The effect of a non-uniform pulse-width modulated magnetic field with different angles on the swinging ferrofluid droplet formation
Graphical abstract
Introduction
Numerous studies in engineering and biological fields have focused on providing appropriate conditions for fast and monodispersed droplet formation and manipulation [1]. The droplet behavior can be controlled by applying external forces. Manipulation of droplet motion using any external sources is classified as an active approach, while passive methods do not rely on any external forces except for the intermolecular interactions in the fluids acting on droplets [30]. Magnetic, thermal and electrical forces have been mostly utilized in active methods.
Among these mechanisms, the magnetic force can be effectively imposed on magneto-fluid to control droplets. In many biomedical applications, magnetic actuation is used to manipulate the droplet movement toward a specified target. Ferrofluids are suspended magnetite nanoparticles (usually Fe3O4) in a carrier fluid (water or oil), which are coated with surfactant for the purpose of stabilization to avoid the agglomeration of nanoparticles. Due to the magnetic nature of these nanoparticles, ferrofluids are manipulated in the presence of a magnetic field leading to diverse applications [2], [3], [31]. Ferrofluids benefit from the flowability of the carrier fluid as well as the magnetic property of magnetite oxide nanoparticles.
Microfluidic approaches for generating droplets by exploiting different configurations such as T-junction [4], [5], flow-focusing [6], co-flow [7], and step emulsification [8] devices have been investigated in many studies in the last decade. Researchers have utilized the magnetic field for controlling the ferrofluid droplet generation [9], [10], [11], [12], manipulation [13], and splitting [9] within these configurations. The effect of a uniform magnetic field on the ferrofluid droplet volume in T-junction and flow-focusing devices was experimentally investigated by Tan and Nguyen [14]. They showed that by increasing the magnetic flux density, the droplet volume increases in the flow-focusing device due to parallel direction of flow and magnetic field, whereas it decreases in T-junction configuration because the flow direction is perpendicular to the magnetic field direction. Also, their results indicated that the magnetic pole does not have any effect on the droplet volume. Wu et al. [15] experimentally investigated the effect of a magnetic field on the ferrofluid droplet formation in a flow-focusing device. In addition, the influence of different flow rates, magnetic flux densities and directions on the droplet volume was investigated. They showed that the effect of the magnetic field on the droplet volume decreases by increasing the flow rate. Besides, they also reported that the droplet neck size versus remaining time was scaled with a power-law equation. Moreover, they demonstrated that by increasing the magnetic flux density, the power of this equation increases. Ma et al. [16] investigated the effect of a permanent magnet on the dynamics of a ferrofluid droplet breakup in a T-junction configuration. They studied the regimes of the droplet break up as well as the evolution of the droplet neck versus time, and correlated the necking process with a power-law equation. The results indicated that the magnetic field can affect the necking process and accelerate the droplet break up.
In the above studies, the magnetic force is perpendicular to gravity, and the gravity force does not play an important role in the ferrofluid droplet formation. For a long time, droplet formation from nozzles has been thoroughly investigated due to its rich underlying physics and vast applications in industry. The gravitational force has a considerable effect on droplet formation from nozzles. Several researchers have investigated the passive droplet formation from a nozzle experimentally [17], theoretically [18], and numerically [19]. Besides, there are few studies that have exploited the magnetic field parallel to the gravity in order to control the ferrofluid droplet breakup from the nozzle. The pinch-off mechanism of the ferrofluid droplet was investigated using upward and downward magnetic fields by Jiang and Li [20]. Self-similar behavior of the pinch-off mechanism was observed, which is independent of the direction of the magnetic field with respect to the gravity (upward or downward). In a similar study [21], the same group studied the effect of upward and downward magnetic fields on the droplet volume and droplet formation frequency as well as the droplet shape evolution. They showed that by increasing the magnetic flux density, the droplet volume decreases whereas the droplet formation frequency increases. They concluded that upward and downward magnetic fields do not have any effect on the shape evolution of the droplet; the only difference is that a higher threshold for magnetic flux density is needed in the upward magnetic field, and the magnetic direction only affects the initial stage of the pinch-off process. In another study, Fabian et al. [22] experimentally studied the effect of a homogenous magnetic field on the ferrofluid droplet formation. The homogenous magnetic field was produced by the Helmholtz coils. The effects of parallel and perpendicular magnetic fields with respect to the gravity on the droplet volume and pinch-off process were investigated. The results showed that by increasing the perpendicular magnetic flux density the droplet volume increases, whereas for the parallel magnetic field configuration, the droplet volume first decreases and then increases. They also observed the pinch-off self-similarity in the last stage of the droplet breakup, which was independent of the magnetic field.
