A Life @ Low Reynolds Number

A Scientific Conference at the National Academy of Sciences Building

May 19-21, 2024

A Scientific Conference at the National Academy of Sciences Building

May 19-21, 2024

Abstracts — Alphabetical by Author Last Names

John L. **Anderson**^{1,2}

^{1}Department of Chemical and Biological Engineering, Illinois Institute of Technology

^{2}President, National Academy of Engineering

Monday 20 May 9:00-9:30 pm

Rodolfo **Brandão**^{1}

^{1}Department of Mechanical and Aerospace Engineering, Princeton University

Monday 20 May 5:00-5:20 pm

Experiments have shown that a straight elastic filament bends as it settles under gravity in a viscous fluid. Previous theoretical studies have argued that the observed bending is due to nonlocal hydrodynamic interactions between different parts of the filament. In this talk, we propose an alternative explanation that does not rely on nonlocal effects. Instead, we employ a simpler, local model based on the Resistive Force Theory, where hydrodynamic forces depend on the local orientation and velocity along the filament. We focus on steady states, in which case our model involves a single dimensionless compliance parameter, *η*. Irrespective of *η*, the model predicts two trivial solutions, corresponding to perfectly horizontal and vertical filaments. However, for *η* above a critical value, a new branch of solution emerges, corresponding to filaments exhibiting non-trivial shapes. The theoretical shapes are in good agreement with those observed in experiments. To gain further insight into our predictions, we consider the limit of flexible filaments (large *η*) and derive closed-form asymptotic formulae for the filament shape and settling speed.

Henry **Chu**^{1}

Tuesday 21 May 4:10-4:30 pm

Diffusiophoresis refers to the deterministic motion of particles induced by a surrounding concentration gradient of solutes. Recent experiments demonstrated and measured colloid diffusiophoresis in porous media, but existing theories cannot predict the observed colloid motion. In this work, utilizing regular perturbation method, we develop a mathematical model that can predict the diffusiophoretic mobility of a charged colloidal particle driven by a binary monovalent electrolyte concentration gradient in porous media. The porous medium is modeled as a Brinkman medium with a constant Darcy permeability. The linearized Poisson-Boltzmann equation is invoked to model a weakly or moderately charged particle. We report three new significant findings. First, compared to diffusiophoresis in a free electrolyte solution, we show that the particle mobility can be significantly hampered by a porous medium due to the additional hydrodynamic drag. Second, we demonstrate that particle diffusiophoresis in response to a change in the electrolyte concentration in a porous medium can be qualitatively different from that in a free electrolyte solution. Third, a comparison between our model predictions and experiments demonstrates excellent agreements within the scope of the model, highlighting the predictive power of the model. The mathematical developed here can be employed to design diffusiophoretic colloid transport in porous media, which are central to applications such as nanoparticle drug delivery and enhanced oil recovery.

Kokou S.E. **Dadzie**^{1}

^{1}School of Engineering and Physical Sciences, Heriot-Watt University, Edinburgh, Scotland, UK

Monday 20 May 2:00-2:25 pm

In the classical compressible Navier-Stokes context, the rate of change in fluid density is associated with the divergence of the flow velocity. Predictions made by this mathematical structure of the compressible flow equations, where noticeable variations in fluid thermodynamic properties can occur, can become very ambiguous. A typical example is the failure of the Navier-Stokes equations to accurately predict shock wave structures in gases. The concept of "volume diffusion" exhibits fluid velocity not only as a mechanical property but also as influenced by gradients of thermodynamic variables such as density, pressure, or temperature. A full derivation of the compressible flow equations under this refinement of the concept of fluid velocity reveals several new aspects of a compressible flow. On one hand, constitutive equations accompanying the momentum and energy conservation in fluid flows systematically involve explicit contributions of gradients of the thermodynamic variables. On the other hand, applications of advanced boundary conditions, such as the slip boundary conditions, do not only involve the Maxwell-type slip boundary conditions (i.e., involving only the strain rate), but can also include various gradients of the three thermodynamic variables. These extended forms of the Navier-Stokes equations appear not only to give better predictions in some unconventional flow configurations, such as gas flow in microchannels, but they are also compatible with other preceding theories that compensate for some of these effects, such as the Korteweg models for fluids exhibiting phase changes and the "Ghost Effects" that are flows induced by temperature fields in rarefied gases.

Robert H. **Davis**^{1} and Gesse Roure^{1,2}

^{1}Department of Chemical and Biological Engineering, University of Colorado Boulder

^{2}Department of Mechanical and Aerospace Engineering, University of Missouri (current address)

Tuesday 21 May 4:30-4:50 pm

The collection of hydrophobic mineral particles from aqueous suspension that also includes hydrophilic waste particles is typically achieved by froth flotation, but this process is ineffective for very fine particles that flow around the rising air bubbles. As an alternative approach, a fast-agglomeration process was proposed (Van Netten, Borrow & Galvin, *IECR*, **56**, 2017) using salt-water drops covered with a thin oil layer. The oil layer is water-permeable, and the drops swell due to osmotic flow of freshwater across this layer, thereby facilitating particle capture.

