Magneto-coalescence phenomena in colliding ferrofluid droplets

Abstract

We explore the collision hydrodynamics of a ferrofluid droplet falling freely onto a sessile droplet of the same liquid, in the presence of a horizontal magnetic field; a configuration that couples droplet-on-droplet coalescence with concomitant field-governed wetting and spreading. Using high-speed imaging, we track the events through crown formation, radial spreading, and rim detachment (under specific conditions), across three ferrofluid concentrations, two substrates of different wettability (glass and PET), and a range of impact velocities and magnetic field strengths. The maximum crown height is noted to scale as $H_{c,\max}/D_t\sim Fr^{0.5}$ ($Fr:$ Froude number); well below the ballistic upper bound of $H_{c,\max}/D_t\sim Fr$. At zero-field, the maximum spreading collapses onto the boundary-layer scaling $β_{0,\max}\sim (We_0/Oh)^{1/6}$ ($We_0$: Weber number, $Oh:$ Ohnesorge number) when expressed in terms of the merged impact velocity, and coalesced-drop size . With the field applied, a bulk-dissipation energy balance predicts $β_{\max}\sim Z^{1/5}$, where $Z$ combines the magnetic-driving, and inertial-capillary-viscous terms, but the observations instead follow a markedly weaker $\sim Z^{1/11}$, a deficit traced to enhanced dissipation from the magnetoviscous effects, and manifested via an effective Ohnesorge number. Finally, rim detachment occurs beyond a field- and height-dependent threshold, described by a size-independent criterion $Fr^2Bo\approx 3550$ ($Bo:$ Bond number), above which the rim may fragment into daughter droplets. These scalings provide predictive tools for magnetically assisted printing, droplet-on-demand systems, and coating processes, where repeated droplet collisions occur on the residual liquid droplet or layer.