Particle-wall Hydrodynamic Interactions Research Articles

Frame-invariant sub-grid corrections to the Fictitious Domain Method for the simulation of particulate suspensions in nonlinear flows using OpenFOAM

A particle-scale simulation method for non-Brownian suspensions at low Reynolds numbers is presented, which is well suited to nonlinear flows. It is based on a Fictitious Domain Method supplemented by sub-grid corrections (Gallier et al., 2014 [16]). In the original method, the standard sub-grid corrections involve the underlying suspension linear flow. The conditions required to remove this ambient flow from the sub-grid corrections, while keeping frame indifference, are determined. A sub-grid correction matrix is built for the particle-particle and particle-wall hydrodynamic interactions, such that the mentioned conditions inherently hold. The method is validated against various flows that involve a few particles or a concentrated suspension in linear and nonlinear flows, with various boundary conditions.

Motion of submicrometer particles in micrometer-size channel measured by defocusing nano-particle image velocimetry

Understanding the motion of colloidal particles flowing in small spaces is a general issue in various fields such as thermal engineering and micro/nanofluidics. In the present study, we investigated the motion of fluorescent submicrometer particles in a 3-μm microchannel by defocusing nanoparticle image velocimetry. An optical measurement system with controlled spherical aberration and an algorithm for processing defocused particle images with multiple diffraction rings were developed. By detecting the centroid position and the diameter of the outermost diffraction ring, which is proportional to the distance between the focal plane and the particle, the position of particles was determined with the spatial resolutions of 154–204 nm in the streamwise direction and 76–311 nm in the depthwise direction, which are comparable to or smaller than the optical diffraction limit. A reusable microfluidic device containing a size-regulated microchannel made of glass was developed, which is suitable for optical measurements and precise flow control. By controlling the strength of low-temperature glass bonding, detachment of the bonded glass substrates, washing, and reuse were achieved. Based on this method and technology, the velocity of particles with diameters of 199, 457, and 1114 nm was successfully measured in pressure-driven laminar flow. Results suggested that for larger particles comparable to the channel size, the particle velocity is slowed from the flow velocity by particle–wall hydrodynamic interactions. Therefore, the motion of colloidal particles in 100-μm spaces is considered to be affected by particle–wall hydrodynamic interactions, as well as 102-μm spaces reported previously.

Will we ever wash our hands of lubrication theory?

Lubrication theory is used to investigate how weakly bound particles can be transported away from the vicinity of the wall when two spatially periodic rough surfaces are sheared relative to one another at constant velocity U while immersed in fluid. The aim is to model what could be an important process during decontamination of hands by washing and is motivated by Mittal et al. [“The flow physics of COVID-19,” J. Fluid Mech. 894, F2 (2020)] who remark “Amazingly, despite the 170+ year history of hand washing in medical hygiene, we were unable to find a single published research article on the flow physics of hand washing.” Under the assumption that the roughness wavelength is large compared with the spacing of the surfaces, a, the lubrication approximation permits closed-form expressions to be found for the time-varying velocity components. These are used to track the motion of a particle that is initially trapped in a potential well close to one of the surfaces, and experiences a drag force proportional to the difference between its velocity and that of the surrounding fluid. Complications such as particle-wall hydrodynamic interactions, finite size effects, and Brownian motion are ignored for now. Unsurprisingly, particles remain trapped unless the flow driven by the wall motion is strong compared to the depth of the trapping potential well. Perhaps less obvious is that for many starting positions the process of escape to large distances from the wall takes place over a large number of periods , essentially because the no-slip boundary condition means that fluid velocities relative to the wall are small close to the wall, and thus the velocities of particles along or away from the wall are also small. With reasonable estimates for the various dimensional parameters, the escape times in these cases are found to be comparable in magnitude to the washing times recommended in hand washing guidelines.

Gravity induced formation of spinners and polar order of spherical microswimmers on a surface

We study numerically the hydrodynamics of a self-propelled particle system, consisting of spherical squirmers sedimented on a flat surface. We observe the emergence of dynamic structures, due to the interplay of particle-particle and particle-wall hydrodynamic interactions. At low coverages, our results demonstrate the formation of small chiral spinners: two or three particles are bound together via near-field hydrodynamic interactions and form a rotating dimer or trimer respectively. The stability of the self-organised spinners can be tuned by the strength of the sedimentation. Increasing the particle concentration leads more interactions between particles and the spinners become unstable. At higher area fractions we find that pusher particles can align their swimming directions leading to a stable polar order and enhanced motility. Further, we test the stability of the polar order in the presence of a solid boundary. We observe the emergence of a particle vortex in a cylindrical confinement.

