Acoustic microswimmers present great potential for microuidic applications and targeted drug delivery. Here we introduce armoured microbubbles (size range, 10 − 20 µm) made by threedimensional microfabrication which allows the bubbles to last for hours even under forced oscillations. The acoustic resonance of the armoured microbubbles is found to be dictated by capillary forces and not by gas volume, and its measurements agree with a theoretical calculation. We further measure experimentally and predict theoretically the net propulsive ow generated by the bubble vibration. This ow, due to steady streaming in the uid, can reach 100 mm/s, and is aected by the presence of nearby walls. Finally, microswimmers in motion are shown, either as spinning devices or free swimmers. I.

The cytoskeleton plays a key role in establishing robust cell shape. In animals, it is well established that cell shape can also influence cytoskeletal organization. Cytoskeletal proteins are well conserved between animal and plant kingdoms; nevertheless, because plant cells exhibit major structural differences to animal cells, the question arises whether the plant cytoskeleton also responds to geometrical cues. Recent numerical simulations predicted that a geometry-based rule is sufficient to explain the microtubule (MT) organization observed in cells. Due to their high flexural rigidity and persistence length of the order of a few millimeters, MTs are rigid over cellular dimensions and are thus expected to align along their long axis if constrained in specific geometries. This hypothesis remains to be tested in cellulo. Here, we explore the relative contribution of geometry to the final organization of actin and MT cytoskeletons in single plant cells of Arabidopsis thaliana. We show that the cytoskeleton aligns with the long axis of the cells. We find that actin organization relies on MTs but not the opposite. We develop a model of self-organizing MTs in three dimensions, which predicts the importance of MT severing, which we confirm experimentally. This work is a first step toward assessing quantitatively how cellular geometry contributes to the control of cytoskeletal organization in living plant cells.

A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a timeperiodic forcing in the bulk or along a boundary is enhanced by inertia to induce a non-zero net flow. Building on classical work for simple geometrical forcing and motivated by the complex shape oscillations of elastic capsules and bubbles, we develop the mathematical framework to quantify the steady streaming of a spherical body with arbitrary axisymmetric time-periodic boundary conditions. We compute the flow asymptotically for small-amplitude oscillations of the boundary in the limit where the viscous penetration length scale is much smaller than the body. In that case, the flow has a boundary layer structure and the fluid motion is solved by asymptotic matching. Our results, presented in the case of no-slip boundary conditions and extended to include the motion of vibrating free surfaces, recovers classical work as particular cases. We illustrate the flow structure given by our solution and propose one application of our results for small-scale force-generation and synthetic locomotion. * Electronic address: e.lauga@damtp.cam.ac.uk arXiv:1512.00048v1 [physics.flu-dyn] 30 Nov 2015

Acoustic micropropulsors present great potential for microfluidic applications. The propulsion is based on encapsulated 20 μm bubbles excited by a contacless ultrasonic transducer. The vibrating bubbles then generate a powerful streaming flow, with speeds 1-100 mm s in water, through the action of viscous stresses. In this paper we introduce a full toolbox of micropropulsors using a versatile three-dimensional (3D) microfabrication setup. Doublets and triplets of propulsors are introduced, and the flows they generate are predicted by a theoretical hydrodynamic model. We then introduce whole surfaces covered with propulsors, which we term active surfaces. These surfaces are excited by a single ultrasonic wave, can generate collective flows and may be harnessed for mixing purposes. Several patterns of propulsors are tested, and the flows produced by the two most efficient mixers are predicted by a simple theoretical model based on flow singularities. In particular, the vortices generated by the most efficient pattern, an L-shaped mixer, are analysed in detail.

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Specific cell and tissue form is essential to support many biological functions of living organisms. During development, the creation of different shapes at the cellular and tissue level fundamentally requires the integration of genetic, biochemical and physical inputs. It is well established that the cortical microtubule network plays a key role in the morphogenesis of the plant cell wall by guiding the organisation of new cell wall material. Moreover, it has been suggested that light or mechanical stresses can orient the microtubules thereby controlling wall architecture and plant cell shape. The cytoskeleton is thus a major determinant of plant cell shape. What is less clear is how cell shape in turn influences cytoskeletal organization. Recent in vitro experiments and numerical simulations predicted that a geometry-based rule is sufficient to explain some of the microtubule organization observed in cells. Due to their high flexural rigidity and persistence length of the order of a few millimeters, MTs are rigid over cellular dimensions and are thus expected to align along their long axis if constrained in specific geometries. This hypothesis remains to be tested in cellulo . Here we present an experimental approach to explore the relative contribution of geometry to the final organization of actin and microtubule cytoskeletons in single plant cells. We show that, in cells constrained in rectangular shapes, the cytoskeleton align along the long axis of the cells. By studying actin and microtubules in cells with the same system we show that while actin organisation requires microtubules to be present to align the converse is not the case. A model of self organizing microtubules in 3D predicts that severing of microtubules is an important parameter controlling the anisotropy of the microtubule network. We experimentally confirmed the model predictions by analysing the response to shape change in plant cells with altered microtubule severing dynamics. This work is a first step towards assessing quantitatively how cell geometry contributes to the control of cytoskeletal organization in living plant cells.

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

Retinal haemorrhage is often observed following brain injury. The retinal circulation is supplied (drained) by the central retinal artery (vein) which enters (leaves) the eye through the optic nerve at the optic disc; these vessels penetrate the nerve immediately after passing through a region of cerebrospinal fluid (CSF). We consider a theoretical model for the blood flow in the central retinal vessels, treating each as multi-region collapsible tubes, where we examine how a sudden change in CSF pressure (mimicking an injury) drives a large amplitude pressure perturbation towards the eye. In some cases, this wave can steepen to form a shock. We show that the region immediately proximal to the eye (within the optic nerve where the vessels are strongly confined by the nerve fibres) can significantly reduce the amplitude of the pressure wave transmitted into the eye. When the length of this region is consistent with clinical measurements, the CSF pressure perturbation generates a wave of significantly lower amplitude than the input, protecting the eye from damage. We construct an analytical framework to explain this observation, showing that repeated rapid propagation and reflection of waves along the confined section of the vessel distributes the perturbation over a longer lengthscale.