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We present here a comprehensive derivation for the speed of a small bottom-heavy sphere forced by a transverse acoustic field and thereby establish how density inhomogeneities may play a critical role in acoustic propulsion. The sphere is trapped at the pressure node of a standing wave whose wavelength is much larger than the sphere diameter. Due to its inhomogeneous density, the sphere oscillates in translation and rotation relative to the surrounding fluid. The perturbative flows induced by the spheres rotation and translation are shown to generate a rectified inertial flow responsible for a net mean force on the sphere that is able to propel the particle within the zero-pressure plane. To avoid an explicit derivation of the streaming flow, the propulsion speed is computed exactly using a suitable version of the Lorentz reciprocal theorem. The propulsion speed is shown to scale as the inverse of the viscosity, the cube of the amplitude of the acoustic field and is a non trivial function of the acoustic frequency. Interestingly, for some combinations of the constitutive parameters (fluid to solid density ratio, moment of inertia and centroid to center of mass distance), the direction of propulsion is reversed as soon as the frequency of the forcing acoustic field becomes larger than a certain threshold. The results produced by the model are compatible with both the observed phenomenology and the orders of magnitude of the measured velocities.
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Marangoni propulsion is a form of locomotion wherein an asymmetric release of surfactant by a body located at the surface of a liquid leads to its directed motion. We present in this paper a mathematical model for Marangoni propulsion in the viscous regime. We consider the case of a thin rigid circular disk placed at the surface of a viscous fluid and whose perimeter has a prescribed concentration of an insoluble surfactant, to which the rest of its surface is impenetrable. Assuming a linearized equation of state between surface tension and surfactant concentration, we derive analytically the surfactant, velocity and pressure fields in the asymptotic limit of low Capillary, Peclet and Reynolds numbers. We then exploit these results to calculate the Marangoni propulsion speed of the disk. Neglecting the stress contribution from Marangoni flows is seen to over-predict the propulsion speed by 50%.
Understanding mixing and transport of passive scalars in active fluids is important to many natural (e.g. algal blooms) and industrial (e.g. biofuel, vaccine production) processes. Here, we study the mixing of a passive scalar (dye) in dilute suspensions of swimming Escherichia coli in experiments using a two-dimensional (2D) time-periodic flow and in a simple simulation. Results show that the presence of bacteria hinders large scale transport and reduce overall mixing rate. Stretching fields, calculated from experimentally measured velocity fields, show that bacterial activity attenuates fluid stretching and lowers flow chaoticity. Simulations suggest that this attenuation may be attributed to a transient accumulation of bacteria along regions of high stretching. Spatial power spectra and correlation functions of dye concentration fields show that the transport of scalar variance across scales is also hindered by bacterial activity, resulting in an increase in average size and lifetime of structures. On the other hand, at small scales, activity seems to enhance local mixing. One piece of evidence is that the probability distribution of the spatial concentration gradients is nearly symmetric with a vanishing skewness. Overall, our results show that the coupling between activity and flow can lead to nontrivial effects on mixing and transport.
Water vapor condensation is common in nature and widely used in industrial applications, including water harvesting, power generation, and desalination. As compared to traditional filmwise condensation, dropwise condensation on lubricant-infused surfaces (LIS) can lead to an order-of-magnitude increase in heat transfer rates. Small droplets (with the diameter below 100 $mu$m) account for nearly 85 percent of the total heat transfer and droplet sweeping plays a crucial role in clearing nucleation sites, allowing for frequent re-nucleation. Here, we focus on the dynamic interplay of microdroplets with the thin lubricant film during water vapor condensation on LIS. Coupling high-speed imaging, optical microscopy, and interferometry, we show that the initially uniform lubricant film re-distributes during condensation. Governed by lubricant height gradients, microdroplets as small as 2 $mu$m in diameter undergo rigorous and gravity-independent self-propulsion, travelling distances multiples of their diameters at velocities up to 1100 $mu$m/s. Although macroscopically the movement appears to be random, we show that on a microscopic level capillary attraction due to asymmetrical lubricant menisci causes this gravity-independent droplet motion. Based on a lateral force balance analysis, we quantitatively find that the sliding velocity initially increases during movement, but decreases sharply at shorter inter-droplet spacing. The maximum sliding velocity is inversely proportional to the oil viscosity and is strongly dependent of the droplet size, which is in excellent agreement with the experimental observations. This novel and non-traditional droplet movement is expected to significantly enhance the sweeping efficiency during dropwise condensation, leading to higher nucleation and heat transfer rates.
We propose a new approach to the generation of acoustic frequency combs (AFC) -- signals with spectra containing equidistant coherent peaks. AFCs are essential for a number of sensing and measurement applications, where the established technology of optical frequency combs suffers from fundamental physical limitations. Our proof-of-principle experiments demonstrate that nonlinear oscillations of a gas bubble cluster in water insonated by a low-pressure single-frequency ultrasound wave produce signals with spectra consisting of equally spaced peaks originating from the interaction of the driving ultrasound wave with the response of the bubble cluster at its natural frequency. The so-generated AFC posses essential characteristics of optical frequency combs and thus, similar to their optical counterparts, can be used to measure various physical, chemical and biological quantities.
The unsteady, lineal translation of a solid spherical particle through viscoelastic fluids described by the Johnson-Segalman and Giesekus models is studied analytically. Solutions for the pressure and velocity fields as well as the force on the particle are expanded as a power series in the Weissenberg number. The momentum balance and constitutive equation are solved asymptotically for a steadily translating particle up to second order in the particle velocity, and rescaling of the pressure and velocity in the frequency domain is used to relate the solutions for steady lineal translation to those for unsteady lineal translation. The unsteady force at third order in the particle velocity is then calculated through application of the Lorentz reciprocal theorem, and it is shown that this weakly nonlinear contribution to the force can be expressed as part of a Volterra series. Through a series of examples, it is shown that a truncated representation of this Volterra series, which can be manipulated to describe the velocity in terms of an imposed force, is useful for analyzing specific time-dependent particle motions. Two examples studied using this relationship are the force on a particle suddenly set into motion and the velocity of a particle in response to a suddenly imposed steady force. Additionally, the weakly nonlinear response of particle captured by a harmonic trap moving lineally through the fluid is computed. This is an analog to active microrheology experiments, and can be used to explain how weakly nonlinear responses manifest in active microrheology experiments with spherical probes.
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