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Register a new userTheory of Nonlinear Acoustic Forces Acting on Inhomogeneous Fluids
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Recently, the phenomena of streaming suppression and relocation of inhomogeneous miscible fluids under acoustic fields were explained using the hypothesis on mean Eulerian pressure. In this letter, we show that this hypothesis is unsound and any assumption on mean Eulerian pressure is needless. We present a theory of non-linear acoustics for inhomogeneous fluids from the first principles, which explains streaming suppression and acoustic relocation in both miscible and immiscible inhomogeneous fluids inside a microchannel. This theory predicts the relocation of higher impedance fluids to pressure nodes of the standing wave, which agrees with the recent experiments.
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The lift and drag forces acting on a small, neutrally-buoyant spherical particle in a single-wall-bounded linear shear flow are examined via numerical computation. The effects of shear rate are isolated from those of slip by setting the particle velocity equal to the local fluid velocity (zero slip), and examining the resulting hydrodynamic forces as a function of separation distance. In contrast to much of the previous numerical literature, low shear Reynolds numbers are considered ($10^{-3} lesssim Re_{gamma} lesssim 10^{-1}$). This shear rate range is relevant when dealing with particulate flows within small channels, for example particle migration in microfluidic devices being used or developed for the biotech industry. We demonstrate a strong dependence of both the lift and drag forces on shear rate. Building on previous theoretical $Re_{gamma} ll 1$ studies, a wall-shear based lift correlation is proposed that is applicable when the wall lies both within the inner and outer regions of the disturbed flow. Similarly, we validate an improved drag correlation that includes higher order terms in wall separation distance that more accurately captures the drag force when the particle is close to, but not touching, the wall. Application of the new correlations shows that the examined shear based lift force is as important as the previously examined slip based lift force, highlighting the need to account for shear when predicting the near-wall movement of neutrally-buoyant particles.
The lift and drag forces acting on a small spherical particle moving with a finite slip in single-wall-bounded flows are investigated via direct numerical simulations. The effect of slip velocity on the particle force is analysed as a function of separation distance for low slip and shear Reynolds numbers ($10^{-3} leq Re_{gamma}, Re_{text{slip}} leq 10^{-1}$) in both quiescent and linear shear flows. A generalised lift model valid for arbitrary particle-wall separation distances and $Re_{gamma}, Re_{text{slip}} leq 10^{-1}$ is developed based on the results of the simulations. The proposed model can now predict the lift forces in linear shear flows in the presence or absence of slip,and in quiescent flows when slip is present. Existing drag models are also compared with numerical results for both quiescent and linear shear flows to determine which models capture near wall slip velocities most accurately for low particle Reynolds numbers. Finally, we compare the results of the proposed lift model to previous experimental results of buoyant particles and to numerical results of neutrally-buoyant (force-free) particles moving near a wall in quiescent and linear shear flows. The generalised lift model presented can be used to predict the behaviour of particle suspensions in biological and industrial flows where the particle Reynolds numbers based on slip and shear are $mathcal{O}(10^{-1})$ and below.
We present a theoretical expression for the acoustic interaction force between small spherical particles suspended in an ideal fluid exposed to an external acoustic wave. The acoustic interaction force is the part of the acoustic radiation force on one given particle involving the scattered waves from the other particles. The particles, either compressible liquid droplets or elastic microspheres, are considered to be much smaller than the acoustic wavelength. In this so-called Rayleigh limit, the acoustic interaction forces between the particles are well approximated by gradients of pair-interaction potentials with no restriction on the inter-particle distance. The theory is applied to studies of the acoustic interaction force on a particle suspension in either standing or traveling plane waves. The results show aggregation regions along the wave propagation direction, while particles may attract or repel each other in the transverse direction. In addition, a mean-field approximation is developed to describe the acoustic interaction force in an emulsion of oil droplets in water.
The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles Barker-Henderson density functional, thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapour interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced towards the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.
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