In this presentation, after remarks on inspiration over the years from Howard Brenner, I will discuss how the water permeability reduces the lubrication resistance of a particle approaching a drop surface, how the drops swell with a competition between dilution of the salt water by freshwater and diffusion of salt from the drop interior to the diluted zone, and how the particle collection rate is affected by these processes. For the typical case of large Péclet numbers, diffusion effects are constrained to a thin concentration boundary layer just inside the expanding drop interface, with fast swelling at small times, followed by a slower expansion (drop radius increasing in proportion to the square root of time) at large times. Drop expansion increases the particle collection efficiency of the process, especially for very small particles (which are the most difficult to capture by froth flotation). In practice, the binders are agglomerates of many drops, and a network model shows that the agglomerates behave in a similar fashion to single drops but with an effective diffusivity.

Kevin D. **Dorfman**^{1}, Abbie Davidson^{2}, Jurij Kotar^{2} and Pietro Cicuta^{2}

^{1}Department of Chemical Engineering and Materials Science, University of Minnesota

^{2}Department of Physics, Cavendish Laboratory, Cambridge University, Cambridge, UK

Monday 20 May 11:10-11:30 am

When two colloidal particles are held in place by an optical trap, the cross-correlation in their positions relative to their respective trap centers provides information about the hydrodynamic interactions (HI) between the colloids; the minimum in the cross-correlation is directly connected to the eigenvalues of the mobility tensor. We have measured these interactions for two colloidal particles confined in a microfluidic slit at the midpoint between the upper and lower walls at varying distances between the particle centers and distances from the side wall. The overall results are consistent with hydrodynamic screening theory, with a statistically significant difference between the measured minimum in the cross-correlation for confined colloid and an unconfined colloid when the colloid occupies 35% of the cross-section, while the effect of confinement is not measurable for a colloid that occupies 20% of the cross-section.

Stephanie R. **Dungan**^{1}

^{1}Departments of Chemical Engineering and Food Science and Technology, University of California Davis

Tuesday 21 May 11:00-11:20 am

Phospholipid vesicles, or liposomes, can act as colloidal carriers for hydrophobic solutes, affecting and effecting release of aromas, hydrophobic drugs, nutrients, or agrichemicals. Researchers often assume that release of hydrophobic molecules from vesicles—including the phospholipid molecules themselves—occurs through fusion/disintegration of the vesicle at a surface, and thus dismiss the role of diffusion of the individual molecules themselves from the particles. In our research, dynamic surface tension measurements were used to probe transport kinetics of the phospholipids dilauroyl or dimyristoyl phosphatidylcholine from dispersed unilamellar vesicles to an air–water interface. Careful analysis of adsorption rates using mass transfer theory allowed us to distinguish roles of vesicles versus dissolved molecules in delivering phospholipids to the interface. Adsorption dynamics were measured for different phospholipid structures, temperatures, vesicle diameters and in the presence or absence of convection, to explore these effects on the controlling pathway (via direct vesicle transport and adsorption, or via transport as dissolved monomer) and the steps within. At sufficiently high vesicle concentrations, the kinetics were found to be controlled by monomer diffusion coupled to the rate of monomer release from vesicles, and not to depend on rates of direct vesicle diffusion or interfacial adsorption. This controlling mechanism remained at lower vesicle concentrations; however, vesicle diffusion limitations complicated the dynamics. Adsorption kinetics could be quantitatively predicted with a reaction–enhanced molecular diffusion theory, with a reaction rate associated with PL release from the vesicle. In this theory and in experimental results, the aqueous solubility of the phospholipid was shown to play a central role. These insights were extended to interpreting adsorption dynamics from mixed dispersions, combining single–tailed lysolauroyl phosphatidylcholine (LLPC) with dilauroyl phosphatidylcholine vesicles. The effect of the more soluble LLPC on the adsorption dynamics was assessed by comparing dynamic tension results to theoretical predictions based on reaction–enhanced molecular diffusion.

David A. **Edwards**^{1,2}

^{1}John A. Paulson School of Engineering and Applied Sciences, Harvard University

^{2}Center for Nanomedicine, Johns Hopkins University

Tuesday 21 May 9:50-10:10 am

Transpiration is a phenomenon common to natural and manufactured materials, whereby the accumulation of macromolecules near an evaporating hydrogel surface sets up osmotic pressure differences that can attain thousands of atmospheres. Osmotic pressure gradients induce equal and opposite pervadic pressure gradients, which, in the case of a transpiring leaf, pull water from distant roots in proportion to local vapor pressure deficit (VPD). This pull of water is accompanied by compression of leaf matter up to a threshold VPD above which the leaf wilts. Rising global temperatures with steady relative humidity and local variations in temperature and water scarcity are amplifying VPD globally and regionally, threatening the survivability of plants and other ecosystems. Our recent work suggests that a similar evapotranspiration process may govern water evaporation from the human larynx and trachea such that human respiratory health may be at risk as well. The mucus transpiration hypothesis is grounded on the assumption that healthy airway mucus, a dilute solution of salts (0.9%), globular proteins (1.1%) and mucin macromolecules (0.5%), actually exhibits the transpiration behavior of irreversible hydrogels, as has been studied for over a century since Darwin. We explore by fluid mechanics whether water evaporation over a human laryngeal/tracheal mucus layer might exhibit the signature transpiration features associated with irreversible hydrogels. We confirm that upper airway mucus exhibits emergent properties of porous transpiring hydrogels. These characterize compressive airway stresses that grow with VPD to promote cough and bronchoconstriction. Topical hydration reduces compression-induced dysfunction as in the case of dry leaves. We confirm our predictions with in vitro and human in vivo measurements.

