An experimentally verified theoretical study of the falling cylinder viscometer

Lohrenz, John; Swift, George W.; Kurata, Fred

doi:10.1002/aic.690060408

Cited by 53 publications

(18 citation statements)

References 4 publications

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“…Wehbeh et al 7 measured the drag of long cylinders of various radii settling in closed and open-ended tubes. When the tube was closed, as expected, the discrepancy between the experimental data and the one-dimensional solution [1][2][3] decreased as the cylinder's length to radius ratio increased. This was not the case, however, when Wehbeh et al 7 …”

Section: Introductionmentioning

confidence: 52%

“…Using small gap approximation, numerous researchers [1][2][3] have produced the solution when ϭ0. Here, we provide the straightforward extension for the case of 0.…”

Section: Long Concentric Cylindermentioning

confidence: 99%

“…Most of the studies to date have been motivated by the needle viscometer and have focused on long, axisymmetrically [1][2][3] and eccentrically 4,5 translating cylinders in closed tubes. Davis 6 approximated the finite cylinder as an array of equally spaced disks and studied the forces acting on cylinders translating in an infinite medium and axisymmetrically in tubes.…”

Section: Introductionmentioning

confidence: 99%

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On the translation of a cylinder in a long tube

Liu

Bau

2004

Physics of Fluids

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We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle's dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a "leaky" piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle's motion as functions of the particle's position and dimensions. When the particle is short, a superpositionbased algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory. We study the motion of a cylindrical particle translating slowly in a long tube as a function of the particle's dimensions and placement both in the presence and the absence of external pressure gradients. The cylinder acts as a ''leaky'' piston, generating both fluid recirculation and through flow. When the particle is long, analytic expressions are obtained for both the velocity field and the force needed to sustain the particle's motion as functions of the particle's position and dimensions. When the particle is short, a superposition-based algorithm is outlined to facilitate economical numerical calculations. When the particle is placed off center in the tube, torque will act on the particle. When the particle is unguided, this torque will preclude coaxial motion and cause the particle to follow an oscillatory trajectory.

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Section: Introductionmentioning

confidence: 52%

“…Using small gap approximation, numerous researchers [1][2][3] have produced the solution when ϭ0. Here, we provide the straightforward extension for the case of 0.…”

Section: Long Concentric Cylindermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the translation of a cylinder in a long tube

Liu

Bau

2004

Physics of Fluids

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“…Under the further assumption that entrance and exit effects are negligible, Lohrenz (8) determined that for a falling cylinder of radius KR, moving in the negative z direction through a tube of radius R filled with fluid:…”

Section: Theorymentioning

confidence: 99%

“…Theoretical studies to date on the falling cylinder viscometer ( 1 , 3, 5,8) assumed that entrance and exit effects could be neglected. Thus, experimentalists employing the falling cylinder viscometer (6,10,11) found it necessary to calibrate their viscometers to compensate for entrance and exit effects.…”

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confidence: 99%

Analysis of entrance and exit effects in a falling cylinder viscometer

Chen

Swift

1972

AIChE Journal

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Theoretical studies to date on the falling cylinder viscometer ( 1 , 3, 5, 8) assumed that entrance and exit effects could be neglected. Thus, experimentalists employing the falling cylinder viscometer (6, 10, 11) found it necessary to calibrate their viscometers to compensate for entrance and exit effects.This paper presents the development and solution of equations for incompressible, Newtonian fluid flow in the falling cylinder viscometer including entrance and exit effects, and experimental data corroborating the calculated results for N R~ < 25. THEORYFor a steady, axisymmetric flow of an isothermal, inconipressible, Newtonian fluid with the assumption that p = f ( 2 ) o~$y, the equations of continuity and motion in cylindrical &ordinates are:Under the further assumption that entrance and exit effects are negligible, Lohrenz (8) determined that for a falling cylinder of radius KR, moving in the negative z direction through a tube of radius R filled with fluid:

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