Surface-active microrobots can propel through blood faster than inert microrobots

Abstract

Microrobots that can move through a network of blood vessels have promising medical applications. Blood contains a high volume fraction of blood cells, so in order for a microrobot to move through the blood, it must propel itself by rearranging the surrounding blood cells. However, swimming form effective for propulsion in blood is unknown. This study shows numerically that a surface-active microrobot, such as a squirmer, is more efficient in moving through blood than an inert microrobot. This is because the surface velocity of the microrobot steers the blood cells laterally, allowing them to propel themselves into the hole they are digging. When the microrobot size is comparable to a red blood cell or when the microrobot operates under a low Capillary number, the puller microrobot swims faster than the pusher microrobot. The trend reverses under considerably smaller microrobot sizes or high Capillary number scenarios. Additionally, the swimming speed is strongly dependent on the hematocrit and magnetic torque used to control the microrobot orientation. A comparative analysis between the squirmer and Janus squirmer models underscores the extensive applicability of the squirmer model. The obtained results provide new insight into the design of microrobots propelled efficiently through blood, paving the way for innovative medical applications.

Keywords: Janus particle; microrobots; red blood cells; squirmer; swimming.

Fig. 1.

Numerical setup and locomotion of a microrobot. A) Schematic of a microrobot propelled through an RBC suspension. 44 RBCs are placed in a cubic main domain (black frame) with each side length defined as L. Enlarged view shows the detailed setting of the microrobot with surface velocity and magnetic field. The orientation ($\mathit{e}$) and magnetization direction (${\mathit{n}}_{\mathrm{M}}$) of the squirmer are identical, and the direction of the external magnetic field (B) is in the diagonal direction of the cubic domain. B–E) Flow-fields around four kinds of microrobots in an infinite domain (lab frame). Puller type microrobot with $\beta =1$ (B); Neutral type microrobot with $\beta =0$ (C); Pusher type microrobot with $\beta =-1$ (D); Force-driven microrobot (E). F and G) Locomotion characteristics of the neutral type microrobot propelled through an RBC suspension with $\varphi =25\mathrm{\%}$, $Ca=0.5$, and $ϵ=0.8$ under a dimensionless maximum magnetic torque $T_{\mathrm{m}}^{*}$ of 10. Microrobot trajectory (F). Simulations are not terminated until the observed microrobot reaches the virtual plane of $x+y+z=3L$ shown in the inset view. The diagonal ($U_{\mathrm{d}}$) and perpendicular ($U_{\mathrm{r}}$) velocity components of the microrobot, as well as the orientation and magnetization of the microrobot with respect to magnetic field (G).

Fig. 2.

Effect of magnetic torque. The relative resistance coefficient A) and lateral drift B) of the various microrobots. ϕ, Ca, and $ϵ$ are set to 25%, 0.5, and 0.8, respectively. Each data point for microrobot locomotion shows the means and standard errors of five independent trials. Angle (θ) between the external magnetic field and squirmer orientation (orientation of squirming velocity and magnetization) for the puller ($\beta =1$) C), neutral ($\beta =0$) D), and pusher ($\beta =-1$) E) microrobots. We performed five independent simulations, with each curve corresponding to the mean from five independent trials.

Fig. 3.

Effect of radius ratio. The relative resistance coefficient A) and lateral drift B) of the various microrobots ($\varphi =25\mathrm{\%}$, $Ca=0.5$, and $T_m^{*}=10$). Each data point for microrobot locomotion shows the means and standard errors of five independent trials. C) Minimum distance between the RBC surface and center of the puller ($\beta =1$) and pusher ($\beta =-1$) microrobots and the corresponding ${\theta }_R$ during simulations. Insert panel shows the definition of ${\theta }_R$. A green dot represents the nearest point on the RBC surface to the microrobots. $\mathit{e}$ and ${\mathit{r}}_{\min }$ are the microrobot orientation and the vector from the microrobot center to the nearest point on the RBC surface, respectively. D) Velocity of the squirmer-type microrobots in the x direction under the influence of a solitary RBC, with varied $ϵ$. Insert panel illustrates the simulation setup, where the microrobot orientation $\mathit{e}$ (same as the direction of magnetization $\mathit{M}$) are aligned along the x-axis initially. The external magnetic field $\mathit{B}$ is always aligned along the x-axis. The angle (${\theta }_c$) between the normal vector of the RBC plane (${\mathit{n}}_{\mathrm{RBC}}$) and x-axis is tuned.

Fig. 4.

Effect of Capillary number (Ca). The relative resistance coefficient A) and lateral drift B) of the various microrobots. C–F) Corresponding normalized number density of RBCs (Nd) for the squirmer and force-driven microrobots under different Ca values: 0.2 (C), 0.5 (D), 0.8 (E), and 1.1 (F). The cyan area corresponds to the radius of the microrobots. The inset provides a detailed view of the puller microrobots and surrounding RBCs at the final observation time point. $T_m^{*}$, ϕ, and $ϵ$ are held constant at 10, 25%, and 0.8, respectively. Each data point for microrobot locomotion shows the means and standard errors of five independent trials.

Fig. 5.

Comparative analysis of the squirmer and Janus squirmer models. A) The surface velocity profiles for Puller-type Janus squirmer and squirmer microrobots with $\beta =1.5$. The orientation ($\mathit{e}$) and magnetization direction (${\mathit{n}}_{\mathrm{M}}$) of the squirmer and Janus squirmer microrobots are identical. B) The relative resistance coefficient and lateral drift of the various microrobots under $\varphi =25\mathrm{\%}$, $Ca=0.5$, $ϵ=0.8$, and $T_m^{*}=10$. Each data point for microrobot locomotion shows the means and standard errors of five independent trials.