Michael **Graham**^{1}

Tuesday 21 May 10:10-10:30 am

As they flow, red blood cells migrate toward the center of a blood vessel, leaving a cell-free layer at the vessel wall, while white blood cells and platelets are preferentially found near the walls, a segregation phenomenon called margination. We present direct simulations of blood flow as well as mechanistic theory that aim to describe and understand these phenomena. We also describe collaborative work with the laboratory of Wilbur Lam that demonstrates the importance of these phenomena in medicine.

To disentangle effects of shape, size, and deformability, we first describe direct simulations of multicomponent suspensions of deformable capsules. Observations indicate that margination can be driven by contrasts of size, stiffness or shape — for example, a trace component of stiff or small particles will marginate in a suspension whose majority component is large and soft. A mechanistic theory predicts, in good agreement with experiments and our simulations, that the cell-free layer thickness follows a master curve with confinement ratio and volume fraction. It also predicts several regimes of segregation, depending on the value of a dimensionless "margination parameter" that quantifies the effect of cell-cell collisions as well as hydrodynamic migration of particles away from walls.

These segregation phenomena have important physiological and clinical consequences. Treatment of patients with drugs such as dexamethasone or epinephrine lead to softening of white blood cells, and thus to their demargination. In blood disorders such as sickle cell disease and iron deficiency anemia, the aberrant cells are smaller and stiffer than healthy red blood cells, and our simulations predict that these cells will strongly marginate. We also predict that that these marginated cells generate large shear stress fluctuations on the vessel walls, a phenomenon that may explain clinical observations of vascular inflammation in persons with these disorders.

Daniel A. **Hammer**^{1}

^{1}Department of Chemical and Biomolecular Engineering, University of Pennsylvania

Tuesday 21 May 9:30-9:50 am

Adhesive Dynamics (AD) is a computational tool to simulate bioadhesion. AD was originally designed to simulate the receptor-mediated adhesion of leukocytes to blood vessel walls under hydrodynamic flow. A key element of AD is the calculation of the motion of a cell based on its drag; the motion of the cell results from a force balance and is derived using the mobility matrix. Goldman, Cox and Brenner’s landmark derivation of elements of the mobility matrix for a sphere under Couette flow near a wall (Chem Eng Sci 22:653 (1967)) was central to the assembly of the full mobility matrix for a cell near a wall, which in turn was critical for the implementation of AD. I will explain my original thinking in developing AD and describe the novel insights into bio-adhesion that resulted from these initial simulations, such as how to separate adhesion molecules can act in synergy to facilitate bioadhesion. I will then describe several modifications to AD to understand the interaction of multiple adhesive particles under flow near a wall (multi-particle adhesive dynamics), to understand how biological signaling can affect the adhesion of cells under flow (integrated signaling adhesive dynamics) and the extension of AD to the binding of virus particles to cell surfaces (viral adhesive dynamics). Finally, we describe recent work to understand how spring-like bonds in series can affect the detachment of biological cells, with the surprising finding that apparent catch bonding (where detachment becomes less likely with applied force) can appear when neither bond is intrinsically catch by itself.

Reghan J. **Hill**^{1}

^{1}Department of Chemical Engineering, McGill University, Montreal, Quebec, Canada

Monday 20 May 9:40-10:00 am

Impedance spectroscopy is widely applied for probing the charge and charge-mobility of soft ion-conducting media, such as synthetic membranes and biological tissue. The spectra exhibit a variety of distinctive signatures, but the physical basis of these is not well understood. This work explores a theoretical continuum model by which non-linear thermodynamics and linearized dynamics of a viscous electrolyte and compressible, elastic polyelectrolyte network are coupled under the forcing of an oscillatory electric field. Although the frequency may be very high, the fluid dynamics are of low Reynolds number due to the nano-scaled micro-structure. Here, the model is solved in a one-dimensional spatially periodic unit cell, reporting conductivity and dielectric permittivity spectra, including Nyquist representations. For heterogeneous anionic microstructures, hydrodynamic and elastic forces are demonstrated to produce a strongly diverging low-frequency dielectric permittivity, as first revealed by pioneering experiments conducted in the 1980s on Nafion membranes. For polyelectrolyte films bearing alternating layers of cationic and anionic charge, the model captures several distinctive features of experimentally reported impedance spectra, including those of fuel-cell membranes. In addition to 'electro-poro-elastic' dynamics, the conductivity spectra reflect counterion-release and strong low-frequency electrostatic polarization due to charge heterogeneity. The one-dimensional solutions computed herein provide a foundation more challenging computations in two- and three-dimensions.

