## 2 Background
### Ferrofluid Behaviour  
The viscosity of a magnetic fluid, or ferrofluid, varies significantly under the influence of a magnetic field. This variation is due to the alignment and interaction of the magnetic nanoparticles suspended in the carrier fluid [25]. The increase in viscosity under a magnetic field enhances the energy dissipation capacity of the fluid, making it more effective in controlling oscillations. By altering the strength of the magnetic field, the viscosity of the fluid can be dynamically tuned, allowing the TLD to respond to varying vibration amplitudes and frequencies in real-time. In the absence of a magnetic field, the nanoparticles are randomly distributed and move freely within the fluid. Viscosity primarily depends on the base carrier fluid and  
Figure 4: 3D view of Helmholtz coil and magnetic field lines on plane z = 0. Orange loops represent current-carrying coils, blue arrows show the magnetic field direction and relative magnitude. Figure 3: Magnetic field created by an electric current flowing through a coil. the concentration of magnetic particles. The fluid behaves as a Newtonian fluid (constant viscosity, independent of shear rate) under low particle concentrations [26]. When a magnetic field is applied, three effects occur. First, the magnetic nanoparticles align along the magnetic field lines [27]. This alignment can increase the internal resistance to flow, effectively increasing the viscosity of the fluid. Second, at higher field strengths, the particles may form chains or structures along the field lines. These structures disrupt the fluid flow, leading to a significant increase in viscosity. In some cases, the fluid can exhibit non-Newtonian behavior, with the viscosity depending on the shear rate [28; 29]. Third, the dependence of viscosity on the strength of the applied magnetic field is known as the magnetoviscous effect. This relationship is typically nonlinear: small increases in field strength can cause significant changes in viscosity [30]. These effects occur when the magnetic field is activated, also known as the on-state. The chain-like arrangement is a reversible process, and particles flow freely when the magnetic field is no longer activated (off-state). This behavior is depicted in Figure 5.  
Several factors affect how viscosity changes under a magnetic field. Higher particle concentrations lead to more pronounced viscosity changes, while larger particles or broader size distributions can enhance alignment and chain formation. Stronger magnetic fields cause more alignment and structure formation. Higher temperatures can reduce the effect of the magnetic field due to increased thermal agitation. The properties of the carrier fluid also influence the overall magnetoviscous behavior. It must be noted that the temperature alone is a parameter that can significantly alter the fluid viscosity, depending on its specific properties. For this reason, in this work the temperature has been controlled throughout the tests and has been included in the analysis to account for its potential influence on viscosity variation. Several authors have investigated the dependence of magnetic fluid viscosity on external magnetic fields, employing both theoretical and experimental approaches. [PERSON] and [PERSON] [31] calculated the effective viscosity of magnetic fluids at the particle scale. They compared their results with classical constitutive equations and proposed a new equation according to their numerical findings. [PERSON] [32] investigated the simultaneous effects of magnetic field and temperature on the capillary viscosity of magnetic nanofluids. The study provided experimental data and proposed theoretical explanations for the observed changes in effective viscosity under varying magnetic field strengths and orientations. Additionally, [PERSON] et al. [33] measured the effective viscosity of a ferrofluid as a function of an applied magnetic field oriented perpendicular to the capillary flow.