Passive cell body plays active roles in microalgal swimming via nonreciprocal interactions

TL;DR

The paper addresses whether the cell body of flagellated microalgae acts merely as a passive load or actively enhances swimming through hydrodynamic interactions. It employs boundary-element simulations of a two-flagellated Chlamydomonas model with experimentally measured flagellar waveforms, and a three-sphere abstraction to disentangle interaction components, all at low Reynolds number $Re$. The key findings are that body-flagella hydrodynamic interactions significantly boost swimming speed and efficiency, with an optimal body size arising from a balance between enhanced interactions and viscous drag, and that these interactions are effectively nonreciprocal across the beating cycle. The results offer a hydrodynamic explanation for the observed body size in microalgae and provide design principles for biohybrid microrobots leveraging nonreciprocal hydrodynamic coupling.

Abstract

The cell body of flagellated microalgae is commonly considered to act merely as a passive load during swimming, and a larger body size would simply reduce the speed. In this work, we use numerical simulations based on a boundary element method to investigate the effect of body-flagella hydrodynamic interactions (HIs) on the swimming performance of the biflagellate, \textit{C. reinhardtii}. We find that body-flagella HIs significantly enhance the swimming speed and efficiency. As the body size increases, the competition between the enhanced HIs and the increased viscous drag leads to an optimal body size for swimming. Based on the simplified three-sphere model, we further demonstrate that the enhancement by body-flagella HIs arises from an effective non-reciprocity: the body affects the flagella more strongly during the power stroke, while the flagella affect the body more strongly during the recovery stroke. Our results have implications for both microalgal swimming and laboratory designs of biohybrid microrobots.

Figures (6)

• Figure 1: Model of swimming C. reinhardtii. (a) Flagellar waveform measured from experiments. Blue indicates recovery stroke, and red indicates power stroke. (b) Time-averaged disturbance flow field generated by the swimming model.
• Figure 2: Effect of cell body size on swimming performance: (a) $\langle U_\mathrm{b}\rangle/U_{\mathrm{0}}$ as a function of $b/L$; (b) swimming efficiency $\eta$ as a function of $b/L$. The shaded areas indicate the distribution of $b/L$ from experimental measurements. The vertical dashed lines mark the value of $b/L$ of the sample cell. Other parameters are given in table \ref{['table1']}.
• Figure 3: Effect of body-flagella HIs on (a) instantaneous swimming speed $U_\mathrm{b}(t)$ and (b) instantaneous displacement $y_\mathrm{b}(t)$. Insets show the differences between the results obtained with and without body–flagella HIs for (a) $U_\mathrm{b}(t)$ and (b) $y_\mathrm{b}(t)$ over a beating period. Red and blue regions indicate power and recovery strokes, respectively.
• Figure 4: (a) Schematic of the three-sphere model. (b) Effect of different components of body-flagella HIs on the body speed $U_\mathrm{b}$ in the three-sphere model. The radius of the flagellar sphere is $r_\mathrm{f} = 0.1\ r_\mathrm{b}$. (c) Average of the normalized drag forces $\langle \hbox{\boldmath $F$}_{i\to \mathrm{b}} \hbox{\boldmath $\cdot$} \hat{\hbox{\boldmath $y$}} / \hbox{\boldmath $F$}_\mathrm{b}^0 \hbox{\boldmath $\cdot$} \hat{\hbox{\boldmath $y$}}\rangle$ and $\langle \hbox{\boldmath $F$}_{\mathrm{b}\to i} \hbox{\boldmath $\cdot$} \hat{\hbox{\boldmath $y$}} / \hbox{\boldmath $F$}_i^0 \hbox{\boldmath $\cdot$} \hat{\hbox{\boldmath $y$}}\rangle$ (see text) over the power and recovery strokes.
• Figure 5: Comparison of the numerical results for a rigid scallop model, obtained from a nonlocal slender body theory and the hybrid boundary element and regularized Stokeslet method used in this work. The two filaments are separated by a small distance at the hinge point to avoid overlapping. The number of line elements $N=100$ and $m=6$.