Gerald B. **Kasting**^{1} and Johannes M. Nitsche^{2}

^{1}James L. Winkle College of Pharmacy, University of Cincinnati

^{2}Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York

Tuesday 21 May 9:10-9:30 am

Human skin is a composite membrane comprising three distinct layers – stratum corneum (SC), viable epidermis (ED) and dermis (DE). The SC provides the primary diffusion barrier for chemicals entering or exiting the body. It is also a composite membrane comprised of flattened, cornified cells surrounded by a lipid matrix and pierced by skin appendages including hair follicles and sweat ducts. The ED is a cellular tissue that produces the SC, and the DE is a largely collagenous tissue that harbors the blood supply and provides mechanical strength and elasticity.

We developed an effective medium model for the SC composite matrix, a simple approximation for the ED and a distributed clearance model for the DE, then combined these approximations into a one-dimensional trilaminate membrane model (UB/UC) suitable for rapid, spreadsheet-based computation of transient transport (Dancik et al., Adv Drug Deliv Rev, 2013). Since this development many features have been added to UB/UC and adapted by others to multiple platforms. The talk will highlight a few of these features as well as model applications in the pharmaceutical and personal care industries as well as human health and safety.

Aditya **Khair**^{1}

^{1}Department of Chemical Engineering, Carnegie Mellon University

Monday 20 May 10:00-10:20 am

Application of an electric field across the curved interface of two fluids of low but nonzero conductivities, or "leaky dielectrics," gives rise to sustained electrohydrodynamic (EHD) fluid flow. In a uniform dc electric field the electric and velocity fields around an isolated, neutrally buoyant leaky dielectric drop are fore-aft and azimuthally symmetric about the applied field axis. Consequently, the drop remains stationary. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal. Here, in two dimensions drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, drops form stratified chains, or combine into a single dynamic sheet.

Sangtae **Kim**^{1}

^{1}Charles D. Davidson School of Chemical Engineering, Purdue University

Monday 20 May 3:40-4:00 pm

The ellipsoid (along with its degenerate forms) is the workhorse in mathematical models that capture the role of nonspherical particle shapes in all branches of the natural sciences. For Stokes flow, Brenner’s 1964 paper stands out as the classic for the field. The utility of these models has steered generations of students to master the mathematics of elliptic integrals and related functions. And yet thanks to Howard Brenner, for sixty years we have known that one of the most important microhydrodynamic entities, namely the surface traction of the ellipsoid has a relatively simple form: essentially the same formula as the sphere and no elliptic integrals if expressed in terms of multipole moments (force, torque, stresslet, etc.). The explanation is rooted in the theory of integral operators as applied to single- and double-layer hydrodynamic potentials as discovered by this presenter in 2015. These findings open the door to new velocity representations for ellipsoids in Stokes flow as well as furnishing a useful framework for the exploration of the eigenspace for the general triaxial ellipsoid.

Dmitry I. **Kopelevich**^{1} and Jason E. Butler^{1}

^{1}Department of Chemical Engineering, University of Florida

Monday 20 May 11:30-11:50 am

Simultaneous application of axial electric and flow fields within a microfluidic channel containing polyelectrolyte molecules, such as DNA, can drive transverse migration of polyelectrolytes. This transverse motion has been used to trap and concentrate polyelectrolytes within microfluidic devices and to separate long and flexible polyelectrolytes from other molecules. The transverse migration is caused by electrohydrodynamic interactions between different portions of the polymer molecule, i.e. interactions due to disturbances in the fluid flow caused by motion of charged particles (polymer backbone and counterions), which in turn are induced by an external electric field. The driving force for transverse migration increases monotonically with the magnitude of the electric field and therefore it is expected that polyelectrolyte concentration increases with the field strength. However, both experiments and simulations show the opposite trend for sufficiently strong electric fields.

In this talk, we demonstrate that this apparent paradox is caused by electrohydrodynamic dispersion induced by coupling between thermal fluctuations of a polyelectrolyte molecule and electrohydrodynamic interactions. We present a model for the electrohydrodynamic dispersion which shows that, for electric fields of magnitude commonly used in microfluidic devices, the magnitude of this dispersion-induced diffusivity is comparable with or exceeds diffusivity due to the regular Brownian forces. This model is developed by a combination of a numerical solution and a theoretical analysis of the Langevin and Fokker-Planck equations for dynamics of the polymer backbone. This analysis yields a mean-field model for the polyelectrolyte transport, namely an effective convective-diffusion equation for the center of mass of the polymer, with the internal degrees of freedom of the polymer modeled by effective diffusion and convection terms. Predictions of this model are in quantitative agreement with Brownian dynamics simulations and in qualitative agreement with experiments.

