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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]

There are several numerical approaches to define a permanent magnet in terms of mathematical equations, and each approach has progressed since its inception, but still endures some limitations on specific numerical phenomena. This study seeks to propose a novel numerical representation of a permanent magnet without incorporating its effect through boundary conditions, which overcomes the limitations of previous studies and enables us to introduce a magnetic field of desired strength at any location. A self-correcting method is modified to incorporate the magnetic field effects, while a simplified lattice Boltzmann method is utilized to solve the governing equations for flow field and interface. The validity of the proposed method is ensured by simulating some benchmark phenomena with and without the external magnetic field. This study also investigates the wetting dynamics of a sessile ferrofluid droplet deposited on solid substrates with different wettabilities. The influence of uniform and non-uniform magnetic fields on droplet spreading is discussed in detail. It is observed that for a non-uniform magnetic field in vertical direction, the ferrofluid droplet on a hydrophilic surface does not observe the spherical cap approximation unless the magnetic field strength is below saturation magnetization. Moreover, if the magnet is located above, the droplet undergoes large deformations and achieves pointy shapes with sharp tips on less wettable surfaces. [ABSTRACT FROM AUTHOR]

In this article, we present the motion, deformation, and coalescence of ferrofluid droplets suspended in a nonmagnetic fluid, subjected to a uniform magnetic field in both vertical and horizontal directions. A coupling between the simplified multiphase lattice Boltzmann method and the self‐correcting scheme is constructed to numerically solve the two‐dimensional flow field and the magnetostatics equations, respectively. The Cahn‐Hilliard equation is employed to seize the diffuse interface between magnetic and nonmagnetic fluids. In order to validate the model, deformation of a ferrofluid droplet suspended in nonmagnetic fluid is simulated as a test case and the results are compared with numerical and experimental results. Furthermore, a detailed analysis on the behavior of falling ferrofluid droplets and the coalescence between a pair of ferrofluid droplets under the effect of different magnetic fields and different droplets configurations are also presented in this article. The results provide significant insight and a better understanding of these phenomena. It is found that for higher values of magnetic bond number and susceptibility, the droplet deformation is significant and the falling process is faster while a reverse behavior is observed for higher values of Eötvös number. Moreover, the magnetic energy density exhibits an interesting behavior in the vicinity of the droplets. It is concentrated between the droplets with a nonuniform distribution when the droplets are close to each other. [ABSTRACT FROM AUTHOR]

In the present study, a fractional-step-based multiphase lattice Boltzmann (LB) method coupled with a solution of a magnetic field evolution is developed to predict the interface behavior in magnetic multiphase flows. The incompressible Navier–Stokes equations are utilized for the flow field, while the Cahn–Hilliard equation is adopted to track the interface, and these governing equations are solved by reconstructing solutions within the LB framework with the prediction–correction step based on a fractional-step method. The proposed numerical model inherits the excellent performance of kinetic theory from the LB method and integrates the good numerical stability from the fractional-step method. Meanwhile, the macroscopic variables can be simply and directly calculated by the equilibrium distribution functions, which saves the virtual memories and simplifies the computational process. The proposed numerical model is validated by simulating two problems, i.e., a bubble rising with a density ratio of 1000 and a viscosity ratio of 100 and a stationary circular cylinder under an external uniform magnetic field. The interfacial deformations of a ferrofluid droplet in organic oil and an aqueous droplet in ferrofluid under the external magnetic field are, then, simulated, and the underlying mechanisms are discussed. Moreover, the rising process of a gas bubble in the ferrofluid is investigated, which shows that the rising velocity is accelerated under the effect of the external magnetic field. All the numerical examples demonstrate the capability of the present numerical method to handle the problem with the interfacial deformation in magnetic multiphase flows. [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]

An experimental investigation of a magneto hydrodynamics power generator using a low-melting-point Gallium alloy at high Reynolds numbers is presented in this paper. The power output is found to increase with increasing the flow Reynolds number. By considering the non-uniform distribution of the magnetic field in the test channel, theoretical evaluation gives a more accurate prediction to the experimental data. The present generator demonstrates the maximum power generation efficiency of $$8.3\times 10^{-4}$$ % and the maximum output electric power of 1.5 mW. [ABSTRACT FROM AUTHOR]

Abstract: The dynamic rheological properties of viscoelastic magnetic fluids in externally applied uniform magnetic fields are investigated by a laboratory-made cone-plate rheometer in this study. In particular, the effects of the magnetic field on the viscoelastic properties (the complex dynamic modulus) of the viscoelastic magnetic fluids are studied. In the investigation, three viscoelastic magnetic fluids are made by mixing a magnetic fluid and a viscoelastic fluid with different mass ratios. As a supplementation to the experimental investigation, a theoretical analysis is also presented. The present study shows that the viscosity and elasticity of the viscoelastic magnetic fluids are significantly influenced by the magnetic field and the concentrations of the magnetic particles in the test fluids. Theoretical analysis qualitatively explains the present findings. [Copyright &y& Elsevier]

Abstract: Experiments of ammonia–water falling film absorption were performed in magnetic fields of different intensities and different directions as well as under varied operating conditions. Experimental results showed that the outlet concentration of ammonia–water, the outlet temperature of cooling water and the amount of absorption heat and mass in downward magnetic field are higher than those in non-magnetic field. However, all of them decreased in the upward magnetic field. Therefore, it can be concluded that the magnetic field with the same direction as falling film enhances the absorption, and the magnetic field with the direction against falling film weakens the absorption of ammonia–water. The results also showed the effect of magnetic field on absorption was more obvious in solutions with low inlet concentration. The influences of the cooling water flow rate, the cooling water inlet temperature and the solution flow rate on absorption in magnetic field were similar to those without magnetic field. [Copyright &y& Elsevier]

