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In this article, we propose the feasibility of replacing traditional materials with ferrofluid droplets to actively regulate their behavior as they traverse an orifice in the presence of an external magnetic field. The traversal behavior of the droplet is investigated using both rectangular and curved orifice boundaries. We employed a simplified multiphase lattice Boltzmann method (SMLBM) to simulate the flow field and interface, which considerably improves computational efficiency. For magnetic field generation, a self-correction procedure is coupled with SMLBM. For curved boundaries, we used our recently developed immersed boundary approach, which can specify wetting boundary conditions for both stationary and moving boundaries, in the same way as flat boundaries are handled. To check the validity of our methods, we first simulated three benchmark phenomena and compared our results with experimental and numerical findings. This research includes orifice geometries, including straight and curved boundaries, and investigates the dynamic behavior of droplets traversing through narrow opening, increased orifice thicknesses, and large diameter droplets passing through confined and multiple orifices. All simulations are initially carried out without the use of magnetic fields, then the experiments are repeated and compared with the addition of a uniform magnetic field. It is found that, in the absence of a magnetic field, the droplets can successfully pass only through wide orifices. However, for narrow or thick orifices, a significant portion of droplet volume adheres to the orifice walls, causing an apparent decrease in falling velocity. In contrast, the addition of a magnetic field enables the droplet to efficiently traverse through even narrower and thicker orifices, attaining faster speeds and reduced mass loss. Furthermore, the influence of Reynold number and magnetic field strengths on the droplet velocity, its wetting dynamics, and relative shedding area are also discussed in detail. [ABSTRACT FROM AUTHOR]

This study numerically examines the Rosensweig instability of a ferrofluid-infused surface (FIS), which is an overlayer surface formed on the top of a porous substrate into which the ferrofluid is infused. FIS inherits the lubricating property of liquid-infused surfaces and the magnetic property of the ferrofluid, allowing an external control by a magnetic field. Currently, the evolution mechanisms of the Rosensweig instability of the FIS remain unclear. By using the recently developed coupled numerical scheme, which consists of the simplified multiphase lattice Boltzmann method and the self-correcting method for the Maxwell magnetic field equations, the intriguing mechanism and evolution dynamics of the ferrofluid spikes on the FIS are investigated systematically by examining the effects of overlayer thickness, substrate pore size, and magnetic field strength. The results are also analyzed by the Rosensweig instability theory. This study provides a theoretical and numerical basis for the magnetic field control of droplet or bubble motions on the FIS. [ABSTRACT FROM AUTHOR]

This article presents experimental and theoretical studies of the impacting behavior of ferrofluid droplets on porous substrates under the influence of magnetic fields. The effects of magnetic field strength and porous substrates on the falling, impacting, and spreading of the droplets are investigated. Theoretical models are successfully derived to predict the droplet impacting velocity in the presence of the magnetic field and the maximum spreading factor of the droplets on the porous substrates without considering magnetic field effects, respectively. Moreover, a universal scaling law is constructed for the maximum spreading factor of the ferrofluid droplets on both of the porous and smooth substrates in the presence of the magnetic field. The findings of this study can provide a foundation for understanding the impacting dynamics of ferrofluid droplets on the substrates and optimizing their applications in various fields, such as three-dimensional printing and microfluidic technology. [ABSTRACT FROM AUTHOR]

In this paper, the dynamical mechanism and a general deformation law of a ferrofluid droplet suspended between the air and a liquid substrate under the action of the applied vertical uniform magnetic field are investigated by a numerical model. A generalized conservative phase-field simplified multiphase lattice Boltzmann model is adopted to solve the flow field and phase field, which has a good ability to simulate the problems of ternary fluid flows with large density ratios. Subsequently, the Maxwell equation of static magnetic field is used to solve the magnetic field using a self-correcting scheme. We used this model to numerically study the dynamic evolvement process of ferrofluid droplets placed between the air and a liquid substrate, which are exposed in a vertical uniform magnetic field. Some typical characteristics are employed to characterize the droplet shape, and it is found that the aspect ratio, the elongated velocity, and the height of the mass center of the ferrofluid droplet are related to the magnetic Bond number. Furthermore, the numerical results obtained with the model are in good agreement with the experimental results available in the literature. Finally, the quantitative power law relation between the magnetic Bond number and the aspect ratio of ferrofluid droplets is obtained by using the method of scaling law, which provides a theoretical basis for the study of the deformation mechanism and the universal laws of a ferrofluid droplet placed between the air and a liquid substrate under the action of the vertical uniform magnetic fields with different intensities. [ABSTRACT FROM AUTHOR]