Stokesian simulation of two unequal spheres in a pressure-driven creeping flow through a cylinder

In this paper, a novel numerical technique is generalized for analysis of mutual flow interactions between unequal particles in cylinder-bound pressure-driven flow of highly viscous fluid. The methodology is general enough to account for any polydisperse many-sphere system confined in a circular channel. The scheme is especially useful for the geometric configurations where both interparticle and particle-wall hydrodynamic interactions are significant. In such situation, particulate dynamics is governed by strong spatial variation of mobility tensors relating motion-inducing quantities (like force and torque on the bodies along with the pressure-drop in the vessel) to motion-defining ones (like translational and rotational velocities of each sphere as well as the flow-rate). Accordingly, the mobility tensors are evaluated as spatial functions to solve two different problems. First, we compute force and torque due to incoming fluid on two particles when these are fixed at a specific position inside the flow-domain. Then, we assume both to be freely suspended, and determine their motion driven by the transporting medium. In both problems, the additional pressure-loss in the channel due to the presence of the particles is also calculated representing the increase in channel-resistivity and effective viscosity, respectively.

Transport of a dilute active suspension in pressure-driven channel flow

Confined suspensions of active particles show peculiar dynamics characterized by wall accumulation, as well as upstream swimming, centreline depletion and shear trapping when a pressure-driven flow is imposed. We use theory and numerical simulations to investigate the effects of confinement and non-uniform shear on the dynamics of a dilute suspension of Brownian active swimmers by incorporating a detailed treatment of boundary conditions within a simple kinetic model where the configuration of the suspension is described using a conservation equation for the probability distribution function of particle positions and orientations, and where particle–particle and particle–wall hydrodynamic interactions are neglected. Based on this model, we first investigate the effects of confinement in the absence of flow, in which case the dynamics is governed by a swimming Péclet number, or ratio of the persistence length of particle trajectories over the channel width, and a second swimmer-specific parameter whose inverse measures the strength of propulsion. In the limit of weak and strong propulsion, asymptotic expressions for the full distribution function are derived. For finite propulsion, analytical expressions for the concentration and polarization profiles are also obtained using a truncated moment expansion of the distribution function. In agreement with experimental observations, the existence of a concentration/polarization boundary layer in wide channels is reported and characterized, suggesting that wall accumulation in active suspensions is primarily a kinematic effect that does not require hydrodynamic interactions. Next, we show that application of a pressure-driven Poiseuille flow leads to net upstream swimming of the particles relative to the flow, and an analytical expression for the mean upstream velocity is derived in the weak-flow limit. In stronger imposed flows, we also predict the formation of a depletion layer near the channel centreline, due to cross-streamline migration of the swimming particles towards high-shear regions where they become trapped, and an asymptotic analysis in the strong-flow limit is used to obtain a scale for the depletion layer thickness and to rationalize the non-monotonic dependence of the intensity of depletion upon flow rate. Our theoretical predictions are all shown to be in excellent agreement with finite-volume numerical simulations of the kinetic model, and are also supported by recent experiments on bacterial suspensions in microfluidic devices.

Particle motion in square channel flow of a viscoelastic liquid: Migration vs. secondary flows

The viscoelasticity-induced migration of a sphere in pressure-driven flow in a square-shaped microchannel is investigated under inertialess conditions. The effects of fluid rheology, i.e. of shear thinning and normal stresses, is studied by means of 3D finite element simulations. Two constitutive models are selected, in order to highlight differences due to rheological properties.A strong influence of the suspending fluid rheology on the migration phenomenon is shown, by particle trajectory analysis. When the second normal stress difference is negligible and, as a consequence, no secondary flows appear, the particle migrates towards the channel centerline or the closest corner, depending on its initial position. As shear thinning is increased, the center-attractive region is reduced, and the migration rate is faster. On the other hand, the existence of secondary flows, linked to the existence of a second normal stress difference, alters the migration scenario. The competition between the particle-wall hydrodynamic interactions, promoting the migration mechanism, and the secondary flow velocity components gives rise to further ‘equilibrium’ positions within the channel cross-section. Particles driven towards such positions trace out a spiral trajectory, following the vortex structure of the secondary flows. However, as the particle dimension is increased or the Deborah number is reduced, the cross-streamline migration velocity overcomes the secondary flow velocity. In this case, most of the particles are driven towards the channel centerline, i.e. a strong flow-focusing effect results.