Anthony J.C. **Ladd**^{1}, Piotr Szymczak^{2} and Vitalii Starchenko^{3}

^{1}Department of Chemical Engineering, University of Florida

^{2}Institute of Theoretical Physics, Faculty of Physics, University of Warsaw, Warsaw, Poland

^{3}Chemical Science Division, Oak Ridge National Laboratory

Monday 20 May 2:50-3:10 pm

Extensive laboratory studies of chemical reactions between mineral and aqueous phases have been unable to predict the rates of chemical weathering that are observed in the field. Reaction rates from laboratory measurements are typically several orders of magnitude faster than rates inferred from field measurements.

To try to reconcile these discrepancies, reactive-transport models were developed, combining chemical reactions between minerals and aqueous ions with the flow and transport of reactants and products. These models make extensive use of homogenization theory, which in the context of porous media was pioneered by Howard Brenner in a seminal paper, "Dispersion resulting from flow through spatially periodic porous media", published in 1980.

Our work has used these ideas to try to develop an understanding of mechanisms controlling the stability of dissolution and precipitation fronts in the subsurface. In this talk, I will present a summary of results from analytic analysis, numerical simulations and laboratory experiments.

Work was supported by the U.S. Department of Energy Basic Energy Sciences, DE-FG02-98ER14853 & DE-SC0018676, and by the National Science Center (Poland) 2012/07/E/ST3/01734.

David T. **Leighton**^{1}

^{1}Department of Chemical and Biomolecular Engineering, University of Notre Dame

Monday 20 May 4:20-4:40 pm

The classic paper by Howard Brenner (Chem Eng Sci, 1961) detailing the solution of the zero Re approach of a sphere to a plane has been cited in excess of 2000 times, more than any of his other research publications. Indeed, this work continues to have a significant impact on the field, garnering in excess of 70 citations/year more than 60 years after original publication. There are several key aspects to this work which have caused this lasting impact. First, the resistance of a sphere’s motion relative to a plane is critical to applications as diverse as falling ball rheometry, particle capture and detachment in microfluidic systems, and Brownian diffusion near surfaces. Second, the elegant solution to the exact problem in bispherical coordinates was a precursor to a whole host of similar solutions for low Re flows of spheres and other particles in bounded domains. Finally, the exact solution is useful in application of the Lorentz Reciprocal Theorem to determining the lift on a sphere due to inertia and other effects. To provide perspective on this I will describe its influence on two problems in my early work and two of the many problems published in the past year.

Michael **Loewenberg**^{1} and Rostacia Lewis^{1}

^{1}Department of Chemical and Environmental Engineering, Yale University

Monday 20 May 11:50 am – 12:10 pm

Howard Brenner did ground-breaking research on the dynamics of particles in creeping flows, influencing generations of fluid mechanics research, and paving the way for today’s microfluidic technology. Microfluidic devices offer attractive features such as portability and low cost but micron scale flows have unique characteristics that can frustrate attempts to manipulate suspended particles. Particle focusing and separation in microfluidic flows and devices has been an area of active investigation because of its broad relevance for point-of-care testing in biomedical and environmental applications that involve counting, sorting, and detecting or trapping particles or cells. An important example is microfluidic flow cytometry which requires a single-file stream of particles or cells to allow individual optical interrogation. In this talk, I present a numerical analysis of inertia- and size-based focusing and sorting mechanisms for particles encountering an orifice plate within a microfluidic channel. Focusing depends on the ratio of particle size to aperture size and a parameter that characterizes particle inertia. Pressure-driven and electroosmotic flows are considered. A boundary-integral formulation is used in the analysis exploiting a Green's function that incorporates the no-slip boundary conditions on a perforated boundary thus, discretization for numerical solution is required only on the spherical particle surface. Particle inertia leads to exponential alignment through a sequence of orifice plates, and a critical value of the inertia parameter is determined for optimal focusing. Neutrally buoyant particles can also be aligned by contact interactions between particles and aperture edges. These mechanisms can be used to sort particles by size or density.

Charles **Maldarelli**^{1}

^{1}Levich Institute, City College of New York

Monday 20 May 4:40-5:00 pm

Autonomous, chemically powered, synthetic locomotors are engineered colloids (100 nm–10 μm in size) designed to react with fuel in a solution in which the colloids are immersed and convert the chemical reaction energy into self-propulsion. They are designed to move within small scale landscapes in a wide range of potential applications including hovering around a fixed object or pushing cargo. The aim of this study is to understand theoretically how the purely hydrodynamic interaction of the locomotor with an object can allow the locomotor to either hover around or move an object. We adopt an engine model consisting of a spherical Janus colloid (radius *a*) coated with a symmetrical catalyst cap (Θ_{cap}) which converts fuel into product. The product is repelled from the colloid through a repulsive interaction, creating a slip velocity proportional to the gradient of product concentration along the surface. This slip propels the particle in a direction opposite to the accumulation of product, i.e. with the cap at the back end of the motion, in typically inertialess flows. The object is modelled as a sphere of radius *λa*, and we define the orientation of the cap relative to the object through the orientation angle Ψ, measured between the line connecting the centers of the object and locomotor and the line between the locomotor and center of the cap.