Preventing droplets from splashing after impacting a thin layer or liquid pool is crucial in reducing cross-contamination, the spread of pathogens, and rough surfaces in three-dimensional (3D) printing. In this article, we demonstrate that an external magnetic field can be useful to actively control the post-impact dynamics of ferrofluid droplets. A simplified lattice Boltzmann method (SLBM) is applied to simulate the flow field with lower computational cost. For the magnetic field, a self-correcting procedure is coupled with SLBM by setting a permanent magnet of desired magnetic field strength at any location of the computational domain. In this article, four different phenomena are simulated, including static contact angle, dynamic contact angle, splashing droplet on a thin layer, and falling droplet into a pool same liquid. From the first two examples, it is deduced that a vertical non-uniform magnetic field not only controls the spreading diameter and apex height but also the puffy shape appearing at droplet laterals. In examples three and four, even more intricate crown structures and wave propagation are successfully controlled with the help of a permanent magnet. It is also discovered that a magnetic field introduced at an optimal starting moment improves control and speeds up the whole procedure. [ABSTRACT FROM AUTHOR]

In this work, a comprehensive numerical study of the magnetic field-induced dynamic self-assembly process of multiple bubbles inside the ferrofluid is presented. For multiple bubbles inside the ferrofluid, the magnetic attraction force between bubbles is usually greater and lasts longer than the magnetic repulsion force, resulting in self-assembly movement. This process can be influenced by a number of factors, such as surface tension, inertia force, and initial position, and their specific mechanisms have not been fully understood. Particularly, what roles the magnetic field strength, the surface tension coefficient, and the initial position play are our major interest. Results show that higher magnetic field strength is unfavorable for improving self-assembly efficiency as it leads to stronger magnetic interactions, including attraction and repulsion. In contrast, an increase in the surface tension coefficient can enhance the effect of attraction and weaken the effect of repulsion. Further analysis of the influence of the initial position shows that the magnetic repulsive force can be enhanced by increasing the horizontal gap, which causes a reversing motion along the magnetic field direction. However, an increase in the vertical gap has a nonlinear effect on the efficiency of the self-assembly process, and there is a critical distance below which the self-assembly process could be accelerated with the increase in the vertical gap. [ABSTRACT FROM AUTHOR]

In this work, the dynamics of bubbly flow in a dielectric ferrofluid under a uniform magnetic field has been numerically studied by a self-correcting procedure-based lattice Boltzmann flux solver. The investigation cases focus specifically on two bubbles merging and a single bubble rising in ferrofluid with a large density ratio under an applied uniform magnetic field. By accounting for the effects of the magnetic field intensity, susceptibility, Reynolds number, and Eotvos number, the mechanisms of bubble motion and deformation in the ferrofluid under the external magnetic field are analyzed. [ABSTRACT FROM AUTHOR]

This research presents a numerical analysis of the normal field instability for an initially flat layer of ferrofluid under the influence of magnetic field. A coupling between the simplified lattice Boltzmann method and the self-correcting procedure is developed to capture the velocity field and magnetic field. The proposed method has the ability to simulate complex hedgehog and comb-like spike structures without using an additional magnetization equation. A single dipole permanent magnet is defined instead of multiple point dipoles which makes this method much simpler and more efficient compared to the numerical approaches available in the literature. A comparison between the simulation results and experimental findings is provided to verify the validity of our method. A criterion for the prediction of spikes is presented for uniform magnetic fields. This study also investigates the effects of different types of magnetic fields, their strengths, and the effect of surrounding non-magnetic fluid on the spike structures. Moreover, the description of magnetic field lines, distribution of magnetic flux density, and energy estimation are also provided in this work which gives a useful insight into the hydrodynamic as well as the magnetostatic behavior of ferrofluids. [ABSTRACT FROM AUTHOR]

In this article, the dynamics of ferrodroplet deformation and bubbles merging within the ferrofluid under a uniform magnetic field are studied through numerical simulations. A recently developed simplified multiphase lattice Boltzmann method (SMLBM) is used to capture the hydrodynamic behavior of ferrofluids, the Cahn-Hilliard (CH) equation is employed as the interface tracking algorithm, whose solution is also obtained within the lattice Boltzmann framework and a self-correcting procedure is used to solve the magnetic field along with conjugate boundary conditions for a smooth transition of magnetic permeability at the interface. A series of numerical simulations are performed for a range of magnetic field strength, magnetic susceptibility and Ohnesorge number (Oh), along with a comparison between obtained results and previous experimental and numerical results. The dynamical behavior of ferrodroplets and bubbles merging in ferrofluids is analyzed through the distribution of magnetic field and magnetic flux density, velocity contours, pressure variations, the magnetic energy density and the effect of inertia. Findings of this study may help to explain the mechanism of ferrodroplet deformation and merging of bubbles within the ferrofluid and provide a useful insight into the distribution of flow variables during these deformations and merging phenomena. [ABSTRACT FROM AUTHOR]