## 3 Passive Systems
### Field-Passive Fluids
#### 3.1.1 Shear Thickening Fluids  
It can be found frequently in scientific and technological documents the indistinct use of the terms shear thickening, dilatancy and rheopexy. Despite the fact that they all imply an increase in the viscosity of the described fluid, they are not synonyms and the physics behind them are not the same (106; 107; 108; 109; 110; 111; 112; 113; 114). * Shear thickening describes a reversible increase in viscosity with increasing the applied shear rate or shear stress. It is due solely to lubrication hydrodynamic forces arising when particles are driven by the shear flow into close proximity, hydrodynamic clusters are formed and shear thickening results (hydroclustering formation mechanism). It is typical for stable colloidal dispersions. * Dilatancy is due to a flow-induced volume expansion as a consequence of frictional interactions between particles. It is typical for granular dispersions. * Rheopexy refers to an increase of the viscosity with time upon the application of a constant shear rate. It is typical of unstable colloidal dispersions. It is also important to note that there are different types of shear thickening behavior. By increasing the particle concentration in the dispersion, the sample suffers a transition from continuous to discontinuous shear thickening behavior. At lower particle concentration, continuous shear thickening shows a sort of plateau at high shear rates in the steady state viscosity curve. At high concentrations, the shear thickening becomes discontinuous and the sample, above the critical shear rate, shows an increase in the viscosity without increasing the shear rate. According to [PERSON] and [PERSON] [115; 116], by fitting the results from a steady state experiment in a rotational rheometer to a power law \(\tau\propto\dot{\gamma}^{\alpha}\), the value of \(\alpha\) will tell us the type of shear thickening behavior. Thus, \(\alpha=1\) is for Newtonian fluid, \(1\leq\alpha<2\) is for continuous shear thickening, \(\alpha=2\) is for inertia effects and \(\alpha>2\) is for discontinuous shear thickening, with \(\alpha\) approaching infinity as the critical packing fraction is reached (Figure 3) and frictional contacts between particles are more likely to happen [117; 118; 119]. Despite the fact that shear thickening behavior can cause serious troubles in certain industrial processes like coating, spraying, pumping, etc. for obvious reasons, the use of STFs can be very useful for the development and fabrication of passive dissipative devices due to their viscous damping and elastic stiffness capabilities [120; 121; 122]. Additionally, these liquids do not require the application of a magnetic/electric field, since they spontaneously activate under stress, unless in the particular case of field responsive shear thickening fluid [123; 124], where increase in the viscosity and shear stress is due to the application of a predetermined shear rate and, optionally, a predetermined magnetic or electrical field. The rheological characterization of shear thickening fluids (STFs) has been traditionally based on viscosity curves. This rheological information is insufficient to predict the flow behavior under complex dynamics and that may be the reason behind the lack of constitutive models for STFs beyond ad-hoc Generalized Newtonian Fluid models [125; 126; 127]. Since the beginning of XXI Century, the amount of studies dealing with the dynamic, transient and the extensional rheology of STFs has risen considerably [128; 129; 130], coinciding with the eclosion of industrial applications of STFs. In many of these applications [141], STF is used in combination with a flexible porous material, i.e., fabrics, open-cell foams, etc., either by coating or impregnating it [142; 143]; in other applications, the shear thickening fluid is held between plates in a sandwich structure or in reservoirs.