For axisymmetric motion, with the locomotor approaching a fixed object of size *λ* with the engine cap at the back end, the particle intersects the object when cap angles are smaller than a critical value (Θ_{cap} < Θ_{cap,cr}), or hovers in front of the object when Θ_{cap} > Θ_{cap,cr}. Hovering is caused by an accumulation of product in the gap between the object and the locomotor. Θ_{cap} increases as *λ * decreases and for fixed (Θ_{cap}, *λ*) is stable to perturbations in separation. For nonaxisymmetric motion of the locomotor towards a fixed particle (again with the cap at the back end), a basin of attraction exists for small orientation angles from axisymmetry in which the locomotor rotates and comes to a hovering position to one side of the object. For larger angles, the locomotor scatters away from the object.

When the object is a moveable cargo, and the locomotor axisymmetrically approaches the cargo (with the cap at the back end), the cargo is pushed by direct contact when the cap angle is smaller than the critical value defined for hovering (Θ_{cap}). For larger cap values, the locomotor and cargo can move in-tandem with a finite separation difference (contactless towing). These hydrodynamic results provide guidelines for the design of locomotors that can hover over fixed particles or transport cargo in contact and noncontact mode without building in steering or braking mechanisms.

Ali **Nadim**^{1}, William Ceely^{1}, Marina Chugunova^{1} and James Sterling^{2}

^{1}Institute of Mathematical Sciences, Claremont Graduate University

^{2}Henry E. Riggs School of Applied Life Sciences, Keck Graduate Institute

Tuesday 21 May 10:40-11:00 am

Polyelectrolyte brushes consist of a set of charged linear macromolecules each tethered at one end to a surface. An example is the glycocalyx which refers to hair-like negatively charged sugar molecules that coat the outside membrane of all cells. We consider the transport and equilibrium distribution of ions, and the resulting electrical potential, when such a brush is immersed in a salt buffer containing monovalent cations (sodium and/or potassium). By including the distinct binding affinities of these counter-ions with the brush, and their so-called Born radii, which account for Born forces acting on them when the dielectric parameter is non-uniform, we propose modified Poisson-Boltzmann and Poisson-Nernst-Planck continuum models that show the distinct profiles that may result depending on those ion-specific properties.

Vivek **Narsimhan**^{1}, Cheng-Wei Tai^{1}, Shiyan Wang^{1} and Tanvi Apte^{1}

^{1}Davidson School of Chemical Engineering, Purdue University

Tuesday 21 May 2:40-3:00 pm

When particles are in a pressure-driven flow of a non-Newtonian fluid, the particles can acquire lift forces due to the imbalance of normal stresses on the particle surface. This phenomenon has been well-studied for spherical particles, but the role of particle shape is still in its early stages. In this work, we develop a theory to describe the rigid body motion of a non-spherical particle in a polymeric fluid. The theory is based on a retarded expansion in the Deborah number (i.e., second-order fluid model), for the case when the particle is in a quadratic (i.e., pressure-driven) flow. We find that for particles in a circular tube flow, spherical particles move to the center of the tube faster than prolate and oblate particles of the same volume, due to the unique orientation dynamics of the spheroids in the polymeric fluid. We also find that prolate particles move slower than oblate particles of the same aspect ratio. These trends are verified by performing microfluidic experiments where we visualize polystyrene particles of various shapes moving through circular capillaries in a Boger fluid with weak viscoelasticity (*De* = *O*(10^{–2})) and vanishing inertia (*Re* = *O*(10^{–4})).

In the last part of the talk, we will discuss preliminary results for how non-spherical particles alter the effective stress in a viscoelastic fluid (i.e., shear viscosity, extensional viscosity, normal stress differences). We will compute the averaged stress in a dilute suspension of spheroids, akin to Einstein viscosity, but in viscoelastic medium. We will also discuss some reduced-order theories (based on multiple time scale analysis) we developed to characterize the orientation dynamics of spheroids in viscoelastic fluids.

Johannes M. **Nitsche**^{1} and Zixuan Ye^{2}

^{1}Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York

^{2}Department of Mathematics, University at Buffalo, The State University of New York

Monday 20 May 3:10-3:30 pm

This talk addresses the determination of the effective conductivity (or diffusivity) of a composite material. A new twist on this classic problem, which dates back to Maxwell and Rayleigh, arises in cases where the microscopic conductivity (or diffusivity) varies with temperature (or solute concentration). Such a complication arises, e.g., in drug or chemical diffusion through the stratum corneum (SC, barrier) layer of skin, and other biological tissues, where thermodynamic nonideality of non-dilute aqueous solutions produces concentration-dependent diffusion coefficients. A regular perturbative approach based on matching microscopic and macroscopic steady state concentration profiles leads to an explicit asymptotic expansion for the effective conductivity (or diffusivity) for arbitrary microstructures in the one-dimensional case. The analysis and results are presented within the context of Howard Brenner's seminal contributions to effective medium theory ("macrotransport"), and the relation to his moment-matching approach is described. Broader aspects of Brenner's scientific legacy are also discussed.