Influence of wall slip in dilute suspensions

Navier's (1823) slip condition, where the tangential velocity is proportional to the shear stress, may apply at micro-scales for a viscous liquid on walls with modified surfaces, e.g. hydrophobic ones in water. Experiments by Lumma et al (2003) show the difficulties involved in measuring such a slip.At small scales, particle-wall hydrodynamic interactions are important. They are modeled here for a dilute suspension of spherical solid particles near a slip wall. Consider a translating and rotating sphere (on which the no-slip condition applies) in an ambient parabolic flow. Analytical solutions of Stokes equations for the various elementary flow fields were obtained (Feuillebois et al 2009, 2011) as series in bispherical coordinates. The coefficients in the series are solutions of an infinite linear system, which is solved by an extension of Thomas' algorithm, allowing to calculate a large number of terms. Accurate results are available for the force, torque and stresslet on a sphere, velocity of a freely moving sphere and diffusion tensor.The Aris-Taylor dispersion of Brownian particles in a shear flow near a slip wall gives a large bias in the measurement of slip (Vinogradova et al, 2009). It is calculated here from the advection-diffusion equation, using the expressions for the particle velocity and diffusion tensor near a slip wall.

Rotational Diffusion of Spherical Colloids Close to a Wall

There is currently no experimental technique available to probe spatially resolved rotational diffusion of nanoparticles in the vicinity of a wall. We present the first experimental study of rotational diffusion of small spherical colloids, using dynamic evanescent wave scattering. A setup is used where the wave vector components parallel and perpendicular to the wall can be varied independently, and an expression is derived for the first cumulant of the intensity correlation function in VH evanescent wave geometry for optically anisotropic spheres. The experimental results are in agreement with theoretical predictions that take particle-wall hydrodynamic interactions into account.

Motion of a sphere parallel to plane walls in a Poiseuille flow. Application to field-flow fractionation and hydrodynamic chromatography

The motion of a solid spherical particle entrained in a Poiseuille flow between parallel plane walls has various applications to separation methods, like field-flow fractionation and hydrodynamic chromatography. Various handy formulae are presented here to describe the particle motion, with these applications in mind. Based on the assumption of a low Reynolds number, the multipole expansion method coupled to a Cartesian representation is applied to provide accurate results for various friction factors in the motion of a solid spherical particle embedded in a viscous fluid between parallel planes. Accurate results for the velocity of a freely moving solid spherical particle are then obtained. These data are fitted so as to obtain handy formulae, providing e.g. the velocity of the freely moving sphere with a 1% error. For cases where the interaction with a single wall is sufficient, simpler fitting formulae are proposed, based on earlier results using the bispherical coordinates method. It appears that the formulae considering only the interaction with a nearest wall are applicable for a surprisingly wide range of particle positions and channel widths. As an example of application, it is shown how in hydrodynamic chromatography earlier models ignoring the particle-wall hydrodynamic interactions fail to predict the proper choice of channel width for a selective separation. The presented formulae may also be used for modeling the transport of macromolecular or colloidal objects in microfluidic systems.

Novel perspectives for the application of total internal reflection microscopy

Total Internal Reflection Microscopy (TIRM) is a sensitive non-invasive technique to measure the interaction potentials between a colloidal particle and a wall with femtonewton resolution. The equilibrium distribution of the particle-wall separation distance z is sampled monitoring the intensity I scattered by the Brownian particle under evanescent illumination. Central to the data analysis is the knowledge of the relation between I and the corresponding z, which typically must be known a priori. This poses considerable constraints to the experimental conditions where TIRM can be applied (short penetration depth of the evanescent wave, transparent surfaces). Here, we introduce a method to experimentally determine I(z) by relying only on the distance-dependent particle-wall hydrodynamic interactions. We demonstrate that this method largely extends the range of conditions accessible with TIRM, and even allows measurements on highly reflecting gold surfaces where multiple reflections lead to a complex (z).

