Feature Enforcing PINN (FE-PINN): A Framework to Learn the Underlying-Physics Features Before Target Task

In this work, a new data-free framework called Feature Enforcing Physics Informed Neural Network (FE-PINN) is introduced. This framework is capable of learning the underlying pattern of any problem with low computational cost before the main training loop. The loss function of vanilla PINN due to the existence of two terms of partial differential residuals and boundary condition mean squared error is imbalanced. FE-PINN solves this challenge with just one minute of training instead of time-consuming hyperparameter tuning for loss function that can take hours. The FE-PINN accomplishes this process by performing a sequence of sub-tasks. The first sub-task learns useful features about the underlying physics. Then, the model trains on the target task to refine the calculations. FE-PINN is applied to three benchmarks, flow over a cylinder, 2D heat conduction, and an inverse problem of calculating inlet velocity. FE-PINN can solve each case with, 15x, 2x, and 5x speed up accordingly. Another advantage of FE-PINN is that reaching lower order of value for loss function is systematically possible. In this study, it was possible to reach a loss value near 1e-5 which is challenging for vanilla PINN. FE-PINN also has a smooth convergence process which allows for utilizing higher learning rates in comparison to vanilla PINN. This framework can be used as a fast, accurate tool for solving a wide range of Partial Differential Equations (PDEs) across various fields.Comment: 23 pages, 8 figures, 3 table

Magnetically Driven Manipulation of Nonmagnetic Liquid Marbles: Billiards with Liquid Marbles

Liquid marbles are droplets encapsulated by a layer of hydrophobic nanoparticles and have been extensively employed in digital microfluidics and lab-on-a-chip systems in recent years. In this study, magnetic liquid marbles were used to manipulate nonmagnetic liquid marbles. To achieve this purpose, a ferrofluid liquid marble (FLM) was employed and attracted toward an electromagnet, resulting in an impulse to a water liquid marble (WLM) on its way to the electromagnet. It was observed that the manipulation of the WLM by the FLM was similar to the collision of billiard balls except that the liquid marbles exhibited an inelastic collision. Taking the FLM as the projectile ball and the WLM as the other target balls, one can adjust the displacement and direction of the WLM precisely, similar to an expert billiard player. Firstly, the WLM displacement can be adjusted by altering the liquid marble volumes, the initial distances from the electromagnet, and the coil current. Secondly, the WLM direction can be adjusted by changing the position of the WLM relative to the connecting line between the FLM center and the electromagnet. Results show that when the FLM or WLM volume increases by five times, the WLM shooting distance approximately increases by 200% and decreases by 75%, respectively

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

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

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

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

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