Migration of ferrofluid droplets in shear flow under a uniform magnetic field

On-demand ferrofluid droplet formation with non-linear magnetic permeability in the presence of high non-uniform magnetic fields

The magnetic actuation of ferrofluid droplets offers an inspiring tool in widespread engineering and biological applications. In this study, the dynamics of ferrofluid droplet generation with a Drop-on-Demand feature under a non-uniform magnetic field is investigated by multiscale numerical modeling. Langevin equation is assumed for ferrofluid magnetic susceptibility due to the strong applied magnetic field. Large and small computational domains are considered. In the larger domain, the magnetic field is obtained by solving Maxwell equations. In the smaller domain, a coupling of continuity, Navier Stokes, two-phase flow, and Maxwell equations are solved by utilizing the magnetic field achieved by the larger domain for the boundary condition. The Finite volume method and coupling of level-set and Volume of Fluid methods are used for solving equations. The droplet formation is simulated in a two-dimensional axisymmetric domain. The method of solving fluid and magnetic equations is validated using a benchmark. Then, ferrofluid droplet formation is investigated experimentally, and the numerical results showed good agreement with the experimental data. The effect of 12 dimensionless parameters, including the ratio of magnetic, gravitational, and surface tension forces, the ratio of the nozzle and magnetic coil dimensions, and ferrofluid to continuous-phase properties ratios are studied. The results showed that by increasing the magnetic Bond number, gravitational Bond number, Ohnesorge number, dimensionless saturation magnetization, initial magnetic susceptibility of ferrofluid, the generated droplet diameter reduces, whereas the formation frequency increases. The same results were observed when decreasing the ferrite core diameter to outer nozzle diameter, density, and viscosity ratios.

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.

Digital Microfluidics: Magnetic Transportation and Coalescence of Sessile Droplets on Hydrophobic Surfaces

Magnetic digital microfluidics is advantageous over other existing droplet manipulation methods, which exploits magnetic forces for actuation and offers the flexibility of implementation in resource-limited point-of-care applications. This article discusses the dynamic behavior of a pair of sessile droplets on a hydrophobic surface under the presence of a permanent magnetic field. A phase field method-based solver is employed in a two-dimensional computational domain to numerically capture the dynamic evolution of the droplet interfaces, which again simultaneously solves the magnetic and flow fields. On a superhydrophobic surface (i.e., θ_c = 150°), the nonuniform magnetic field forces the pair of sessile droplets to move toward each other, which eventually leads to a jumping off phenomenon of the merged droplet from the solid surface after coalescence. Also, there exists a critical magnetic Bond number Bo_m^cr, beyond which no coalescence event between droplets is observed. Moreover, on a less hydrophobic surface (θ_c ≤ 120°), the droplets still coalesce under a magnetic field, although the merged droplet does not experience any upward flight after coalescence. Also, the merging phenomenon at lower contact angle values (i.e., θ_c = 90°) appears significantly different than at higher contact angle values (i.e., θ_c = 120°). Additionally, if the pair of sessile droplets is dispersed to a different surrounding medium, the viscosity ratio plays a significant role in the upward flight of the merged droplet, where the coalesced droplet exhibits increased vertical migration at higher viscosity ratios.

Splitting dynamics of ferrofluid droplets inside a microfluidic T-junction using a pulse-width modulated magnetic field in micro-magnetofluidics

Micro-magnetofluidics offers a promising tool for better control over the ferrofluid droplet manipulation which has been vastly utilized in biomedical applications in recent years. In this study, the ferrofluid droplet splitting under an asymmetric Pulse-Width-Modulated (PWM) magnetic field in a T-junction is numerically investigated using a finite volume method and VOF two-phase model. By utilizing the PWM magnetic field, two novel regimes of ferrofluid droplet splitting named as Flowing through the Same Branch (FSB) and Double Splitting (DS) have been observed for the first time. In the FSB regime, the daughter droplets move out of the same microchannel outlet, and in the DS regime, the droplet splitting occurs two times which results in generating three daughter droplets. The main problem related to the asymmetric droplet splitting under a steady magnetic field is daughter droplet trapping. By using a PWM magnetic field, this issue is resolved and the trapped/escaped regions are obtained in terms of the duty cycle and dimensionless magnetic field frequency. The effects of six important dimensionless parameters on the splitting ratio, including magnetic Bond number, duty cycle, dimensionless magnetic field frequency, capillary number, dimensionless mother droplet length, and dimensionless dipole position are investigated. The results showed that the splitting ratio increases with increasing magnetic Bond number or duty cycle, or decreasing the dimensionless magnetic field frequency. Eventually, a correlation is offered for the splitting ratio based on the dimensionless variables with an average relative error of 2.67%.

