1/31/2024 0 Comments Newtonian fluid image![]() What do you do to succeed in the task? You smack the bottle, and hard: this way, the shear rate increases (think about the relative velocity between the ketchup and the internal walls of the bottle) and viscosity decreases.Įxamples of shear-thickening fluids are quicksand and the famous "oobleck" (starch+water): the faster you apply the stress, the higher the viscosity. For others, called shear-thinning, viscosity decreses with stress.įor example, ketchup is a shear-thinning liquid: you may have noticed if you've ever had difficulties in making it come out of the bottle. Examples of Newtonian fluids are water, gasoline and alcohol.įor non-Newtonian fluids, it is important to consider how fast we apply the stress: there are some fluids, called shear-thickening, for which viscosity increases with stres. the response to the stress, will be constant. the force exerted on the surface will be large and it will be difficult to make the liquid flow (for example inside a pipe).įor Newtonian fluids, it doesn't matter how fast you apply the stress: the viscosity, i.e. The viscosity $\eta$ is a measure of the resistence of the fluid to an applied shear stress: if a fluid has a large viscosity, even a small shear rate will generate a large shear stress, i.e. Ok, nice equations: but what does this all mean? $$\tau = \eta \left(T, \frac v h \right) \cdot \left( \frac v h \right)$$ ![]() So that for the sliding plates case we have $$\tau = \eta(T, \dot \gamma) \cdot \dot \gamma$$ (because since $h$ is small we can make the approximation that the velocity of the fluid is approximatively constant and equal to the velocity of the plate).įor a non-newtonian fluid, the viscosity $\eta$ also depends on the shear rate: If we a "sandwich" of two plates containing a fluid layer of small thickness $h$, with one plate fixed an another moving with velocity $v$, we will simply have Where $v_i$ are the components of the velocity field of the fluid. broken covalent bonds in a polymer chain) and will be unable to return to its undeformed state when the load is removed. Note: Only an idealisation, as in reality no material can be indefinitely compressed or stretched, instead there are thresholds of deformation beyond which the material will undergo permanent change (e.g. These are materials that exhibit linear elasticity, and deform proportionally to the applied load. Hookean solid: $\sigma = \gamma \epsilon$ ($\sigma$ denotes the applied stress, $\gamma$ the elastic modulus and $\epsilon$ the deformation). Let's wrap up by reminding the definitions: Good example of such materials are honey and silly putty. For example a hysteresis stress-strain curve can often be observed, hinting at the fact that unlike Hookean solids, viscoelastic materials do dissipate energy when under load. Depending on the rate with which we are shearing the material its behaviour varies between that of the elastic solids and viscous fluids. Now you may have also heard of viscoelastic materials, which as the name suggests, exhibit both viscous (they can flow) and elastic (they can also act stiff) characteristics when subject to a shear stress. how stiff they are, how much do they elongate, whereas for fluids, when one applies a shearing stress, their response is to move (as they have no stiffness) which is determined by their viscosity. ![]() Now in the case of solids and their elastic behaviour, we apply a stress to them and study their mechanical response, e.g. This in turn means that we can define a characteristic constant of stiffness for the elastic behaviour of the solid and similarly a characteristic dynamic viscosity for the fluid. For example both fall into a first-order linear approximation response theory and therein lies the intuition: The response of the solid (deformation-strain) or the fluid (rate of change of deformation over time-strain rate) to the applied stress differs only by a proportionality constant, meaning the system (and more precisely its behaviour to external influences) will not undergo permanent changes (no non-linear effects), no matter how quickly, weakly or strongly it is being sheared. Since you're looking for an intuitive picture, it may help to draw analogy between Hookean solids (solids whose elastic behaviour is well captured by the Hooke's law) and Newtonian fluids.
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