Editing Magnetorheological fluid (section)

==Material behavior==
To understand and predict the behavior of the MR fluid it is necessary to model the fluid mathematically, a task slightly complicated by the varying material properties (such as [[yield stress]]). 
As mentioned above, smart fluids are such that they have a low viscosity in the absence of an applied magnetic field, but become quasi-solid with the application of such a field. In the case of MR fluids (and [[Electrorheological fluid|ER]]), the fluid actually assumes properties comparable to a solid when in the activated ("on") state, up until a point of yield (the [[shear stress]] above which shearing occurs). This yield stress (commonly referred to as apparent yield stress) is dependent on the magnetic field applied to the fluid, but will reach a maximum point after which increases in [[magnetic flux density]] have no further effect, as the fluid is then magnetically saturated. The behavior of a MR fluid can thus be considered similar to a [[Bingham plastic]], a material model which has been well-investigated.

However, MR fluid does not exactly follow the characteristics of a Bingham plastic. For example, below the yield stress (in the activated or "on" state), the fluid behaves as a [[viscoelastic]] material, with a [[absolute value|complex modulus]] that is also known to be dependent on the magnetic field intensity. MR fluids are also known to be subject to [[shear thinning]], whereby the viscosity above yield decreases with increased shear rate. Furthermore, the behavior of MR fluids when in the "off" state is also [[non-Newtonian fluid|non-Newtonian]] and temperature dependent, however it deviates little enough for the fluid to be ultimately considered as a Bingham plastic for a simple analysis.

Thus our model of MR fluid behavior in the shear mode becomes:

:<math>\tau =\tau_y(H) + \eta\frac{dv}{dz}, \tau>\tau_y</math>

Where <math>\tau</math> = shear stress; <math>\tau_y</math> = yield stress; <math>H</math> = Magnetic field intensity <math>\eta</math> = Newtonian viscosity; <math>\frac{dv}{dz}</math> is the velocity gradient in the z-direction.

=== Shear strength ===

Low [[shear strength]] has been the primary reason for limited range of applications. In the absence of external pressure the maximum shear strength is about 100 kPa. If the fluid is compressed in the magnetic field direction and the compressive stress is 2 MPa, the shear strength is raised to 1100 kPa.<ref>{{cite book |last1=Wang |first1=Hong-yun |last2=Zheng |first2=Hui-qiang |last3=Li |first3=Yong-xian |last4=Lu |first4=Shuang |chapter=Mechanical properties of magnetorheological fluids under squeeze-shear mode |editor-first1=Yetai |editor-first2=Kuang-Chao |editor-first3=Rongsheng |editor-last1=Fei |editor-last2=Fan |editor-last3=Lu |title=Fourth International Symposium on Precision Mechanical Measurements |date=17 December 2008 |volume=7130 |pages=71302M |doi=10.1117/12.819634 |chapter-url=https://ui.adsabs.harvard.edu/abs/2008SPIE.7130E..2MW/abstract |bibcode=2008SPIE.7130E..2MW|s2cid=137422177 }}</ref> If the standard magnetic particles are replaced with elongated magnetic particles, the shear strength is also improved.<ref>{{cite journal |last1=Vereda |first1=Fernando |last2=de Vicente |first2=Juan |last3=Hidalgo-Álvarez |first3=Roque |title=Physical Properties of Elongated Magnetic Particles: Magnetization and Friction Coefficient Anisotropies |journal=ChemPhysChem |date=2 June 2009 |volume=10 |issue=8 |pages=1165–1179 |doi=10.1002/cphc.200900091 |pmid=19434654 |url=https://archive.today/20130105064549/http://www3.interscience.wiley.com/journal/122380920/abstract|url-access=subscription }}</ref>
=== Particle sedimentation ===

Ferroparticles settle out of the suspension over time due to the inherent density difference between the particles and their carrier fluid. The rate and degree to which this occurs is one of the primary attributes considered in industry when implementing or designing an MR device. [[Surfactant]]s are typically used to offset this effect, but at a cost of the fluid's magnetic saturation, and thus the maximum yield stress exhibited in its activated state.

=== Common MR fluid surfactants ===

MR fluids often contain [[surfactant]]s including, but not limited to:<ref>{{Cite journal|last1=Unuh|first1=Mohd Hishamuddin|last2=Muhamad|first2=Pauziah|last3=Waziralilah|first3=Nur Fathiah|last4=Amran|first4=Mohamad Hafiz|year=2019|title=Characterization of Vehicle Smart Fluid using Gas Chromatography-Mass Spectrometry (GCMS)|url=http://www.akademiabaru.com/doc/ARFMTSV55_N2_P240_248.pdf|journal=Journal of Advanced Research in Fluid Mechanics and Thermal Sciences|publisher=Penerbit Akademia Baru|volume=55|issue=2|pages=240–248|issn=2289-7879}}</ref>

* [[oleic acid]]
* [[tetramethylammonium hydroxide]]
* [[citric acid]]
* [[soy lecithin]]

These surfactants serve to decrease the rate of ferroparticle settling, of which a high rate is an unfavorable characteristic of MR fluids. The ideal MR fluid would never settle, but developing this ideal fluid is as highly improbable as developing a [[perpetual motion machine]] according to our current understanding of the laws of physics. Surfactant-aided prolonged settling is typically achieved in one of two ways: by addition of surfactants, and by addition of spherical ferromagnetic nanoparticles. Addition of the nanoparticles results in the larger particles staying suspended longer since the non-settling nanoparticles interfere with the settling of the larger micrometre-scale particles due to [[Brownian motion]]. Addition of a surfactant allows [[micelles]] to form around the ferroparticles. A surfactant has a [[chemical polarity|polar]] head and non-polar tail (or vice versa), one of which [[adsorption|adsorbs]] to a ferroparticle, while the non-polar tail (or polar head) sticks out into the carrier medium, forming an inverse or regular [[micelle]], respectively, around the particle. This increases the effective particle diameter. [[steric effects|Steric]] repulsion then prevents heavy agglomeration of the particles in their settled state, which makes fluid remixing (particle redispersion) occur far faster and with less effort. For example, [[magnetorheological dampers]] will remix within one cycle with a surfactant additive, but are nearly impossible to remix without them.

While surfactants are useful in prolonging the settling rate in MR fluids, they also prove detrimental to the fluid's magnetic properties (specifically, the magnetic saturation), which is commonly a parameter which users wish to maximize in order to increase the maximum apparent yield stress. Whether the anti-settling additive is nanosphere-based or surfactant-based, their addition decreases the packing density of the ferroparticles while in its activated state, thus decreasing the fluids on-state/activated viscosity, resulting in a "softer" activated fluid with a lower maximum apparent yield stress. While the on-state viscosity (the "hardness" of the activated fluid) is also a primary concern for many MR fluid applications, it is a primary fluid property for the majority of their commercial and industrial applications and therefore a compromise must be met when considering on-state viscosity, maximum apparent yields stress, and settling rate of an MR fluid.