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Register a new userLift and drag forces acting on a particle moving in the presence of slip and shear near a wall
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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.
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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.
In a recent paper, Liu, Zhu and Wu (2015, {it J. Fluid Mech.} {bf 784}: 304) present a force theory for a body in a two-dimensional, viscous, compressible and steady flow. In this companion paper we do the same for three-dimensional flow. Using the fundamental solution of the linearized Navier-Stokes equations, we improve the force formula for incompressible flow originally derived by Goldstein in 1931 and summarized by Milne-Thomson in 1968, both being far from complete, to its perfect final form, which is further proved to be universally true from subsonic to supersonic flows. We call this result the textit{unified force theorem}, which states that the forces are always determined by the vector circulation $pGamma_phi$ of longitudinal velocity and the scalar inflow $Q_psi$ of transverse velocity. Since this theorem is not directly observable either experimentally or computationally, a testable version is also derived, which, however, holds only in the linear far field. We name this version the textit{testable unified force formula}. After that, a general principle to increase the lift-drag ratio is proposed.
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.
We consider waves radiated by a disturbance of oscillating strength moving at constant velocity along the free surface of a shear flow which, when undisturbed, has uniform horizontal vorticity of magnitude $S$. When no current is present the problem is a classical one and much studied, and in deep water a resonance is known to occur when $tau=|boldsymbol{V}|omega_0/g$ equals the critical value $1/4$ ($boldsymbol{V}$: velocity of disturbance, $omega_0$: oscillation frequency, $g$: gravitational acceleration). We show that the presence of the sub-surface shear current can change this picture radically. Not only does the resonant value of $tau$ depend strongly on the angle between $boldsymbol{V}$ and the currents direction and the shear-Froude number $mathrm{Frs}=|boldsymbol{V}|S/g$; when $mathrm{Frs}>1/3$, multiple resonant values --- as many as $4$ --- can occur for some directions of motion. At sufficiently large values of $mathrm{Frs}$, the smallest resonance frequency tends to zero, representing the phenomenon of critical velocity for ship waves. We provide a detailed analysis of the dispersion relation for the moving, oscillating disturbance, in both finite and infinite water depth, including for the latter case an overview of the different far-field waves which exist in different sectors of wave vector space under different conditions. Owing to the large number of parameters, a detailed discussion of the structure of resonances is provided for infinite depth only, where analytical results are available.
We numerically investigate the effect of entrance condition on the spatial and temporal evolution of multiple three-dimensional vortex pairs and wall shear stress distribution in a curved artery model. We perform this study using a Newtonian blood-analog fluid subjected to a pulsatile flow with two inflow conditions. The first flow condition is fully developed while the second condition is undeveloped (i.e. uniform). We discuss the connection along the axial direction between regions of organized vorticity observed at various cross-sections of the model and compare results between the different entrance conditions. We model a human artery with a simple, rigid $180^circ$ curved pipe with circular cross-section and constant curvature, neglecting effects of taper, torsion and elasticity. Numerical results are computed from a discontinuous high-order spectral element flow solver. The flow rate used in this study is physiological. We observe differences in secondary flow patterns, especially during the deceleration phase of the physiological waveform where multiple vortical structures of both Dean-type and Lyne-type coexist. We highlight the effect of the entrance condition on the formation of these structures and subsequent appearance of abnormal inner wall shear stresses - a potentially significant correlation since cardiovascular disease is known to progress along the inner wall of curved arteries under varying degrees of flow development.
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