Frequency-Dependent Magnetic modulation of deposition morphology

This paper presents a novel approach for magnetic modulation of deposition morphology in an evaporating ferrofluid droplet. The magnetic field strength and ferrofluid concentration are kept unchanged, while the actuation frequencies are varied from 0.016 Hz to 5 Hz. In the absence of a magnetic field, a coffee-ring formation is observed and consistent with previous studies\cite{deegan1997capillary,deegan2000contact,saroj2019drying}. The application of a time-dependent magnetic field significantly modifies the deposition morphology. The periodic magnetic field induces the formation of multiple concentric rings during evaporation. The number of rings initially increases with increasing actuation frequency of the electromagnet. However, beyond a critical actuation frequency ($f_c = 0.2\,\text{Hz}$), the number of rings decreases. At higher actuation frequencies, magnetic particles preferentially deposit in the central region of the droplet, resulting in suppression of the coffee-ring effect. Additionally, the thickness of the inner rings and the ring spacing decrease with increasing actuation frequency up to critical actuation frequency. The transition from multi-ring formation to coffee-ring suppression is governed by the competition among magnetic forcing, capillary flow, and particle diffusion. The underlying physical mechanisms responsible for droplet dynamics and deposition morphology under periodic magnetic fields are evaluated using scaling arguments. The results demonstrate that diffusive particle transport plays a dominant role in determining the deposition pattern. A non-dimensional magnetic switching number, based on the magnetic perturbation timescale, is introduced as a control parameter to characterize the frequency-dependent deposition behavior.