Chiral swimmer with a regular arbitrary active patch

Abstract We study the low Reynolds number hydrodynamics of a spherical-shaped chiral swimmer with an active patch. The rest of the surface is hydrophobic in nature. The active patch covers a portion of the surface and exhibits chiral activity that is prescribed as a function of θ and φ on the swimmer’s surface. In this study, we consider two types of active patches: (i) a symmetric active patch (SP, independent of φ ) and (ii) an arbitrary active patch (AP, dependent on both θ and φ ). We analytically calculate velocity, rotation rate, and flow field for this model swimmer. We observe that these quantities vary significantly depending on the configuration of the active patch and the strength of hydrophobicity. Thus, we investigated to find the optimal configurations of the active patch corresponding to cases (i) and (ii), having higher velocity and maximum efficiency. We find that for the symmetric patch model, the swimmer’s velocity is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mtext>SP</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:msqrt> <mml:mn>2</mml:mn> </mml:msqrt> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>s</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , where <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>s</mml:mtext> </mml:msub> </mml:mrow> </mml:math> is the velocity of a swimmer whose surface is fully covered with chiral activity as a reference. For the arbitrary patch model, the velocity is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msub> <mml:mi>U</mml:mi> <mml:mrow> <mml:mtext>AP</mml:mtext> </mml:mrow> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.45</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:msub> <mml:mi>U</mml:mi> <mml:mtext>s</mml:mtext> </mml:msub> </mml:mrow> </mml:math> , which is higher than that of the symmetric patch model. Further, our results indicate that swimmers with low hydrophobicity exhibit efficient swimming characteristics. Additionally, due to the active patch being limited to a small portion of the swimmer’s surface, the Stokeslet and Rotlet terms appear in the flow field generated by the swimmer, which is a deviation compared to the case of a swimmer whose surface is fully covered with chiral activity. We analyse the flow fields of the model swimmer in detail. This study provides insights useful for designing synthetic active particles, which can be applied, for example, in targeted drug delivery, chemotaxis, and phototaxis.