Axisymmetric spheroidal squirmers and self-diffusiophoretic particles

Cortex-driven cytoplasmic flows in elongated cells: fluid mechanics and application to nuclear transport in Drosophila embryos

The Drosophila melanogaster embryo, an elongated multi-nucleated cell, is a classical model system for eukaryotic development and morphogenesis. Recent work has shown that bulk cytoplasmic flows, driven by cortical contractions along the walls of the embryo, enable the uniform spreading of nuclei along the anterior-posterior axis necessary for proper embryonic development. Here, we propose two mathematical models to characterize cytoplasmic flows driven by tangential cortical contractions in elongated cells. Assuming Newtonian fluid flow at low Reynolds number in a spheroidal cell, we first compute the flow field exactly, thereby bypassing the need for numerical computations. We then apply our results to recent experiments on nuclear transport in cell cycles 4-6 of Drosophila embryo development. By fitting the cortical contractions in our model to measurements, we reveal that experimental cortical flows enable near-optimal axial spreading of nuclei. A second mathematical approach, applicable to general elongated cell geometries, exploits a long-wavelength approximation to produce an even simpler solution, with errors below [Formula: see text] compared with the full model. An application of this long-wavelength result to transport leads to fully analytical solutions for the nuclear concentration that capture the essential physics of the system, including optimal axial spreading of nuclei.

Arrested-motility states in populations of shape-anisotropic active Janus particles

The emergence of large-scale collective phenomena from simple interactions between individual units is a hallmark of active matter systems. Active colloids with alignment-dominated interparticle interactions tend to develop orientational order and form motile coherent states, such as flocks and swarms. Alternatively, a combination of self-propulsion and excluded-volume interactions results in self-trapping and active phase separation into dense clusters. Here, we reveal unconventional arrested-motility states in ensembles of active discoidal particles powered by induced-charge electrophoresis. Combining experiments and computational modeling, we demonstrate that the shape asymmetry of the particles promotes the hydrodynamically assisted formation of active particles' bound states in a certain range of excitation parameters, ultimately leading to a spontaneous collective state with arrested motility. Unlike the jammed clusters obtained through self-trapping, the arrested-motility phase remains sparse, dynamic, and reconfigurable. The demonstrated mechanism of phase separation seeded by bound state formation in ensembles of oblate active particles is generic and should be applicable to other active colloidal systems.

Hydrodynamics of an Elliptical Squirmer

In this paper the propulsion of elliptical objects (called squirmers) by imposed tangential velocity along the surface is studied. For a symmetric velocity distribution (a neutral squirmer), pushers (increased tangential velocity on the downstream side of the ellipse) and pullers (increased tangential velocity on the upstream side of the ellipse), the hydrodynamic characteristics, are simulated numerically using the immersed boundary-lattice Boltzmann method. The accuracy of the numerical scheme and code are validated. The effects of Reynolds number (Re) and squirmer aspect ratio (AR) on the velocity u*, power expenditure P* and hydrodynamic efficiency η of the squirmer are explored. The results show that the change of u* along radial direction r* shows the relation of u*~r*−2 for the neutral squirmer, and u*~r*−1 for the pusher and puller. With the increase of Re, u* of the pusher increases monotonically, but u* of the puller decreases from Re = 0.01 to 0.3, and then increases from Re = 0.3 to 3. The values of P* of the pusher and puller are the same for 0.01 ≤ Re ≤ 0.3; P* of the pusher is larger than that of the puller when Re > 0.3. η of the pusher and puller increases with increasing Re, but the pusher has a larger η than the puller at the same Re. u* and P* decrease with increasing AR, and the pusher and puller have the largest and least u*, respectively. The values of P* of the pusher and puller are almost the same and are much larger than those of the neutral squirmer. With the increase of AR, η increases for the neutral squirmer, but changes non-monotonically for the pusher and puller.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

The bank of swimming organisms at the micron scale (BOSO-Micro)

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Minimum Dissipation Theorem for Microswimmers

We derive a theorem for the lower bound on the energy dissipation rate by a rigid surface-driven active microswimmer of arbitrary shape in a fluid at a low Reynolds number. We show that, for any swimmer, the minimum dissipation at a given velocity can be expressed in terms of the resistance tensors of two passive bodies of the same shape with a no-slip and perfect-slip boundary. To achieve the absolute minimum dissipation, the optimal swimmer needs a surface velocity profile that corresponds to the flow around the perfect-slip body, and a propulsive force density that corresponds to the no-slip body. Using this theorem, we propose an alternative definition of the energetic efficiency of microswimmers that, unlike the commonly used Lighthill efficiency, can never exceed unity. We validate the theory by calculating the efficiency limits of spheroidal swimmers.