The Control of Self-Propelled Microjets Inside a Microchannel With Time-Varying Flow Rates

We demonstrate the closed-loop motion control of self-propelled microjets inside a fluidic microchannel. The motion control of the microjets is achieved in hydrogen peroxide solution with time-varying flow rates, under the influence of the controlled magnetic fields and the self-propulsion force. Magnetic dipole moment of the microjets is characterized using the U-turn and the rotating field techniques. The characterized magnetic dipole moment has an average of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">1.4× 10⁻¹³</tex></formula> A.m <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">²</tex></formula> at magnetic field, linear velocity, and boundary frequency of 2 mT, 100 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m/s, and 25 rad/s, respectively. We implement a closed-loop control system that is based on the characterized magnetic dipole moment of the microjets. This closed-loop control system positions the microjets by directing the magnetic field lines toward the reference position. Experiments are done using a magnetic system and a fluidic microchannel with a width of 500 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m. In the absence of a fluid flow, our control system positions the microjets at an average velocity and within an average region-of-convergence (ROC) of 119 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m/s and 390 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex> </formula> m, respectively. As a representative case, we observe that our control system positions the microjets at an average velocity and within an average ROC of 90 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m/s and 600 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m and 120 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex> </formula> m/s and 600 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> m when a flow rate of 2.5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> l/min is applied against and along the direction of the microjets, respectively. Furthermore, the average velocity and ROC are determined throughout the flow range (0 to 7.5 <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">μ</tex></formula> l/min) to characterize the motion of the microjets inside the microchannel.