[RASMB] Viscometry question

[John Sumida]

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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