This Letter describes measurements of a single colloidal sphere's diffusion through water in a slit pore formed by two parallel glass surfaces. By positioning a test sphere at selected heights within a slit pore, releasing it and tracking its motions, we are able to measure its height-dependent hydrodynamic coupling to parallel bounding surfaces. Access to the sample volume was provided by two glass tubes bonded to holes drilled through the slide at either end of the longest dimension. The sample was mounted on the stage of an Olympus IMT-2 inverted optical microscope and imaged with a NA 1.4 oil immersion objective lens. Angle brackets indicate an ensemble average.
Solid curves are fits to Eq.
For example, a sphere of radius suspended in an unbounded fluid of viscosity has an isotropic and translation-invariant drag coefficient, . The corresponding free self-diffusion coefficient for the spheres in the present study is . A sphere passing between two rigid parallel walls, on the other hand, experiences a drag which depends both on its position in the slit and also on its direction of motion. Measuring this dependence requires the ability either to track a sphere's motion in three dimensions, or else to position the sphere reproducibly within the slit. We adopted the second approach, using an optical tweezer to place a single sphere in the microscope's focal plane, releasing it for sec to measure its diffusivity, and then retrapping it.