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Friction coefficient of rod-like chains of spheres at very low Reynolds numbers . I . Experiment
| Content Provider | Semantic Scholar |
|---|---|
| Author | Zahn, Klaus J. Lenke, Ralf |
| Copyright Year | 2016 |
| Abstract | We present a new method to measure hydrodynamic friction forces on colloidal particles at very low (ci 10~~) Reynolds numbers with high accuracy. Exploiting magnetic field induced aggregation of microcopic paramagnetic spheres into straight chains of calibrated length, we determine the anisotropic friction coefficient of the chains, with a range from one to 100 particles, by video-microscopic observation of sedimentation speed. The results are found to agree well with the Slender-body theory, even for small chain lengths. The effects of the proximity of a wall are also explored. There are various analytical and numerical solutions of the Stokes equations, which are the limit of the Navier-Stokes equations for vanishing Reynolds number [1-4]. In particular, the friction coefficient of a large class of bodies has been studied, including very long and thin but otherwise arbitrary shapes, the sc-called slender-bodies. These theories were tested with experiments using particles of a few millimeters in size suspended in fluids with high viscosity such as glucose (~t ci 2 kg/ms) is, 6]. In this fashion Reynolds numbers as low as 10~~ were obtained, but a typical problem in these experiments is the relatively large liquid volume required to eliminate effects of the container walls on the measurement of the friction coefficient. The latter corrections are of the order d/h or I/(h In(21/d)) for a body of spherical shape or a slender-body, respectively, where d and I are, respectively, the diameter and length of the body and h its distance from the wall. Thus the typical container size is in the range of one meter [6]. In this paper we present a novel, handy, small scale and accurate experimental technique to measure anisotropic friction coefficients of well defined bodies at fixed orientation. We use (* Present address: Institut Charles Sadron (CRM-EAHP), 6 Rue Boussingault, F-67083 Strasbourg Cedex. 556 JOURNAL DE PHYSIQUE II N°4 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://hal.archives-ouvertes.fr/jpa-00247980/document |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | CRM chromium picolinate Diameter (qualifier value) Experiment Friction Glucose Handy Board Human body Hydrodynamics Liquid substance Magnetic Fields Matthews correlation coefficient Navier–Stokes equations Numerical analysis Sedimentation procedure Solutions Theory Walls of a building millimeter |
| Content Type | Text |
| Resource Type | Article |
