Understanding how fluids respond to various deformations is of great importance to a spectrum of disciplines ranging from bio-medical research on joint replacements to sealing technology in industrial machinery. Specifically, this work addresses the need for probing interfacial rheology to understand how lubricants fail as system scales are reduced from bulk dimensions to molecular length scales. In the pursuit of interfacial rheology, one needs a platform capable of the temporal and spatial range and resolution required to quantify the visco-elastic fluid properties in the interfacial regime. With the availability and versatility of AFMs and the mounting models and data related to the performance of SPM probes in a fluid environment, the AFM is an attractive platform to exploit. This thesis will discuss the use of thermal oscillations of an SPM probe to quantify the visco-elastic properties of fluids via spectral variations. There exist theoretical models for the Fluid-Structure Interactions (FSI) of vibrating bodies in incompressible viscous mediums that have been validated. This thesis will discuss how these models have been extended to develop a new visco-elastic FSI model. The analytical results of these models will be quantitatively compared to thermally driven SPM cantilevers to extract fluid properties. The new theory required for modeling the probe dynamics is outlined and the present limitations, for both the analytical and experimental techniques, are discussed.
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