shear changes dependent on where you are relative to the "equator". Plus, of course, it is an oscillatory movement so shear rate changes sinusoidally through each cycle.

On the whole it is better to forget about shear rates with vibrational instruments. It doesn't matter for Newtonian fluids and for non-Newtonian fluids you have to take a practical approach.

JMW

http://www.ViscoAnalyser.com