3D-printed ultra-small Brownian viscometers

Abstract

Measuring viscosity in volumes smaller than a microliter is a challenging endeavor. A new type of microscopic viscometers is presented to assess the viscosity of Newtonian liquids. Micron-sized flexible polymer cantilevers are created by two-photon polymerization direct laser writing. Because of the low stiffness and high elasticity of the polymer material the microcantilevers exhibit pronounced Brownian motion when submerged in a liquid medium. By imaging the cantilever’s spherically shaped end, these fluctuations can be tracked with high accuracy. The hydrodynamic resistance of the microviscometer is determined by fitting the power spectral density of the measured fluctuations with a theoretical frequency dependence. Validation measurements in water-glycerol mixtures with known viscosities reveal excellent linearity of the hydrodynamic resistance to viscosity, allowing for a simple linear calibration. The stand-alone viscometer structures have a characteristic size of a few tens of microns and only require a very basic external instrumentation in the form of microscopic imaging at moderate framerates (~ 100 fps). Thus, our results point to a practical and simple to use ultra-low volume viscometer that can be integrated into lab-on-a-chip devices.