In a magnetized plasma, naturally occurring pressure anisotropies facilitate instabilities that are expected to modify the transport properties of the system. In this thesis we examine two such instabilities and, where appropriate, their effects on transport. First we consider the collisional (fluid) magnetized magnetorotational instability (MRI) in the presence of the Braginskii viscosity. We conduct a global linear analysis of the instability in a galactic rotation profile for three magnetic field configurations: purely azimuthal, purely vertical and slightly pitched. Our analysis, numerical and asymptotic, shows that the first two represent singular configurations where the Braginskii viscosity's primary role is dissipative and the maximum growth rate is proportional to the Reynolds number when this is small. For a weak pitched field, the Braginskii viscosity is destabilising and when its effects dominate over the Lorentz force, the growth rate of the MRI can be up to 2√2 times faster than the inviscid limit. If the field is strong, an over-stability develops and both the real and imaginary parts of the frequency increase with the coefficient of the viscosity. Second, in the context of the ICM of galaxy clusters, we consider the pressure-anisotropy-driven firehose instability. The linear instability is fast (~ ion cyclotron period) and small-scale (ion Larmor radius ρi) and so fluid theory is inapplicable. We determine its nonlinear evolution in an ab initio kinetic calculation (for parallel gradients only). We use a particular physical asymptotic ordering to derive a closed nonlinear equation for the firehose turbulence, which we solve. We find secular (α t) growth of magnetic fluctuations and a k-||3 spectrum, starting at scales >~ ρi. When a parallel ion heat flux is present, the parallel firehose instability mutates into the new gyrothermal instability. Its nonlinear evolution also involves secular magnetic energy growth, but its spectrum is eventually dominated by modes with a maximal scale ~ρilT/λmfp,(lT is the parallel temperature gradient scale). Throughout we discuss implications for modelling, transport and other areas of magnetized plasma physics.

The existence of hydrodynamically developed, laminar Viscoelastic Secondary Flows (VSFs) of non-Newtonian fluids in straight ducts of non-circular cross-section was proposed in the 1950's. VSFs have since been observed sporadically, and only once with a velocimetric technique. Using axial and transverse full flow-field velocity-position raster maps made with Rheological Nuclear Magnetic Resonance (Rheo-NMR), Newtonian and non-Newtonian fluid flows were quantified in Hagen-Poiseuille and Power Law contexts, over more than two orders of magnitude of flow rate, in ducts of circle, square, triangle, and pentagon cross-section. VSF was reliably and repeatedly observed to occur at between one part in 130 and one part in 600 of the primary axial flow velocity. Velocity measurements ranged from <10 µm/s to approximately 30 cm/s, suggesting a velocity dynamic range >3E4 without optimization. To obtain VSF flow direction information, a novel flow directional phantom was developed and characterized. Aqueous solutions of Polyethylene Oxide (PEO), Viscarin GP-109NF, Viscarin GP-209NF (V209), Hyaluronan (HA) in a Phosphate-Buffered Saline-like solvent, and an aqueous Polyethylene Glycol/PEO-based Boger fluid were investigated. Axial data was corroborated with related data gathered by an independent method. Basic simulations corroborated the VSF observations. Duct hydraulic diameters (>= 1.6 mm) approached the micro-channel regime. VSF detections in HA --- synovial fluid's principal component --- and V209 were novel, as were observations of some artifacts which were subsequently characterized and corrected. The detection of VSF in HA represents the first experimental evidence suggesting that its second normal stress (N_2) is comparable to that of better-characterized fluids. In the first application of a new VSF-based method, a particular Boger fluid's constant viscosity and, in the square duct, its lack of VSF were used with established criteria to suggest that the fluid's N_2 approached zero. The development of a rudimentary, but versatile and inexpensive home-built velocimetric spectrometer is detailed, as are several new components. An exhaustive VSF literature review is included. The remarkable transverse velocimetric ability of Rheo-NMR in both optically opaque and transparent system is highlighted, suggesting that perhaps the technique might represent, in both micro-channels and conventional ducts, the gold-standard in flow velocimetry.