Session D9: Focus Session: The Impact of Andy Acrivos on Today's Fluid Mechanics Science I

Field-driven mesoscale phase transition in polarized colloids in microgravity

An unexpected phase transition in a polarized suspension was reported by Kumar, Khusid, Acrivos, PRL95, 258301, 2005 and Agarwal, Yethiraj, PRL102, 198301, 2009. Following the field application, particles aggregated head-to-tail into chains that bridged the interelectrode gap and then formed a cellular pattern, in which large-scale particle-free voids were enclosed by particle-rich thin walls. Surprisingly, the size of particle-free domains scales linearly with the gap thickness but is insensitive to the particle size and the field strength and frequency. Cellular structures were not observed in simulations of equilibrium in a polarized suspension (Richardi, Weis, J Chem Phys 135, 124502, 2011; Almudallal, Saika-Voivod, PRE 84, 011402, 2011). Nonequilibrium simulations (Park, Saintillan, PRE 83, 041409, 2011) showed cellular-like structures but at a particle concentration much higher than in experiments. A requirement for precise matching of densities between particles and a fluid to avoid gravity effects limits terrestrial experiments to negatively polarized particles. We will present data on positively polarized non-buoyancy-matched particles and the development of experiments in the International Space Station needed to evaluate gravity contribution.   

What makes cilia beat?

There have been numerous attempts at understanding the mechanism responsible for producing steady beat in cilia that propel eukaryotic cells. The core structure of a cilium, known as the axoneme, consists of nine microtubules doublet surrounding a central pair of microtubules. The dynein motors on the doublets generate active shear forces that are responsible for relative sliding and bending of the cilium. Several theories have been put forward over the last sixty years but none are supported through a careful analysis of the ciliary beating. We have combined the methods of slender body theory and multipole expansions -- both developed by Professor Acrivos and his students -- to analyze in detail the hydrodynamics of ciliary beating in ten different cases. The analysis is used to infer the internal dynamics of cilia and, in particular, the active forces generated by the dynein motors along the length of cilia. We find that the properties of the axoneme vary along the length of a cilium. In the central region, the active forces generated are primarily dependent on the rate of sliding of the microtubules. This region therefore appears to be optimized to propagate a wave down the length of the cilium. The proximal region near the cell body appears more complex and may be suitable for creating waves. These conclusions from the hydrodynamic analysis are consistent with a recent study that reports different structures of the axoneme in these two regions. The detailed comparison with various theories of axoneme dynamics/ collective behavior of molecular motors show that none of the existing theories are adequate for predicting the correct active moments generated so that the mechanism for ciliary beating still remains unresolved.   

Transient behavior of liquid drops with a polymerized interface

Capsules consisting of a liquid droplet enclosed by a thin polymerized membrane are commonly encountered in nature or in industry. The mechanical properties of the capsule wall are essential to control particle integrity and release of the internal contents. We have designed a novel method to assess the elastic surface shear modulus Gs of micrometer size capsules. It is based on the comparison between the predictions of a numerical model and the experimental measurement of the steady velocity and deformed profile of a capsule flowing in a square section microfluidic tube. To assess membrane viscosity, we have designed a new set-up, where a capsule exits suddenly from a square channel into a wider rectangular channel. The technique is illustrated for initially spherical capsules with a thin cross-linked albumin (HSA) membrane. From the profile in the square channel, we infer the mean value of Gs. We then follow the transient deformation of the capsule in the rectangular pore. Under the same flow conditions, the experimental relaxation time is about twice the numerical time computed for a capsule with a purely elastic membrane. The HSA membrane has thus some viscosity, probably due to the rearrangement of loose HSA molecules on the inside of the membrane.   

A generalized Oldroyd model for a suspension of rod-like or disk-like particles

Early work on emulsion rheology was performed by Frankel and Acrivos [J. Fluid Mech., 44, 65 (1970)] for dilute emulsions of drops with small deformations. Martin, Zinchenko and Davis [J. Rheol. 58, 759, (2014)] developed a more general approach, valid for larger deformations and based on a 5-parameter Oldroyd model with variable coefficients found from fitting the equation to three viscometric and two extensiometric functions in simple shear and hyperbolic flow, respectively, at arbitrary flow intensities. The method was validated with the Frankel-Acrivos small-deformation theory. We have extended the method to ellipsoidal particles subject to Brownian rotations. The viscometric and extensiometric functions were obtained by numerically solving the Fokker-Planck equation for the particle orientation distribution function through expansions into spherical harmonics. The results compare well with the interpolation models of Hinch and Leal [J. Fluid Mech., 76, 187 (1976)] between the limits of weak and strong flows. A benefit of our general approach to constitutive modeling is that it can be applied to concentrated systems (suspensions, emulsions, etc.), while the prior models are limited to dilute systems of non-interacting particles or drops.   

A coating flow on a rotating vertical disk

A thin viscous film of liquid on a vertical disk can be stopped from dripping off by slowly ($Re\ll1$) rotating the disk about its horizontal axis. When surface tension is neglected, it is known [Phys Fluids 21 103102] that the thickness of the film is constant around circles whose centres are offset from the centre of the disk. Small nonzero surface tension determines the variation of the thickness on the differing circles, and the above paper found the first 4 terms in an expansion for small gravity. Acrivos [Phys Fluids 22, 05901] has speculated on the maximum strength of gravity before dripping starts. A new integro-differential equation in the non-orthogonal coordinates of the eccentric circles is derived and solved for the distribution of thickness across the circles, to test Acrivos's speculation.   

