Drag force on a microrobot propelled through blood

Abstract

Abstract Controlling microrobot locomotion in vessels and capillaries is crucial for precise drug delivery and minimally invasive surgeries. However, this is challenging due to the complex interactions with red blood cells (RBCs) and the difficulty navigating within the dense environment. Here, we construct a numerical framework to evaluate the relative resistance coefficient ( $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> ) of a microrobot propelled through RBC suspensions. Our experiments validate the numerical results. We find that $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> increases for smaller microrobots and higher hematocrit levels, while magnetic force strength weakly impacts $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> is smaller than the resistance coefficient of a macroscale robot estimated from the apparent viscosity of the RBC suspension. The aspect ratio of a prolate ellipsoidal microrobot influences $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> along its long-axis direction. Additionally, machine learning accurately predicts $${C}_{{{{{{{{\rm{r}}}}}}}}}^{* }$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mrow> <mml:mi>C</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>*</mml:mo> </mml:mrow> </mml:msubsup> </mml:math> . These insights could enhance the design and control of microrobots for medical applications.