The flow of charge carriers in materials can, under some circumstances, mimic the flow of viscous fluids. In order to visualize the consequences of such effects, new methodologies must be developed that can probe the quasiparticle flow profile with nm-scale resolution as the geometric parameters of the system are continuously evolved. In this work, scanning tunneling potentiometry (STP) is used to image quasiparticle flow around engineered electrostatic barriers in graphene/hBN heterostructures. Measurements are performed as electrostatic dams - defined by lateral pn-junction barriers - are broken within the graphene sheet, and carriers move through conduction channels with physical widths that vary continuously from pinch-off to um-scale. Local, STP measurements of the electrochemical potential allow for direct characterization of the evolving flow profile, which we compare to finite-element simulations of a Stokesian fluid with varying parameters. Our results reveal distinctly non-Ohmic flow profiles, with charge dipoles forming across barriers due to carrier scattering and accumulation on the upstream side, and depletion downstream. Conductance measurements of individual channels, meanwhile, reveal that at low temperatures the quasiparticle flow is ballistic, but as the temperature is raised there is a Knudsen-to-Gurzhi regime crossover where the fluid becomes viscous and the channel conductance exceeds the ballistic limit set by Sharvin conductance. These results provide a clear illustration of how carrier flow in a Fermi fluid evolves as a function of carrier density, channel width, and temperature. They also demonstrate how STP can be used to extract key parameters of quasiparticle transport, with a spatial resolution that exceeds that of other methods by orders of magnitude.
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