[RASMB] Viscometry question

[Andrew Leech]

Hi John,

I'm no expert either on hydrodynamics or the AMVn (though I would
like one!) so in a spirit of experiment I dropped a tiny ballbearing
into a test tube of water. I guess it took less than a second to drop
15 cm.

Looking at the AMVn manual, the capillary size for low viscosity
(watery buffers) is only 1.6 mm and the ball is 1.5 mm, so I would
expect that the situation is a lot different than dropping through
a "wide" column of liquid. In addition the ball is presumably
rolling along the inside of the capillary - would that be called
laminar flow? I suppose this situation is contrived to increase
the roll time while minimising the sample volume required.

I don't know if you'd need a supercomputer to model a ballbearing
rolling down a narrow capillary, to see whether it is valid to
assume a simple relation between rolling time and viscosity. (I
think I would measure a set of liquids and compare with other
measurement methods before engaging the mathematicians!)

Hope this is helpful,

Andrew

On 22/09/2016 23:30, John Sumida wrote:
> Dear RASMB,
>
> I have a question regarding the determination of viscosity in a falling
> ball viscometer.  In such device, the time required for the ball to
> traverse the measuring length of the capillary is measured in order to
> determine the solution viscosity.  During this process, the
> non-conservative frictional or drag force on the falling ball is
> balanced by the buoyant force and the gravitational force acting on the
> ball such that Fdrag=Fbouyant+Fgravity.  I have included a powerpoint in
> this email in hopes of being clear and in case the images pasted in this
> email are not properly displayed.
>
> The frictional force is formalized in the Stokes equation
>
> Equation 1
>
> .
>
> Using some simple algebra one finds that the characteristic length the
> ball travels is described by the relation
>
>
>
> Equation 2
>
> Where the term
>
>
>
> Equation 3
>
> Corresponds to 1/K, K being the calibration constant one determines in a
> instrument such as an Anton Paar (AP), AMVn Microviscometer.
>
> Question.
>
> The problem I am observing is that when I compare the measured
> calibration constant with constant one would calculate using
>
>
>
> Equation 4
>
> I get very different values.  Moreover, the terminal velocity of the
> ball and the characteristic measuring length one calculates are
> nonsensical and are very different from the velocity that is measured or
> the measuring length that is reported.
>
>
>
> For example at an angle of 70degrees, a rolling time of 19.199 seconds
> is measured and I calculate the following:
>
> Pains were taken to ensure a correct zero point for the viscometer and
> the standard error in rolling times over 100 measurements was less
> 0.0022.  Calibration of the instrument was performed using degassed
> class IV deionized water and a viscosity of 0.01002 Poise
>
>
>
> I have contacted Anton Paar for more information but we are both
> struggling to understand what the discrepancy is in this calculation.  I
> suspect that the formalism for the Stokes equation is not complete and
> that perhaps a correction is required in terms of the contribution of
> non-laminar flow as the ball falls through the capillary, but having
> reached the ends of my limited understanding of hydrodynamics, I thought
> I would reach out to the AUC community for hints and pointers.
>
>
>
> Any comments and advice you may have are greatly appreciated and I thank
> you all for your time in consideration of my question now as well as in
> the past.
>
>
>
> Thank you,
>
> John Sumida Ph.D.
>
> Bionalytical Core Facility Manager
>
> University of Washington
>
> Molecular Engineering & Sciences Rm G22
>
>
>
>
>
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-- 
Dr Andrew Leech                   *  Laboratory Head
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