Effects of magnetic field on the spreading dynamics of an impinging ferrofluid droplet

Numerical Simulation of Maximum Spreading of an Impacting Ferrofluid Droplet under a Vertical Magnetic Field

Theoretical modeling is proposed to predict the maximum spreading of water-based ferrofluid droplets impacting upon dry surfaces influenced by a vertical magnetic field. Constructed on the principle of energy balance, this model demonstrates excellent agreement with numerical findings across various impact velocities, contact angles, and magnetic strengths. Notably, as magnetic field strength escalates, magnetic forces prevail over viscous and capillary forces, exerting a significant influence on spreading dynamics and diminishing the maximum spreading diameter of ferrofluid droplets if the impacting shape is spherical. However, for freely falling droplets, the shape becomes prolate before impacting and the promoted surface energy balances the magnetic inhibitory effect on droplet spreading, thus resulting in an almost unchanged maximum spreading diameter. By postulating complete conversion of initial kinetic energy into magnetic energy, a scaling law is derived for maximum spreading diameter under extremely high magnetic fields. Further interpolation with viscous dissipation and capillary effects enables universal rescaling under diverse impact conditions. Through comparison with numerical outcomes, the validity of our theoretical model is affirmed, establishing a balanced formula between distinct energy components for predicting maximum spreading diameter of ferrofluid droplets accurately.

Singular jets during droplet impact on superhydrophobic surfaces

HYPOTHESIS

The impact of droplets is prevalent in numerous applications, and jetting during droplet impact is a critical process controlling the dispersal and transport of liquid. New jetting dynamics are expected in different conditions of droplet impact on super-hydrophobic surfaces, such as new jetting phenomena, mechanisms, and regimes.

EXPERIMENTS

In this experimental study of droplet impact on super-hydrophobic surfaces, the Weber number and the Ohnesorge number are varied in a wide range, and the impact process is analyzed theoretically.

FINDINGS

We identify a new type of singular jets, i.e., singular jets induced by horizontal inertia (HI singular jets), besides the previously studied singular jets induced by capillary deformation (CD singular jets). For CD singular jets, the formation of the cavity is due to the propagation of capillary waves on the droplet surface; while for HI singular jets, the cavity formation is due to the large horizontal inertia of the toroidal edge during the retraction of the droplet after the maximum spreading. Key steps of the impact process are analyzed quantitatively, including the spreading of the droplet, the formation and the collapse of the spire, the formation and retraction of the cavity, and finally the formation of singular jets. A regime map for the formation of singular jets is obtained, and scaling relationships for the transition conditions between different regimes are analyzed.

Magnetic Control of Water Droplet Impact onto Ferrofluid Lubricated Surfaces

Controlling the impact process of a droplet impacting a liquid film has remained a wide-open challenge. The existing passive techniques lack precise on-demand control of the impact dynamics of droplets. The present study introduces a magnet-assisted approach to control water droplets' impact dynamics. We show that by incorporating a thin, magnetically active ferrofluid film, the overall droplet impact phenomena of the water droplets could be controlled. It is found that by modifying the distribution of the magnetic nanoparticles (MNPs) present inside the ferrofluid using a permanent magnet, the spreading and retraction behavior of the droplet could be significantly controlled. In addition to that, we also show that by altering the impact Weber number (We_i), and the magnetic Bond number (Bo_m), the outcomes of droplet impact could be precisely controlled. We reveal the role of the various forces on the consequential effects of droplet impact with the help of phase maps. Without the magnetic field, we discovered that the droplet impact on ferrofluid film results in no-splitting, jetting, and splashing regimes. On the other hand, the presence of magnetic field results in the no-splitting and jetting regime. However, beyond a critical magnetic field, the ferrofluid film gets transformed into an assembly of spikes. In such scenarios, the droplet impact only results in no-splitting and splashing regimes, while the jetting regime remains absent. The outcome of our study may find potential applications in chemical engineering, material synthesis, and three-dimensional (3D) printing where the control and optimization of the droplet impact process are desirable.