Formation and manipulation of ferrofluid droplets with magnetic fields in a microdevice: a numerical parametric study

We present a numerical model that describes the microfluidic generation and manipulation of ferrofluid droplets under an external magnetic field. We developed a numerical Computational Fluid Dynamics (CFD) analysis for predicting and optimizing continuous flow generation and processing of ferrofluid droplets with and without the presence of a permanent magnet. More specifically, we explore the dynamics of oil-based ferrofluid droplets within an aqueous continuous phase under an external inhomogeneous magnetic field. The developed model determines the effect of the magnetic field on the droplet generation, which is carried out in a flow-focusing geometry, and its sorting in T-junction channels. Three-channel depths (25 μm, 30 μm, and 40 μm) were investigated to study droplet deformation under magnetic forces. Among the three, the 30 μm channel depth showed the most consistent droplet production for the studied range of flow rates. Ferrofluids with different loadings of magnetic nanoparticles were used to observe the behavior for different ratios of magnetic and hydrodynamic forces. Our results show that the effect of these factors on droplet size and generation rate can be tuned and optimized to produce consistent droplet generation and sorting. This approach involves fully coupled magnetic-fluid mechanics models and can predict critical details of the process including droplet size, shape, trajectory, dispensing rate, and the perturbation of the fluid co-flow for different flow rates. The model enables better understanding of the physical phenomena involved in continuous droplet processing and allows efficient parametric analysis and optimization.

Lateral migration of a ferrofluid droplet in a plane Poiseuille flow under uniform magnetic fields

The lateral migration of a two-dimensional (2D) viscous ferrofluid droplet in a plane Poiseuille flow under a uniform magnetic field is studied numerically by using the level set method. Focusing on low droplet Reynolds number flows (Re_{d}≤0.05), several numerical simulations are carried out to analyze the effects of magnetic field direction and strength, droplet size, and viscosity ratio on the lateral migration behavior of the droplet. The results indicate that the magnetic field direction plays a pivotal role in the trajectory of lateral migration of the droplet and the final equilibrium position in the channel. When the magnetic field is parallel to the channel, i.e., α=0^{∘} (the direction of magnetic field), the droplet is found to settle closer to the wall with an increase in magnetic Bond number Bo_{m}, while at α=45^{∘}, the droplet settles closer to the channel center. Varying the initial droplet sizes at a fixed magnetic Bond number Bo_{m} and viscosity ratio λ results in different final equilibrium positions within the channel. Additionally, the effect of different viscosity ratios on the migration behavior of the droplet is examined at variable magnetic Bond numbers Bo_{m}. At α=45^{∘}, a critical steady state of deformation is found for λ=0.5 and 1 where the droplet changes its migration direction and shifts toward the center of the channel, while at λ=0.05, the droplet crosses the center. At α=90^{∘}, the droplet is found to settle exactly at the center of the flow domain irrespective of different magnetic Bond numbers, droplet sizes, and viscosity ratios.

Degenerate states, emergent dynamics and fluid mixing by magnetic rotors

We investigate the collective motion of magnetic rotors suspended in a viscous fluid under a uniform rotating magnetic field. The rotors are positioned on a square lattice, and low Reynolds hydrodynamics is assumed. For a 3 × 3 array of magnets, we observe three characteristic dynamical patterns as the external field strength is varied: a synchronized pattern, an oscillating pattern, and a chessboard pattern. The relative stability of these depends on the competition between the energy due to the external magnetic field and the energy of the magnetic dipole-dipole interactions among the rotors. We argue that the chessboard pattern can be understood as an alternation in the stability of two degenerate states, characterized by striped and spin-ice configurations, as the applied magnetic field rotates. For larger arrays, we observe propagation of slip waves that are similar to metachronal waves. The rotor arrays have potential as microfluidic devices that can mix fluids and create vortices of different sizes.

Microfluidics for Biosynthesizing: from Droplets and Vesicles to Artificial Cells

Fabrication of artificial biomimetic materials has attracted abundant attention. As one of the subcategories of biomimetic materials, artificial cells are highly significant for multiple disciplines and their synthesis has been intensively pursued. In order to manufacture robust "alive" artificial cells with high throughput, easy operation, and precise control, flexible microfluidic techniques are widely utilized. Herein, recent advances in microfluidic-based methods for the synthesis of droplets, vesicles, and artificial cells are summarized. First, the advances of droplet fabrication and manipulation on the T-junction, flow-focusing, and coflowing microfluidic devices are discussed. Then, the formation of unicompartmental and multicompartmental vesicles based on microfluidics are summarized. Furthermore, the engineering of droplet-based and vesicle-based artificial cells by microfluidics is also reviewed. Moreover, the artificial cells applied for imitating cell behavior and acting as bioreactors for synthetic biology are highlighted. Finally, the current challenges and future trends in microfluidic-based artificial cells are discussed. This review should be helpful for researchers in the fields of microfluidics, biomaterial fabrication, and synthetic biology.

Pushing of Magnetic Microdroplet Using Electromagnetic Actuation System

Treatment of certain diseases requires the administration of drugs at specific areas of tissues and/or organs to increase therapy effectiveness and avoid side effects that may harm the rest of the body. Drug targeting is a research field that uses various techniques to administrate therapies at specific areas of the body, including magnetic systems able to drive nano “vehicles”, as well as magnetically labeled molecules, in human body fluids and tissues. Most available actuation systems can only attract magnetic elements in a relatively small workspace, limiting drug target applications to superficial tissues, and leaving no alternative cases where deep targeting is necessary. In this paper, we propose an electromagnetic actuation system able to push and deflect magnetic particles at distance of ~10 cm, enabling the manipulation of magnetic nano- and microparticles, as well as administration of drugs in tissues, which are not eligible for localized drug targeting with state-of-the-art systems. Laboratory experiments and modeling were conducted to prove the effectiveness of the proposed system. By further implementing our device, areas of the human body that previously were impossible to treat with magnetically labeled materials such as drugs, cells, and small molecules can now be accessible using the described system.