![]() However, the underlying idea (the reduction of governing equations to simpler, useful models) is a powerful tool that can be brought to bear in these applications also. These materials are mostly granular media, and require a different physical framework. Similar models are also used for landslides, avalanches, and the dynamics of sand. The rheology of mud and ice has several similarities with that of lava, and the same non-Newtonian fluid models can be used to describe how they flow. Related geological problems include mud flows and glacier mechanics. ![]() But by using asymptotic methods, simpler versions can be built for use by geologists. ![]() Computations with the full three-dimensional equations is an inefficient route for such a model, partly because the rheology of cooling lava is so complicated. That is, a general theoretical model that incorporates the essential physical ingredients and can be used to compute the flow of lava under terrestrial and extra-terrestrial conditions. For example, for lava flow, the main goal is to develop a "shallow-lava theory". My work in this area is focused on simplifying these equations to gain insight into the flow dynamics. Unfortunately, fluid models that build in the rheology significantly complicate the governing equations. In lava, for example, the microstructure is provided by a network of interlocked silicate crystals, and endows the fluid with an internal strength that allows lava to withstand a certain amount of imposed stress before it flows. Often, the 'rheology' arises because the fluid in question builds up a microstructure at the molecular level which becomes sufficiently extensive to affect the macroscopic properties of the fluid. Power-law and Herschel-Bulkley models describe pseudoplastic behavior, in which the slope-the viscosity-of the shear stress versus shear rate curve decreases as the shear rate decreases.Aside from air and water, most of the fluids we encounter in physical and industrial processes are "non-Newtonian" (meaning that there is no simple relationship between the stress and the rate of strain). Pseudoplasticity, or shear thinning, is a non-Newtonian behavior that is desirable for drilling fluids. In the Bingham plastic model, flow will not begin until the shear stress attains a minimum value, the yield stress, after which the flow is similar to that of a Newtonian fluid because the viscosity is constant and does not vary with shear rate. Most successful drilling fluids are non-Newtonian and exhibit behaviors that are described by rheological mathematical models of shear stress, or resistance, as a function of shear rate. dilatant fluids increases with increasing shear rate these fluids exhibit shear thickening behavior.For example, ketchup will squirt through a hole in a bottle top at high velocity but stand still as a dollop on a plate. pseudoplastic fluids decreases with increasing shear rate these fluids exhibit shear thinning behavior. ![]() For example, cream will thicken after continuous stirring. rheopectic fluids increases over time under shearing.For example, solid honey becomes a liquid after continuous stirring. thixotropic fluids decreases over time under shearing.In addition, unlike Newtonian fluids, the viscosity of many non-Newtonian fluids varies with shear rate.įour classes of non-Newtonian fluids depend on how the fluid viscosity-a measure of a fluid’s ability to resist flow-varies in response to the duration and magnitude of applied shear rate. Under certain conditions, a non-Newtonian fluid flows as a liquid and under other conditions, it exhibits elasticity, plasticity and strength similar to a solid. Unlike a Newtonian fluid, which displays liquid behavior, a non-Newtonian fluid has properties of a liquid and of a solid. ![]()
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