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Revista mexicana de física

versión impresa ISSN 0035-001X

Rev. mex. fis. vol.60 no.3 México may./jun. 2014




Brownian motion of a colloidal particle immersed in a polymeric solution near a rigid wall


B. L. Arenas-Gómez and M. D. Carbajal-Tinoco


Departamento de Física, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, México, 07000 D.F., México, e-mail:


Received 27 November 2013
accepted 26 March 2014



By using three-dimensional digital video microscopy (DVM-3D), we study the displacement of a Brownian particle immersed in a polymeric solution located near a rigid wall. The technique takes advantage of the diffraction pattern generated by a fluorescent particle that is found below the focal plane of an optical microscope. The particle is then tracked from the analysis of a sequence of digitized images to reconstruct its trajectory, which provides relevant information about the properties of the system. In a first stage, we obtain the mean square displacement (MSD) of a spherical probe dissolved in a viscoelastic solution. This MSD is then used to determine the elastic and viscous moduli of the suspension. Such measurements are consistent with bulk measurements performed by means of two techniques, namely, diffusing wave spectroscopy and mechanical rheology. Near the rigid wall, the motion of the probe particle can be split in two directions, i.e., parallel and perpendicular to the surface. For short times (but still in the Brownian regime), such motion can be characterized by means of two distance dependent friction coefficients. We observe deviations of the measured friction coefficients in comparison with the Newtonian behavior.

Keywords: Three-dimensional digital video microscopy; Brownian motion; viscoelastic fluid.


PACS: 07.79.Lh; 82.70.Dd; 05.40.-a; 83.10.Mj





We acknowledge helpful discussions with Jose Luis Arauz-Lara, Catalina Haro-Pérez, and Rolando Castillo. This work was supported by CONACyT under Grants No. 152532 and 177679.



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