[RASMB] Viscometry question

Fri Sep 23 05:51:43 PDT 2016

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
>
>
>
>
>
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>

-- 
Dr Andrew Leech                   *  Laboratory Head
Technology Facility               *  Molecular Interactions Laboratory
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