Experimental and Theoretical Investigation on the Dynamic Response of Ferrofluid Liquid Marbles to Steady and Pulsating Magnetic Fields

Liquid marbles are droplets enwrapped by a layer of hydrophobic micro/nanoparticles. Due to the isolation of fluid from its environment, reduction in evaporation rate, low friction with the surfaces, and capability of manipulation even on hydrophilic surfaces, liquid marbles have attracted the attention of researchers in digital microfluidics. This study investigates the manipulation of ferrofluid liquid marbles (FLMs) under DC and pulse width-modulated (PWM) magnetic fields generated by an electromagnet for the first time. At first, the threshold of the magnetic field for manipulating these FLMs is studied. Afterward, the dynamic response of the FLMs to the DC magnetic field for different FLM volumes, coil currents, and initial distances of FLM from the coil is studied, and a theoretical model is proposed. By applying the PWM magnetic field, it is possible to gain more control over the manipulation of the FLMs on the surface and adjust their position more accurately. Results indicate that with a decrease in FLM volume, coil current, and duty cycle, the FLM step length decreases; hence, FLM manipulation is more precise. Under the PWM magnetic field, it is observed that FLM movement is not synchronous with the generated pulse, and even after the coil is turned off, FLMs keep their motion. In the end, with proper adjustment of the electromagnet pulse width, launching of FLMs at a distance farther than the coil is observed.

Coalescence of a Ferrofluid Drop at Its Bulk Surface with or without a Magnetic Field

The coalescence of a ferrofluid drop at its bulk surface, with or without a magnetic field, was investigated experimentally by a high-speed camera. Shape deformations of both the pendant ferrofluid drop and the bulk surface in the axial direction were observed during the approaching process even in the absence of a magnetic field. The angle of the upper pendant peak at the first contact decreases with the magnetic flux density, while the lower ferrofluid peak displays an opposite trend. The coalescing width of the ferrofluid drop follows a power-law relationship. The exponent of 0.64 under medium and high magnetic fields as well as the case without magnetic field confirms the inertial regime of drop coalescence. Under the low magnetic field, the significant exponent increasing from 0.59 to 3.02 at about 4 ms is in coincidence with the sudden change to a smooth coalescing section according to the visualized images. A high-speed microparticle image velocimetry (micro-PIV) technique was employed with a transparent model fluid to reveal the flow fields during the drop coalescence instead of opaque ferrofluids.

Surface behaviors of droplet manipulation in microfluidics devices

In recent years, the rapid development of microfluidic technology has caused a revolutionary impact in the fields of chemistry, medicine, and life sciences. Also, droplet control is one of the most important technologies in the field of microfluidics. In order to achieve different degrees of droplet transport, the dynamic balance of the competing processes of droplet driving force and fluid resistance should be controlled to achieve good selectivity of droplet transport. Here, we focus on the principles of droplet transport in microfluidic devices, including the driving forces for droplet transport in fluids and the effects of transport properties on droplet transport. After that, the effects of external fields on the directional transport of droplets and the advantages and disadvantages of each external field in droplet transport are discussed in detail. Finally, the applications and challenges of droplet microfluidics in chemical, biomedical, and mechanical systems are comprehensively introduced.

Magnetic Field-Assisted Fission of a Ferrofluid Droplet for Large-Scale Droplet Generation

With the presence of an external magnetic field, a ferrofluid droplet exhibits a rich variety of interesting phenomena notably different from nonmagnetic droplets. Here, a ferrofluid droplet impacting on a liquid-repellent surface is systematically investigated using high-speed imaging. The pre- and post-impact, including the droplet stretching, maximum spreading diameter, and final impact modes, are shown to depend on the impact velocity and the magnitude of the external magnetic field. A scaling relation involving the Weber and magnetic Bond numbers is fitted to predict the maximum spreading diameter based on the magnetic field-induced effective surface tension. The impact outcome is also investigated and classified into three patterns depending on the occurrence of the rim interface instability and the fission phenomenon. Two types of fission (i.e., evenly and unevenly distributed sizes of the daughter droplets) are first identified, and the corresponding mechanism is revealed. Last, according to Rayleigh-Taylor instability, a semiempirical formula is proposed to estimate the number of the daughter droplets in the regime of evenly distributed size, which agrees well with the experimental data. The present study can provide more insight into large-scale droplet generation with monodispersive sizes.