Dynamics of Concentrated Hard-Sphere Colloids Near a Wall

We investigate the Brownian motion of hard-sphere colloids near a solid wall by Evanescent Wave Dynamic Light Scattering (EWDLS). We carried out measurements for various volume fractions of sterically stabilized poly(methyl methacrylate) (PMMA) particles over a range of scattering wave vectors, q. While in the dilute regime, the near wall short-time diffusion is significantly slowed down due to particle-wall hydrodynamic interactions (HI); as volume fraction increases, the wall effect is progressively diminished at all q's. We present a new analysis for the EWDLS short-time self- and collective diffusivities applicable to all volume fractions and a simple model for the self-diffusion describing the interplay between particle-wall and particle-particle HI. Moreover, a weaker decay of the near-wall self-diffusion coefficient with volume fraction is predicted by Stokesian dynamics simulations.

Multiparticle Adhesive Dynamics. Interactions between Stably Rolling Cells

A novel numerical simulation of adhesive particles (cells) reversibly interacting with an adhesive surface under flow is presented. Particle–particle and particle–wall hydrodynamic interactions in low Reynolds number Couette flow are calculated using a boundary element method that solves an integral representation of the Stokes equation. Molecular bonds between surfaces are modeled as linear springs and stochastically formed and broken according to postulated descriptions of force-dependent kinetics. The resulting simulation, Multiparticle Adhesive Dynamics, is applied to the problem of selectin-mediated rolling of hard spheres coated with leukocyte adhesion molecules (cell-free system). Simulation results are compared to flow chamber experiments performed with carbohydrate-coated spherical beads rolling on P-selectin. Good agreement is found between theory and experiment, with the main observation being a decrease in rolling velocity with increasing concentration of rolling cells or increasing proximity between rolling cells. Pause times are found to increase and deviation motion is found to decrease as pairs of rolling cells become closer together or align with the flow.

Motion of inertial spheroidal particles in a shear flow near a solid wall with special application to aerosol transport in microgravity

Trajectories of inertial spheroidal particles moving in a shear flow near a solid wall are calculated numerically from the Stokes flow equations by computing the hydrodynamic forces and torques acting on the particles. Near the wall these interactions cause coupling between the particle's rotational and translational motions. Due to this coupling an inertial spheroid is shown to move along an oscillatory trajectory, while simultaneously drifting towards the wall. This phenomenon occurs in the absence of gravity as a combined effect of three factors: particle non-spherical shape, its inertia and particle–wall hydrodynamic interactions. This drift is absent for inertialess spheroids, and also for inertial spherical particles which move along flow streamlines.The drift velocity is calculated for various particle aspect ratios γ and relaxation times τ. An approximate solution, valid for small particle inertia is developed, which allows the contribution of various terms to the drift velocity to be elucidated. It was found that the maximum value of the drift velocity prevails for N(γ)γ2τs∼4, where s is the shear rate and N(γ) is a decreasing function of γ, related to the particle–wall hydrodynamic interactions. In the limiting cases of large and small inertia and also of very long and thin spheroids, the drift vanishes.Possible applications of the results are discussed in the context of transport of micrometre particles in microgravity conditions. It is shown that the model used is applicable for analysis of the deposition of aerosol particles with sizes above 10 μm inhaled in the human respiratory tract in the absence of gravity.

Precise measurement of particle–wall hydrodynamic interactions at low Reynolds number using laser interferometry

The motion of a spherical particle (with radius 1 to 6 mm) in a viscous fluid is measured using laser interferometry. The typical sensitivity on the measured displacement of the sphere is of the order of 50 nm. The particle is moving on the axis of a closed cylinder. The hydrodynamic interactions between the particle and the walls of the cylinder are compared with the theoretical result of Sano [J. Phys. Soc. Jpn. 56, 2713 (1987)] valid for a very small sphere. The agreement is excellent for the smallest sphere used in the experiment. The experiment also agrees with the result from the theory of lubrication when the sphere is close to a plane end wall. The effect of the particle roughness appears at small distances. Laser interferometry appears as a useful tool to study particle–wall hydrodynamic interactions when the geometry is cumbersome.