Ronald J. **Phillips**^{1} and Stephanie R. Dungan^{1,2}

^{1}Department of Chemical Engineering, University of California Davis

^{2}Department of Food Science and Technology, University of California Davis

Monday 20 May 10:20-10:40 pm

In aqueous solutions, nonionic surfactants and hydrophobic solutes interact strongly, such that quantitative prediction of fluxes is impossible without all four components of the 2×2 diffusivity matrix [D]. In this work, those components were measured for aqueous mixtures of nonionic, spherical micelles and very hydrophobic, or insoluble, solutes. The measurements were performed by using the Taylor dispersion method, for systems ranging from dilute to highly concentrated micelle concentrations, over a wide range of surfactant molar ratios. The micelles comprised decaethylene glycol monododecyl ether (C_{12}E_{10}) surfactants, and the solutes were either decane or limonene. With either solute, the diffusivity matrix was highly non-diagonal and concentration-dependent. The radius and aggregation numbers of the micelles were measured by static and dynamic light scattering, and depend weakly on micelle volume fraction, but increase linearly with solute-to-surfactant molar ratio. The experimental diffusion data were described quantitatively, with no adjustable parameters, by using Batchelor’s theory for gradient diffusion of polydisperse hard-sphere suspensions. Even though the theory is based on two-sphere hydrodynamic interactions, and hence is limited to dilute solutions, the theory is in surprisingly good agreement with the data even up to micelle volume fractions up to 47%.

Joel **Plawsky**^{2}, Jose Luchsinger^{1}, Ronald Hedden^{2}, Alex Rishty^{2}, Corey Woodcock^{2}, Shanbin Shi^{3} and Alex Guo^{4}

^{1}Games and Simulation Arts and Sciences Program, Rensselaer Polytechnic Institute

^{2}Department of Chemical and Biological Engineering, Rensselaer Polytechnic Institute

^{3}Department of Nuclear Engineering, Rensselaer Polytechnic Institute

^{4}Department of Chemical and Biological Engineering, University of Wisconsin Madison

Tuesday 21 May 3:50-4:10 pm

Although engineers can control the internal geometry of materials down to the micro- and nano-scale, it is unclear what configuration is ideal for a given transport process. We explore the use of mazes as abstract, representations of natural or engineered systems. Mazes can be easily generated using many different algorithms, then represented as graphs. One can compute from a graph: its * effective tortuous resistance*, which is the resistance to flow; its *average tortuosity*, which is the normalized, average path length; and its *minimum-cut-size*, which is the resilience to flow-path obstruction. These three, dimensionless graph parameters can be related to a maze’s effective transport property (e.g., permeability), average residence time, and robustness, respectively. The effects of maze generation bias, the imposed flow direction, and algorithm randomness on the graph parameters were studied. A composite maze was created and shown to mimic the geometry and permeability of a real commercial membrane. Recently, we have focused on more exotic maze tilings to further understand the effects of randomness and degree of connectedness.

We are using the fun and games aspect of mazes to weave together simulation, gaming, virtual reality, and 3-D printing in an undergraduate lab sequence. The simulation is efficient enough to be run on the home computer, allowing students to iterate on the design of their experiment before bringing it into the lab. Students can look into particle capture, particle separation, or the architecture of a thermal interface material, develop a structure to implement, and print and test its performance.

Fig. 1: Simulation of the flow of a fluid/particle mixture through a maze-like structure that preferentially traps rod-like (red) particles.

Robert **Powell**^{1}

^{1}Departments of Chemical Engineering and Food Science & Technology, University of California Davis

Tuesday 21 May 2:00-2:20 pm

The last test of a nuclear weapon conducted by the United States was on September 23, 1992. Today the safety, security, reliability and effectiveness of the nation’s nuclear weapons are assured through a rigorous procedure called science-based stockpile stewardship. This involves rigorous testing of parts of weapons and, when needed, their replacement. This talk will discuss how this process proceeds, areas where chemical engineers have contributed and possible opportunities in the future.

Carlos M. **Rinaldi-Ramos **^{1}

^{1}Department of Chemical Engineering and J. Crayton Pruitt Family Department of Biomedical Engineering, University of Florida

Monday 20 May 9:20-9:40 am

Magnetic nanoparticles respond to time varying magnetic fields via a combination of internal dipole and whole-particle rotation, depending on factors such as thermal motion, hydrodynamic drag, magnetic torques, and internal barriers to dipole rotation. Depending on the amplitude and frequency of the alternating magnetic field, the nanoparticle’s response can give rise to conversion of magnetic field energy into heat or to a signal which can be used to monitor nanoparticle rotational diffusion or quantify nanoparticle distribution in a subject. This multitude of magnetic responses, coupled with their biocompatibility, makes iron oxide nanoparticles of great interest in sensing, biomedical imaging, drug delivery, and thermal therapy. In this talk I will provide an overview of the theory of magnetic nanoparticle response to time varying magnetic fields, which I began to study as Howard Brenner’s doctoral student, and my group’s work advancing several of these applications, including monitoring nanoparticle mobility in complex and biological fluids, cancer thermal therapy, rewarming of cryopreserved organs, and non-invasive, unambiguous, and quantitative tracking of nanoparticles and cells using magnetic particle imaging.

