Browsing by Author "Robbins, Brian A."

Now showing 1 - 4 of 4
  • Thumbnail Image
    The Correlated Dynamics of Micron-Scale Cantilevers in a Viscous Fluid
    Robbins, Brian A. (Virginia Tech, 2014-12-08)
    A number of microcantilever systems of fundamental importance are explored using theoretical and numerical methods to quantify and provide physical insights into the dynamics of experimentally accessible systems that include a variety of configurations and viscous fluids. It is first shown that the correlated dynamics of both a laterally and vertically offset cantilever pair can be accurately predicted by numerical simulations. This is verified by comparing the correlated dynamics yielded by numerical simulations with experimental measurement. It is also demonstrated that in order to obtain these accurate predictions, geometric details of the cantilever must be included in the numerical simulation to directly reflect the experimental cantilever. A microrheology technique that utilizes the fluctuation-dissipation theorem is proposed. It is shown that by including the frequency dependence of the fluid damping, improvements in accuracy of the predictions of the rheological properties of the surrounding fluid are observed over current techniques. The amplitude spectrum of a 2-D cantilever in a power-law fluid is studied. The resulting amplitude spectrum yielded a curve similar to an overdamped system. It is observed that the amplitude and noise spectrum yield the same qualitative response for a 2-D cantilever in a shear thinning, power-law fluid. The correlated dynamics of a tethered vertically offset cantilever pair is investigated. It is shown that for a range of stiffness ratios, which is the ratio of the spring constant of the tethering relative to the cantilever spring constant, the change in the correlated dynamics of a Hookean spring tethered cantilever pair can be seen in the presence of fluid coupling. The dynamics of a spring-mass tethered, vertically offset cantilever pair is qualitatively studied by simplifying the model to an array of springs and masses. The resulting study found that the correlated dynamics of the displacement of mass of the tethered object yielded newly observed features and characteristics. It is shown that the curve shape of the cross-correlation of the displacement of the mass of the tethered object is similar to that of the auto-correlation of the displacement of the mass representing a step forced cantilever. The cross-correlation of the displacement of the mass of the tethered object, however, is found to be significantly more dependent on the stiffness ratio than the auto-correlation of the displacement of the mass representing a cantilever for t > 0. At t = 0, it is observed that the mass of the tethered object yields the same finite value for the cross-correlation for all studied values of the stiffness ratio. This characteristic is a result of the symmetry of the studied spring-mass system.
  • Thumbnail Image
    Correlations between the thermal vibrations of two cantilevers: Validation of deterministic analysis via the fluctuation-dissipation theorem
    Honig, Christopher D. F.; Radiom, Milad; Robbins, Brian A.; Walz, John Y.; Paul, Mark R.; Ducker, William A. (AIP Publishing, 2012-02-01)
    We validate a theoretical approach for analyzing correlations in the fluctuations of two cantilevers in terms of a deterministic model, using the fluctuation-dissipation theorem [M. R. Paul and M. C. Cross, Phys. Rev. Lett. 92, 235501 (2004)]. The validation has been made possible through measurement of the correlations between the thermally stimulated vibrations of two closely spaced micrometer-scale cantilevers in fluid. Validation of the theory enables development of a method for characterizing fluids, which we call correlation force spectrometry. (C) 2012 American Institute of Physics. [doi:10.1063/1.3681141]
  • Thumbnail Image
    Rheology of fluids measured by correlation force spectroscopy
    Radiom, Milad; Robbins, Brian A.; Honig, Christopher D. F.; Walz, John Y.; Paul, Mark R.; Ducker, William A. (AIP Publishing, 2012-04-01)
    We describe a method, correlation force spectrometry (CFS), which characterizes fluids through measurement of the correlations between the thermally stimulated vibrations of two closely spaced micrometer-scale cantilevers in fluid. We discuss a major application: measurement of the rheological properties of fluids at high frequency and high spatial resolution. Use of CFS as a rheometer is validated by comparison between experimental data and finite element modeling of the deterministic ring-down of cantilevers using the known viscosity of fluids. The data can also be accurately fitted using a harmonic oscillator model, which can be used for rapid rheometric measurements after calibration. The method is non-invasive, uses a very small amount of fluid, and has no actively moving parts. It can also be used to analyze the rheology of complex fluids. We use CFS to show that (non-Newtonian) aqueous polyethylene oxide solution can be modeled approximately by incorporating an elastic spring between the cantilevers. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4704085]
  • Thumbnail Image
    The stochastic dynamics of tethered microcantilevers in a viscous fluid
    Robbins, Brian A.; Radiom, Milad; Ducker, William A.; Walz, John Y.; Paul, Mark R. (American Institute of Physics, 2014-10-28)
    We explore and quantify the coupled dynamics of a pair of micron scale cantilevers immersed in a viscous fluid that are also directly tethered to one another at their tips by a spring force. The spring force, for example, could represent the molecular stiffness or elasticity of a biomolecule or material tethered between the cantilevers. We use deterministic numerical simulations with the fluctuation-dissipation theorem to compute the stochastic dynamics of the cantilever pair for the conditions of experiment when driven only by Brownian motion. We validate our approach by comparing directly with experimental measurements in the absence of the tether which shows excellent agreement. Using numerical simulations, we quantify the correlated dynamics of the cantilever pair over a range of tether stiffness. Our results quantify the sensitivity of the auto-and cross-correlations of equilibrium fluctuations in cantilever displacement to the stiffness of the tether. We show that the tether affects the magnitude of the correlations which can be used in a measurement to probe the properties of an attached tethering substance. For the configurations of current interest using micron scale cantilevers in water, we show that the magnitude of the fluid coupling between the cantilevers is sufficiently small such that the influence of the tether can be significant. Our results show that the cross-correlation is more sensitive to tether stiffness than the auto-correlation indicating that a two-cantilever measurement has improved sensitivity when compared with a measurement using a single cantilever. (C) 2014 AIP Publishing LLC.