Therefore, based on the previous studies, the magnetic force as an active method enables more control on the ferrofluid droplet formation both in lab-on-a-chip devices and nozzles. In the previous studies, the ferrofluid droplet formation in the presence of a DC magnetic field has been studied. To control the droplet volume in the presence of a permanent magnet, the magnet position with respect to the nozzle is the only variable that can be changed [23]. Accordingly, adjusting the magnet position needs an accurate system that makes the device more complicated. In this study, for the first time, the feasibility of using a varying magnetic field to form ferrofluid droplets from a nozzle has been investigated. The varying magnetic field was applied by a Pulse-Width Modulation (PWM) signal. By changing the frequency and the duty cycle of the PWM magnetic field, better control over the droplet volume can be achieved without any need for a sophisticated system to control the position of a magnet. In previous studies, satellite droplet formation as an undesirable phenomenon has been reported under the DC magnetic field. Using PWM magnetic field provides the potential to prevent the formation of satellite droplets. Besides, the effect of different angles of the magnetic coil with respect to gravity on the ferrofluid droplet formation has not been investigated, so far. In this study, the angle of magnetic force with respect to gravity is altered and investigating the effect of the angle on the droplet breakup leads to a better understanding of the physics of droplet formation. Using PWM magnetic field and different angles of the magnetic force provide more options to manipulate the droplet size. Furthermore, in the previous studies, syringe pumps were used for ejecting the ferrofluid, which led to continuous droplet generation. Using an atmospheric boundary condition, in this study, a Drop-on-Demand platform was introduced in which the droplet forms only when the magnetic field is on. For this purpose, first, the effect of the PWM magnetic field characteristics on the regimes of droplet formation was studied and the regime with no satellite droplet formation is reported. Then, the effects of five parameters, i.e. the magnetic flux density, the applied magnetic frequency, the duty cycle, the distance between the nozzle and the center of the upper surface of the coil, and the angle of the magnetic coil with respect to gravity on the droplet formation evolution were investigated. Also, the effects of these parameters on the droplet diameter, formation frequency, and the number of pulses needed for one droplet formation were investigated. At last, a correlation for dimensionless droplet diameter as a function of the five important nondimensionalized variables is obtained.
Section snippets
Experimental setup and procedure
The schematic of the experimental setup is shown in Fig. 1. Oil-based ferrofluid (EFH1, Ferrotec, USA) was used for droplet formation with an average particle diameter of 10 nm and a volume concentration of 7.9%. The nanoparticles were dispersed in the light hydrocarbon oil, and the density and the viscosity of the ferrofluid are 1210 kg/m3, and 6 mPa s, respectively. The initial magnetic susceptibility is 2.64 and the saturation magnetization is 44 m T. The surface tension is equal to 29 mN/m.
For
Physics of droplet formation
According to previous studies [18], [25], [26], there are four main forces acting on a typical droplet generated from a nozzle being injected by a syringe pump: the buoyancy, the interfacial tension, the kinetic and the drag forces. In this paper, the magnetic force is utilized for droplet formation instead of a syringe pump. The ferrofluid is pulled due to the magnetic force, which is a function of the magnetic flux density (B), the gradient of the magnetic flux density (), the ferrofluid
Results and discussion
In this section, the droplet formation under DC and Pulse-Width Modulation (PWM) magnetic fields is investigated. The droplet formation under PWM magnetic field with different parameters is categorized into different regimes. The evolution of droplet formation under DC and PWM magnetic fields is presented and compared with each other. Then, the effects of the different magnetic flux densities, the applied magnetic frequencies, the duty cycles, the distance between the nozzle and the center of
Conclusion
In this paper, the effect of a non-uniform varying magnetic field with different angles on the ferrofluid droplet formation from a nozzle was experimentally investigated. The varying magnetic field was applied using a Pulse-Width Modulation (PWM) signal. Droplet formation evolution in the presence of DC and PWM magnetic fields was studied and compared to each other. A DoD platform was introduced for droplet generation from the nozzle. Droplet formation produced by PWM magnetic field was
Declaration of interests
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
We would like to express our gratitude to the Deputy of Research and Technology of Sharif University of Technology and Sharif Energy Research Institute (SERI) for providing a comfortable working environment to carry out experiments.
References (31)
- et al.
J. Ind. Eng. Chem.
(2018) - et al.
J. Ind. Eng. Chem.
(2018) - et al.
J. Ind. Eng. Chem.
(2018) - et al.
J. Ind. Eng. Chem.
(2012) - et al.
J. Ind. Eng. Chem.
(2018) - et al.
J. Magn. Magn. Mater.
(2018) - et al.
Eur. J. Mech. B: Fluids
(2018) - et al.
Colloids Surf. A: Physicochem. Eng. Asp.
(2018) - et al.
J. Ind. Eng. Chem.
(2017) - et al.
Chem. Eng. Res. Des.
(2016)
J. Magn. Magn. Mater.
Sens. Actuators B: Chem.
Colloids Surf. A: Physicochem. Eng. Asp.
J. Chromatogr. A
Chem. Eng. Sci.
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