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Register a new userCan phoretic particles swim in two dimensions?
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Added by
Jean-Luc Thiffeault
Publication date
2016
fields
Physics
and research's language is
English
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Artificial phoretic particles swim using self-generated gradients in chemical species (self-diffusiophoresis) or charges and currents (self-electrophoresis). These particles can be used to study the physics of collective motion in active matter and might have promising applications in bioengineering. In the case of self-diffusiophoresis, the classical physical model relies on a steady solution of the diffusion equation, from which chemical gradients, phoretic flows and ultimately the swimming velocity, may be derived. Motivated by disk-shaped particles in thin films and under confinement, we examine the extension to two dimensions. Because the two-dimensional diffusion equation lacks a steady state with the correct boundary conditions, Laplace transforms must be used to study the long-time behavior of the problem and determine the swimming velocity. For fixed chemical fluxes on the particle surface, we find that the swimming velocity ultimately always decays logarithmically in time. In the case of finite Peclet numbers, we solve the full advection-diffusion equation numerically and show that this decay can be avoided by the particle moving to regions of unconsumed reactant. Finite advection thus regularizes the two-dimensional phoretic problem.
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The orientational dynamics of inertialess anisotropic particles transported by two-dimensional convective turbulent flows display a coexistence of regular and chaotic features. We numerically demonstrate that very elongated particles (rods) align preferentially with the direction of the fluid flow, i.e., horizontally close to the isothermal walls and dominantly vertically in the bulk. This behaviour is due to the the presence of a persistent large scale circulation flow structure, which induces strong shear at wall boundaries and in up/down-welling regions. The near-wall horizontal alignment of rods persists at increasing the Rayleigh number, while the vertical orientation in the bulk is progressively weakened by the corresponding increase of turbulence intensity. Furthermore, we show that very elongated particles are nearly orthogonal to the orientation of the temperature gradient, an alignment independent of the system dimensionality and which becomes exact only in the limit of infinite Prandtl number. Tumbling rates are extremely vigorous adjacent to the walls, where particles roughly perform Jeffery orbits. This implies that the root-mean-square near-wall tumbling rates for spheres are much stronger than for rods, up to $mathcal{O}(10)$ times at $Rasimeq 10^9$. In the turbulent bulk the situation reverses and rods tumble slightly faster than isotropic particles, in agreement with earlier observations in two-dimensional turbulence.
The active motion of phoretic colloids leads them to accumulate at boundaries and interfaces. Such an excess accumulation, with respect to their passive counterparts, makes the dynamics of phoretic colloids particularly sensitive to the presence of boundaries and pave new routes to externally control their single particle as well as collective behavior. Here we review some recent theoretical results about the dynamics of phoretic colloids close to and adsorbed at fluid interfaces in particular highlighting similarities and differences with respect to solid-fluid interfaces.
The dynamics of inertial particles in Rayleigh-B{e}nard convection, where both particles and fluid exhibit thermal expansion, is studied using direct numerical simulations (DNS). We consider the effect of particles with a thermal expansion coefficient larger than that of the fluid, causing particles to become lighter than the fluid near the hot bottom plate and heavier than the fluid near the cold top plate. Because of the opposite directions of the net Archimedes force on particles and fluid, particles deposited at the plate now experience a relative force towards the bulk. The characteristic time for this motion towards the bulk to happen, quantified as the time particles spend inside the thermal boundary layers (BLs) at the plates, is shown to depend on the thermal response time, $tau_T$, and the thermal expansion coefficient of particles relative to that of the fluid, $K = alpha_p / alpha_f$. In particular, the residence time is constant for small thermal response times, $tau_T lesssim 1$, and increasing with $tau_T$ for larger thermal response times, $tau_T gtrsim 1$. Also, the thermal BL residence time is increasing with decreasing $K$. A one-dimensional (1D) model is developed, where particles experience thermal inertia and their motion is purely dependent on the buoyancy force. Although the values do not match one-to-one, this highly simplified 1D model does predict a regime of a constant thermal BL residence time for smaller thermal response times and a regime of increasing residence time with $tau_T$ for larger response times, thus explaining the trends in the DNS data well.
We investigate the sedimentation of initially packed paramagnetic particles in presence of a homogeneous external magnetic field, in a Hele-Shaw cell filled with water. Although the magnetic susceptibility of the particles is small and the particle-particle induced magnetic interactions are significantly smaller compared to the gravitational acceleration, we do observe a measurable reduction of the decompaction rate as the amplitude of the applied magnetic field is increased. While induced magnetic dipole-dipole interactions between particles can be either attracting or repulsive depending on the particles relative alignment, our observations reveal an effective overall enhancement of the cohesion of the initial pack of particles due to the induced interactions, very likely promoting internal chain forces in the initial pack of particles. The influence of the magnetic field on the particles once they disperse after being decompacted is on the other hand found to remain marginal.
Dynamics of regular clusters of many non-touching particles falling under gravity in a viscous fluid at low Reynolds number are analysed within the point-particle model. Evolution of two families of particle configurations is determined: 2 or 4 regular horizontal polygons (called `rings) centred above or below each other. Two rings fall together and periodically oscillate. Four rings usually separate from each other with chaotic scattering. For hundreds of thousands of initial configurations, a map of the cluster lifetime is evaluated, where the long-lasting clusters are centred around periodic solutions for the relative motions, and surrounded by regions of the chaotic scattering,in a similar way as it was observed by Janosi et al. (1997) for three particles only. These findings suggest to consider the existence of periodic orbits as a possible physical mechanism of the existence of unstable clusters of particles falling under gravity in a viscous fluid.
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