[RASMB] Viscometry question

Fri Sep 23 12:29:38 PDT 2016

This is a great discussion. Seems to ne very simple and taken very much for granted. Keep it comming. Make Your Day Great, Chris McManemin. Prevoius AUC salesperson amd froend of Dr. And Mrs. Beckman.

Sent from my Verizon, Samsung Galaxy smartphone
-------- Original message --------From: John Sumida <jpsumida at uw.edu> Date: 9/23/16  3:09 PM  (GMT-05:00) To: "'Fagan, Jeffrey (Fed)'" <jeffrey.fagan at nist.gov>, 'Andrew Leech' <andrew.leech at york.ac.uk> Cc: rasmb at list.rasmb.org Subject: Re: [RASMB] Viscometry question 
Dear Andrew and Jeff,

Thanks so much for your responses.  Who would have thought that such
physically simple instrument would have such complexity.  Andrews experiment
raised an issue I thought worth looking into and that is the effect of a
narrowness of the tube channel that the ball has to fall through.  The
rolling time I measure at 85deg was 16.533 seconds, close to the measurement
that Andrew made, but when the tube is oriented at 90deg (vertically
relative to the zeropoint horizontal adjustment) the rolling time is
measured at 25.008 seconds!  The Lewis article Jeff had attached as well as
the Hubbard article attached here both treat the dimensions of the gap
between the ball and tube explicitly.  From what I can gather, deviations
from Stokes becomes greater as the gap distance between the ball and the
walls of the tube decreases such that the calibration constant one would
calculate assuming the simple relations outlined in my earlier email are
erroneous.  More over the spinning of the ball results in curvature of
travel (Magnus effect) which also results in further deviations from Stokes
- not sure how to incorporate this yet. 

I imagine similar issues would occur of an AUC cell were not sector shaped?

Once I incorporate the gap distance correction
(Tubediameter^2-Balldiameter^2)/Balldiameter^2 the calibration constants
calculated fall within a factor of 2 for the measured values - so while I'm
not there yet a big improvement.

Best regards,
John Sumida Ph.D.
Bionalytical Core Facility, MolES G22
University of Washington
Dept. Medicinal Chemistry

-----Original Message-----
From: RASMB [mailto:rasmb-bounces at list.rasmb.org] On Behalf Of Fagan,
Jeffrey (Fed)
Sent: Friday, September 23, 2016 5:52 AM
To: Andrew Leech <andrew.leech at york.ac.uk>; John Sumida <jpsumida at uw.edu>
Cc: rasmb at list.rasmb.org
Subject: Re: [RASMB] Viscometry question

Hi John, Andrew,

Without being able to provide a direct link to the solution as it is far
enough back to prevent an easily googled link (but analytical solutions
certainly exist, and derivation of the calibration coefficient is reported
in the article from 1953 http://pubs.acs.org/doi/pdf/10.1021/ac60075a035),
essentially the hydrodynamic conditions of the viscometer, a ball rolling in
confinement, are far from the small particle Reynolds number and infinite
fluid assumptions that define the friction factor in Stokes conditions.
The lubrication nature of the flow and the confinement both severely
increase the drag.

For reference, even small degrees of confinement in a perfect falling ball
case, such as a tube diameter 20X the ball diameter, still result in
substantial reduction in the terminal velocity (for a Dcylinder/Dsphere of
20 the reduction is 11%).  In the ballbearing experiment below, though the
bigger issue will be that Re >>> 1 (guessing ~ 1000), and thus the drag
about an order of magnitude off the creeping flow Stokes drag projection
(see Bird, Stewart and Lightfoot, Transport Phenomena 1960). 

Best regards,
Jeff Fagan

-----Original Message-----
From: RASMB [mailto:rasmb-bounces at list.rasmb.org] On Behalf Of Andrew Leech
Sent: Friday, September 23, 2016 7:35 AM
To: John Sumida <jpsumida at uw.edu>
Cc: rasmb at list.rasmb.org
Subject: Re: [RASMB] Viscometry question

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
>
>
>
>
>
> _______________________________________________
> RASMB mailing list
> RASMB at list.rasmb.org
> http://list.rasmb.org/listinfo.cgi/rasmb-rasmb.org
>

-- 
Dr Andrew Leech                   *  Laboratory Head
Technology Facility               *  Molecular Interactions Laboratory
Department of Biology (Area 15)   *  Tel   : +44 (0)1904 328723
University of York                *  Fax   : +44 (0)1904 328804
Wentworth Way,  York  YO10 5DD    *  Email : andrew.leech at york.ac.uk
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