Inertia in Suspension Flows: Bulk Properties and Recirculating Wakes

The influence of suspensions in which the particle scale inertia is non-negligible is considered by examining the inertial effects upon two distinct aspects of suspension flow through numerical simulations using the lattice-Boltzmann method. In one case, we consider the dependence of the bulk flow properties on the particle-scale Reynolds number, $ Re = \rho \dot{\gamma} a^2/\mu$, where $\rho$ and $\mu$ are, respectively the density and viscosity of the suspending fluid, $\dot{gamma}$ is the shear rate and $a$ is the radius of a spherical suspended particle. We describe briefly the influence of solid fraction for $0< \phi\le 0.35$, and $Re$ on the viscosity and normal stresses, showing how the microstructure induced by the flow plays a role in setting these properties. In the second case, we consider the flow of a suspension of $\phi < 0.1$ past a cylinder of radius large relative to the suspended particles at bulk Reynolds numbers yielding a recirculating wake. It is observed experimentally that the resulting wake is largely depleted of particles. The basis for this observation is explored by LB simulation and is found to be due to a two-part mechanism in which particle migrate to a limit cycle and are then displaced by fluctuations from particle interaction.   

Magnetically Driven Flows of Suspensions of Rods to Deliver Clot-Busting Drugs to Dead-End Arteries

Suspensions of iron particles in the presence of a magnetic field create flows that could significantly increase the delivery of drugs to dissolve clots in stroke victims. An explanation of this flow rests on the foundation of the seminal works by Prof. Acrivos and his students on effective magnetic permittivity of suspensions of rods, hydrodynamic diffusion of particles, and the flow of suspensions. Intravenous administration of the clot dissolving tissue plasminogen activator (tPA) is the most used therapy for stroke. This therapy is often unsuccessful because the tPA delivery is diffusion-limited and too slow to be effective. Observations show that added iron particles in a rotating magnetic field form rotating rods along the wall of the occluded vessel, creating a convective flow that can carry tPA much faster than diffusion.~We present a proposed mechanism for this magnetically driven flow in the form of coupled particle-scale and vessel-scale flow models. At the particle-scale, particles chain up to form rods that rotate, diffuse and translate in the presence of the flow and magnetic fields. Localized vorticity created by the rotating particles drives a macroscopic convective flow in the vessel. Suspension transport equations describe the flow at the vessel-scale. The flow affects the convection and diffusion of the suspension of particles, linking the two scales.~The model equations are solved asymptotically and numerically to understand how to create convective flows in dead-end or blocked vessels.   

Self-diffusiophoresis of catalytically active patchy colloids near a solid boundary

Active colloidal swimmers designed to move along an envisioned path to ascertain various applications in nanotechnology. In diffusiophoresis, gradients in the solute concentration across the colloid create an imbalance force due to the interactions of the solute with the particle. These forces can also be integrated into a self-propulsion by choosing a reactant as a solute which undergoes a surface reaction only on one face of a colloid. The effect of boundaries in self-diffusiophoresis is not purely to retard the motion, because the boundaries also alter the solutal gradient. We developed an analytical approach to investigate the dynamics of swimming colloid near an infinite planar wall assuming constant flux production and a repulsive interaction between product solute and the colloid. The motion of the colloid was decomposed into translational motions perpendicular and parallel to the wall and a rigid body rotation around the third axis. Our analysis indicates when a patchy colloid approaches the boundary with an inclination angle with respect to the unit normal of the wall, the asymmetric distribution of product around the colloid compels it to rotate and redirects its reaction section towards the wall and thereby the colloid will be moved away from the wall.   

Lateral migration and diffusion of a mechanical engineer through emulsion of drops induced by Andy's influence

My initiation to analytical sides of Stokes flow was thorough cyclostyled notes of Andy's Stanford fluid mechanics notes distributed by Ashok Sangani when he taught a course at Hopkins. Since then, reversibility of Stokes flow and singularity solution remained with me during my research carrier. I will discuss how it and Frankel and Acrivos (1970) paper in JFM influenced my research in drop deformation and emulsion rheology at finite inertia, winning the 2009 Acrivos award by my first PhD student Xiaoyi Li. Finally, I will discuss migration of suspended particles, drops, polymers and biological cells caused by breaking of Stokes reversibility due to deformation and viscoelasticity. Here, we show that the migration is induced by the image stresslet field, as was also indicated by Dave Leighton's thesis and a paper with Smart [1991, Phys. Fluid A, 3, 21]. We relate the stresslet field to the Interface tensor, and investigate the effects of drop inclination. In contrast to a plausible notion asserted also in the literature, that reduced inclination (increased alignment with flow) decreases migration, it is shown here that reduced inclination increases the stresslet and thereby the migration velocity.   

Irreversibility in the motion of suspended particles

We discuss the observed irreversibility in the motion of suspended particles in Stokes flow and its effect in a wide range of transport phenomena, from the rheology of non-Brownian suspensions to the separation of colloidal particles in microfluidic devices. The work of Prof. Acrivos in shear-induced diffusion was instrumental to explain the observed irreversible and stochastic behavior in suspensions flows. The same ideas explain the underlying mechanisms in some popular microfluidic devices used for the separation of suspended particles.