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</o:shapelayout></xml><![endif]--></head><body lang=EN-US link="#0563C1" vlink="#954F72"><div class=WordSection1><p class=MsoNormal>Dear RASMB,<o:p></o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal>The frictional force is formalized in the Stokes equation<o:p></o:p></p><p class=MsoCaption style='page-break-after:avoid'>Equation 1<o:p></o:p></p><p class=MsoNormal><img width=181 height=30 style='width:1.8854in;height:.3125in' id="Picture_x0020_5" src="cid:image001.png@01D214E4.E7EC2E80">. <o:p></o:p></p><p class=MsoNormal>Using some simple algebra one finds that the characteristic length the ball travels is described by the relation <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoCaption style='page-break-after:avoid'>Equation 2<o:p></o:p></p><p class=MsoNormal><img width=269 height=54 style='width:2.802in;height:.5625in' id="Picture_x0020_4" src="cid:image002.png@01D214E4.E7EC2E80"><o:p></o:p></p><p class=MsoNormal>Where the term<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoCaption style='page-break-after:avoid'>Equation 3<o:p></o:p></p><p class=MsoNormal><img width=145 height=50 style='width:1.5104in;height:.5208in' id="Picture_x0020_3" src="cid:image003.png@01D214E4.E7EC2E80"><o:p></o:p></p><p class=MsoNormal>Corresponds to 1/K, K being the calibration constant one determines in a instrument such as an Anton Paar (AP), AMVn Microviscometer.<o:p></o:p></p><p class=MsoNormal>Question.<o:p></o:p></p><p class=MsoNormal>The problem I am observing is that when I compare the measured calibration constant with constant one would calculate using <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoCaption style='page-break-after:avoid'>Equation 4<o:p></o:p></p><p class=MsoNormal><img width=264 height=49 style='width:2.75in;height:.5104in' id="Picture_x0020_2" src="cid:image008.jpg@01D214E6.37BDE0B0"><o:p></o:p></p><p class=MsoNormal>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. <o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>For example at an angle of 70degrees, a rolling time of 19.199 seconds is measured and I calculate the following:<o:p></o:p></p><p class=MsoNormal><img width=947 height=246 style='width:9.8645in;height:2.5625in' id="Picture_x0020_1" src="cid:image009.jpg@01D214E6.37BDE0B0"><o:p></o:p></p><p class=MsoNormal>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<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>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.<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p><p class=MsoNormal>Thank you,<o:p></o:p></p><p class=MsoNormal>John Sumida Ph.D.<o:p></o:p></p><p class=MsoNormal>Bionalytical Core Facility Manager<o:p></o:p></p><p class=MsoNormal>University of Washington<o:p></o:p></p><p class=MsoNormal>Molecular Engineering & Sciences Rm G22<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>