Abstract: In this article, natural convections of a magnetic fluid in a cubic cavity under a uniform magnetic field are investigated experimentally and numerically. Results obtained from experiments and numerical simulations reveal that the magnetic field and magnetization are influenced by temperature. There exist relative larger magnetization and magnetic forces in the regions near the upper wall and center inside the cavity than in the region near the bottom and side walls. A weak flow roll occurs inside cavity under the magnetic force, and it brings the low temperature fluid downward in the center region, and streams the high temperature fluid upward along the regions near the sidewalls. With the magnetic field imposed, the heat transfer inside the cavity is enhanced significantly compared to that without the magnetic field, and increasing the strength of the magnetic field the heat transfer is increased further. [Copyright &y& Elsevier]

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]

• A magnetic field coupling FSLB method is proposed to simulate multiphase flows. • The macroscopic governing equations can be fully recovered in second-order accuracy. • We successfully perform the first rigorous numerical simulation on Rosensweig instability. • The velocity of falling ferrofluid droplet is accelerated by an opposite magnetic field. In the present study, a magnetic field coupling fractional step lattice Boltzmann (FSLB) model is proposed to simulate the complex interfacial behaviors in magnetic multiphase flows with severe interface deformation and large density ratio, which can be recovered to the corresponding macroscopic governing equations with fully second-order accuracy. Since the equilibrium and the non-equilibrium terms are obtained by the Chapman-Enskog (C-E) expansion analysis, the basic idea of the present method is to predict the intermediate variables by updating the various moments of equilibrium distribution functions first, and then correct the physical variables by updating the various moments of non-equilibrium distribution functions. Besides, the present magnetic field coupling FSLB method does not need the evolution of distribution functions compared to the existing LB methods. The present method inherits the excellent performance from the conventional LB method and the relatively better numerical stability from the matured fractional-step method, which is more stable than the original LB method and more efficiency and easy-to-implement than the LB flux solver. Owing to those good properties, we successfully perform the first rigorous numerical simulation on the Rosensweig instability, which accurately captures the spikes forming at the surface of a ferrofluid under an applied magnetic field. Moreover, for the first time we numerically reproduce the falling ferrofluid droplet impacted on the solid surface. Intriguingly, our simulation results reveal that the falling velocity of the ferrofluid droplet is slightly accelerated by the elongation, although the direction of the magnetic field is opposite to that of the gravity. All the results for the interfacial behavior and the magnetic interaction highlights the comparative capability, stability, and accuracy of the present magnetic field coupling FSLB method for simulating the problems of complex fluid dynamics associated with a severe interface deformation and large density ratio in magnetic multiphase flows. [ABSTRACT FROM AUTHOR]

Abstract: The magnetic body force in boiling two-phase temperature-sensitive magnetic fluid (TSMF) flow is known to effectively increase the driving force of magnetic fluid in a non-uniform magnetic field. Based on this mechanism, in the present study, a binary TSMF, which is a mixture of the TSMF and a low-boiling-saturation-temperature organic solution, is proposed to be used in a heat transport device to enhance its circulation. In order to see its performance in the heat transport device, the pressure difference at different heated temperatures, magnetic fields and inclination angles of the heating section are investigated experimentally and theoretically. Results showed that the driving force increases remarkably due to more gas phase appearing in the test fluid and the magnetization of it decreasing. At low magnetic field the driving force is enhanced greatly when the inclination angle is close to 60°, while at high magnetic field the driving force is remarkably enhanced due to the effect of the magnetic force in the inclination angle range from 0° to 30° and 60° to 90°. [Copyright &y& Elsevier]

• A magnetic field coupling LB model is proposed for magnetic multiphase flows. • The magnetic effect is physically described by a surface force derived from Lorentz force law. • The elongation of ferrofluid droplet is well consistent with the experiment. • The merging process of the multiple-ferrofluid-droplet system is investigated. The present study concerns the dynamics of ferrofluid droplets in a Newtonian fluid. The incompressible Navier-Stokes (NS) equations are applied for the dynamics of the immiscible magnetic and Newtonian fluids while the Cahn-Hilliard (C-H) equation is adopted to describe the behavior of their interface. A magnetic field coupling lattice Boltzmann (LB) model is developed to solve both the NS equations and the C-H equation. Specially, a mass-correcting term is introduced into the C-H equation, which strongly enforces the mass conservation. The magnetic field is evaluated by a Poisson equation solver with a self-correcting procedure for the static Maxwell equations. The magnetic dipole force is transformed into the magnetic surface force by a rigorous mathematical procedure, which can physically describe the magnetic effect on the interface. Moreover, the magnetic force after this treatment becomes easy-to-implement, which can be directly incorporated into the external force term of the LB model. The capability of the present combination method to simulate the magnetic multiphase flows is demonstrated by three typical numerical examples, i.e., Laplace law for a stationary droplet, a stationary cylinder under an external uniform magnetic field, the deformation of a single ferrofluid droplet. Further, the merging process of multiple-ferrofluid-droplet system in organic oil is investigated. It is found that the elongation of ferrofluid droplet in the direction of magnetic field shows positive impact on the merging process when the orientation of ferrofluid droplets is parallel to the external magnetic field, while negative impact on the merging process when their orientation is perpendicular to the external magnetic field. [ABSTRACT FROM AUTHOR]