Mason number

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A parameter used to characterize ER fluids is the Mason number, Af, which describes the ratio of viscous to electrical forces, and is given by equation 14, where S is the solvent dielectric constant T q, the solvent viscosity 7, the strain or shear rate P, the effective polarizabiUty of the particles and E, the electric field (117). 

The Mason number is related to the parameter k defined in Eq. (8-7) and the Peclet number Pe, defined in Chapter 6 [Eq. (6-12)] by Ma k — (n/4) Pe. For the typical values T s 0.02Pa s, E 1000 V/mm, 3 (and hence = 0.4), and Sg 3, we obtain 1 msec, Ma ss 10 " for y = 0.1, and Ma 1 for y = 1000. The time scale ts is very roughly the time required for a particle to move a distance equal to its own diameter, under a polarization interaction with a nearby particle. Thus, the Mason number is near unity when the shearing is rapid enough to pull particle parrs apart as fast as they can form. Even at Mason numbers much smaller than this, chains of particles can be broken, although particle... 

Figure 8.8 Relative viscosity t]/t s versus Mason number for an ER fluid consisting of hydrated lithium poly(methacrylate) particles in a chlorinated hydrocarbon studied by Marshall et al. (1989) with = 0.23 at various field strengths, compared to predictions of two-dimensional Stokesian dynamics simulations (closed symbols) with and without near-field (NF) interactions at areal fraction = 0.4. Since p in the above was taken from the polarization model with Eq. (8-2), while the experiments were carried out under dc fields for which the effective polarization should be controlled by conduc-tivities [Eq. (8-2a)], the quantitative agreement between simulations and experiment is presumably...

A periodic layered pattern has been observed at low Mason numbers (Mn... 

If one assumes that to scales like A t]/t]s should depend on the sole Mason number and decrease as KMn This gives a good representation of experimental data at low and high Mn but not at intermediate values where hydrodynamic and dipolar forces have comparable magnitudes [325]. 

Figure 4 Relative viscosity as a function of Mason number...

Scaling analysis using the Mason number for ER fluids... 

The Mason number was claimed to be useful for scaling the ER effect under an electric field. The ER perfonnance of the hydrated polymethacrylate with a broad size distribution around 9 pm dispersed into a chlorinated hydrocarbon was found to obey the following scaling equation [44] ... 

It determines the influence of the external magnetic field on the superparamagnetic filament. The number Bj compares dipolar to bending forces and it is proportional to the magnetoelastic number introduced in Refs [4, 73, 74]. An alternative dimensionless number for characterizing the influence of the magnetic field is the Mason number introduced in the literature on magnetorheological suspensions [75, 88],... 

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