Maximum Spreading of Impacting Ferrofluid Droplets under the Effect of Nonuniform Magnetic Field

This article investigates the maximum spreading of ferrofluid droplets impacting on a hydrophobic surface under nonuniform magnetic fields. A generalized model for scaling the maximum spreading is developed. It is observed that, if the magnetic field strength is zero, a ferrofluid droplet not only demonstrates similar spreading dynamics as the water droplet but also obeys the same scaling law for the maximum spreading factor. Therefore, this article emphasizes the effects of magnetic field strength. In this regard, a dimensionless parameter (N_m) is introduced as the ratio between inertial force and Kelvin force, with an assumption that the kinetic energy mainly transforms to thermal energy. This parameter allows us to rescale all experimental data on a single curve with the Padé approximant, which is applicable to a wide range of impact velocities and magnetic field strengths.

Spreading Dynamics of an Impinging Ferrofluid Droplet on Hydrophilic Surfaces under Uniform Magnetic Fields

This paper reports a numerical investigation on the spreading dynamics of an impinging ferrofluid droplet on solid hydrophilic surfaces (i.e., θ_w ≤ 60°) in the presence of uniform magnetic fields. A finite element method-based commercial solver is implemented to perform several numerical simulations, which uses a phase-field (PF) method to couple both the flow and magnetic fields. The results demonstrate that a uniform magnetic field is capable of controlling the spreading dynamics of an impinging droplet on hydrophilic substrates. Additionally, the application of a magnetic field results in the generation of a steady-state droplet shape with a reduced base diameter and an increased apex height at higher magnetic Bond numbers at the end of the spreading process. Moreover, as the viscosity of the droplet decreases, the droplet experiences an increase in its primary spreading diameter, which can be even reduced through the implementation of a vertical uniform magnetic field. Additionally, an oscillatory motion appears in a droplet during the spreading phenomenon at lower Ohnesorge numbers (i.e., Oh = 0.023), which is further sustained for a longer period of time in the relaxation phase with increased amplitudes in the case of an extremely low-viscosity droplet (i.e., Oh = 0.002) before attaining a final equilibrium shape. Furthermore, at Oh = 0.002, the droplet undergoes a breakup event after the impact for a short period of time, while the magnetic field induces an elastic behavior in a droplet at lower viscosities (i.e., Oh = 0.023) during the free fall under gravity.

The role of drop shape in impact and splash

The impact and splash of liquid drops on solid substrates are ubiquitous in many important fields. However, previous studies have mainly focused on spherical drops while the non-spherical situations, such as raindrops, charged drops, oscillating drops, and drops affected by electromagnetic field, remain largely unexplored. Using ferrofluid, we realize various drop shapes and illustrate the fundamental role of shape in impact and splash. Experiments show that different drop shapes produce large variations in spreading dynamics, splash onset, and splash amount. However, underlying all these variations we discover universal mechanisms across various drop shapes: the impact dynamics is governed by the superellipse model, the splash onset is triggered by the Kelvin-Helmholtz instability, and the amount of splash is determined by the energy dissipation before liquid taking off. Our study generalizes the drop impact research beyond the spherical geometry, and reveals the potential of using drop shape to control impact and splash.

The dynamics of droplet impact and splash is important in many applications, yet its analysis involves difficult intertwined aspects. Here Liu et al. make shape parametrically accessible to experiment, with ferrofluidic drops passing a magnetic field in a defined way.

Meniscus of a Magnetic Fluid in the Field of a Current-Carrying Wire: Three-Dimensional Numerical Simulations

Three-dimensional calculations of the meniscus of a magnetic fluid placed around a current carrying vertical and cylindrical wire are presented. Based on the material properties of experimentally used magnetic fluids, the numerically determined menisci are compared with the experimentally measured ones reported by May. The comparison is made for a linear law of magnetisation as well as for the experimentally measured nonlinear magnetisation curve. Up to moderate strengths of the applied current ( I < = 45 A), i.e., up to moderate strengths of the magnetic field close to the wire, the calculated profiles agree satisfyingly with the experimentally measured ones for a linear as well as for a nonlinear law of magnetisation. At a great strength of the applied current ( I = 70 A), i.e., at a large strength of the magnetic field close to the wire, the agreement is less good than in the range up to moderate strengths. Our analysis revealed that the numerically assumed isothermal conditions are not present in the experiment, particularly at the great strength of the applied current. A control of the temperature in the experiment and the implementation of a coupled thermal model in the numerics are considered the most relevant future steps for an improved agreement.