Effects of non-magnetic carbon nanotubes on the performance and stability of magnetorheological fluids containing FeCo-deposited carbon nanotubes

Abstract

Magnetorheological (MR) properties of the carbon nanotube (CNT)–FeCo nanocomposite particle suspension were investigated to find a high-performance MR fluid with great stability. The composites were fabricated by chemical deposition of FeCo on the surface of amine functionalized CNTs. The strong magnetic polarization of the FeCo moiety led to strong MR performance of the nanocomposite particle suspension. The MR fluid exhibits high yield stress value, 4 times greater than that of the suspension including Fe₃O₄-deposited CNT at a magnetic field strength of 86 kA/m. A three-dimensional network-like structure formed by the non-magnetic CNTs in the MR suspension does not contribute to the additional yield stress. The low density and the surface roughness of the CNTs resulted in far better long-term stability for the CNT–FeCo nanocomposite suspension than for the MR suspension of hierarchically structured Fe₃O₄ suspension with a similar density. The effect of the three-dimensional network-like structures by the CNTs on the MR performance depends upon the interaction strength between the magnetic moiety on the CNTs.

Appendix: Particle sedimentation and suspension stability [28]

The sedimentation profile recorded for each sample using Turbiscan is presented in Fig. 8 as a function of time. The light transmission amounts for all three suspensions rapidly increase within 2–3 h. The measured transmission increases gradually over time and eventually stabilizes. After 24 h, the Turbiscan recorded a light transmissions of 72%, 45%, 13%, and 4% for the pure Fe₃O₄, HS-Fe₃O₄, CNT–FeCo, and CNT–Fe₃O₄ suspensions, respectively. Although the density of CNT–FeCo is greater than that of pure Fe₃O₄, the CNT–FeCo suspension is much more stable than the pure Fe₃O₄ suspension. Almost 87% of the CNT–FeCo particles did not settle to the bottom. This excellent stability is attributed to the CNT network-like structure and the surface roughness change [12, 32]. The terminal velocity of a particle in a fluid can be defined as follows,

$${u}_{t}={\left(\frac{4}{3}\frac{Re}{{C}_{D}}\right)}^{1/3}{\left[\frac{{{\rho }_{f}}^{2}}{g\mu ({\rho }_{s}-{\rho }_{f})}\right]}^{-1/3},$$

(3)

where ${\mathrm{Re}}$ is the Reynolds number based on the equivalent spherical diameter of a particle, ${C}_{D}$ is the drag coefficient, ρ_f is the density of the liquid medium, ρ_s is the density of the solid particle, g is gravitational acceleration, and µ is the viscosity of the liquid medium [3, 26, 32]. Terminal velocity ratio between the Fe₃O₄ and CNT–FeCo suspension is approximated as

$$\frac{{u}_{t, CNT-FeCo}}{{u}_{t, HS-Fe3O4}}\approx 0.99* \left( \frac{{Re}_{CNT-FeCo}}{{C}_{D, CNT-FeCo}}\right)^\frac{1}{3}/\left( \frac{{Re}_{HS-Fe3O4}}{{C}_{D, HS-Fe3O4}}\right)^{1/3},$$

(4)

if we neglect the density difference between the HS-Fe₃O₄ (3.32 g/cm³) and the CNT–FeCo particle (3.47 g/cm³) for the simplification. At low Reynolds number, the drag coefficient for a sphere is C_D = 24/Re; for a non-spherical particle, C_D = 24* (1 + 0.18* Re_CNT–FeCo^0.65) /Re_CNT–FeCo [3, 21, 24, 28]. Thus, the terminal velocity at a low Reynolds number is

$$\frac{{u}_{t, CNT-FeCo}}{{u}_{t, HS-Fe3O4}}\approx 0.99* \left( \frac{{Re}_{CNT-FeCo}^{2}}{24 (1+0.18{Re}_{CNT-FeCo}^{0.65} )}\right)^{1/3}/( \frac{{Re}_{HS-Fe3O4}^{2}}{24}{)}^{1/3}\approx 0.99*({Re}_{CNT-FeCo}^{2}/{Re}_{HS-Fe3O4}^{2})^\frac{1}{3}\approx 0.99*\left({D}_{CNT-FeCo} {u}_{t, CNT-FeCo}/{D}_{HS-Fe3O4}{u}_{t, HS-Fe3O4}\right)^{2/3},$$

(5)

where D_CNT–FeCo is the equivalent sphere diameter. Therefore,

$$\frac{{u}_{t, CNT-FeCo}}{{u}_{t, HS-Fe3O4}}\approx 0.97* ({D}_{CNT-FeCo}/{D}_{HS-Fe3O4})^{2}.$$

(6)

Since the hydrodynamic radius of CNT–FeCo is roughly approximated as ~ 90 nm, and D_HS-Fe3O4 ≈ 357 nm [5, 28, 54] the terminal velocity ratio is approximately 0.254. Thus, the terminal velocity of the CNT–FeCo particle is 11.4% of that of a HS-Fe₃O₄ particle, which is close to the experimental measurement (13%), though crude approximations for the density and the equivalent hydrodynamic radius were adopted.