David **Saintillan**^{1}

^{1}Department of Mechanical and Aerospace Engineering, University of California San Diego

Tuesday 21 May 3:30-3:50 pm

The transport of self-propelled particles such as bacteria or phoretic swimmers through porous materials is relevant to many natural and engineering processes, from biofilm formation and contamination processes to transport in soils and biomedical devices. In this talk, I discuss two distinct approaches aimed at predicting the long-time dispersion of self-propelled particles in idealized porous media. In a first approach, Howard Brenner’s generalized Taylor dispersion theory is applied to analyze the long-time statistics of an active Brownian particle transported under an applied flow through the interstices of a periodic lattice. The model is used to unravel the roles of motility, fluid flow, and lattice geometry on the asymptotic mean velocity and dispersion coefficient. Unexpected trends are predicted, including a nonmonotonic dependence of axial dispersion on flow strength and a reduction in dispersion due to swimming activity in strong flows. In a second approach, the case of random media is considered using a statistical framework, and the long-time dispersion coefficient of a run-and-tumble particle swimming though a random distribution of circular obstacles is calculated analytically.

Eric S.G. **Shaqfeh**^{1}

^{1}Department of Chemical Engineering, Stanford University

Tuesday 21 May 2:20-2:40 pm

As a young researcher, Howard Brenner’s papers taught me that Taylor Dispersion was generalizeable to a whole host of physical situations. In each of these examples, particle diffusion sampled a "microscopic" region that coupled to a convective flow such that a "macroscopic" or Generalized Taylor Dispersion phenomena occurred. Throughout my career, I was able to recognize and calculate these coefficients primarily because of the insight that reading Howard's papers as a postdoctoral student provided. Most recently, my group has examined particle drift across streamlines in viscoelastic pressure-driven flow that results from a normal stress imbalance across the particle. We calculate these drift velocities using large scale computational simulation and they are present whether the particle is freely suspended or whether the particle experiences other external body forces. This phenomenon has been now well documented in the experimental literature and can be controlled (e.g. exacerbated) in a variety of ways including applying a body force on the particles either against or along the flow. In this talk, I will discuss how the now famous work of both Shapiro & Brenner [1,2] and Frankel & Brenner [3], led to our calculation of the Taylor dispersion of particles in the presence of these drift velocities. The Taylor dispersion coefficient thus provides a sensitive measure of viscoelastic particle drift, with the drift velocity generally decreasing Taylor dispersion via a simple, calculable power law [4].

[1] M. Shapiro and H. Brenner. Taylor dispersion of chemically reactive species: irreversible first-order reactions in bulk and on boundaries. *Chem. Eng. Sci.* **41**, 1417-1433 (1986).

[2] M. Shapiro and H. Brenner. Chemically reactive generalized Taylor dispersion phenomena. *AIChE Journal* **33**, 1155-1167 (1987).

[3] I. Frankel and H. Brenner. On the foundations of generalized Taylor dispersion theory. *J. Fluid Mech.* **204**, 97-119 (1989).

[4] T. Lin and E.S.G. Shaqfeh. Taylor dispersion in the presence of cross flow and interfacial mass transfer. *Phys. Rev. Fluids* **4**, 034501 (2019).

Chenxian Xu^{1}, Yiran Zhang^{1}, Subinur Ilshat Kemal^{1} and Vivek **Sharma**^{1}

^{1}Department of Chemical Engineering, University of Illinois at Chicago

Monday 20 May 10:40-11:00 am

Iridescent colors that arise from interference in freshly-formed soap films or foam films are replaced by grays of increasing darkness as drainage drives film towards ultrathin thickness (h < 100 nm). Micellar foam films undergo drainage via stratification associated with stepwise thinning and coexistence of thick-thin regions. Darker gray, thinner domains grow at the cost of thicker surroundings, and their expansion speeds up after spots lighter gray and thicker than the surrounding flat regions, appear at the moving front. Using Interferometry Digital Imaging Optical Microscopy (IDIOM) protocols we developed recently, we visualize these spots as mesas (lateral length scale in μm, thickness in nm) that appear after a nanoridge formed at the moving front around expanding domain undergoes a topographical instability. In this contribution, we show that the shape evolution of nanoscopic mesas is self-similar, and the thickness and the radial width of mesa grow over time with exponents of 1/5 and 2/5, respectively. In a scaled variable representation, the mesa shapes collapse onto one universal shape for all concentrations despite the differences in dimensional values of elapsed times, lateral size, and thicknesses.

Kevin **Silmore**^{1}

^{1}Anduril Industries, Boston, MA

Tuesday 21 May 3:00-3:20 pm

What are the rheological properties of a dilute suspension of (not necessarily axisymmetric) ellipsoidal particles? While Jeffery first worked out the fluid mechanics of ellipsoidal particles in Stokes flow over a century ago and certain works have studied the statistical distributions of ellipsoidal particles in Stokes flow (e.g., those by Leal, Hinch, Scheraga, Kuhn, Kuhn, and Saito among others), questions about the rheological behavior of general ellipsoidal particles still remain unanswered, in large part due to computational challenges and the fact that non-axisymmetric ellipsoidal particles exhibit quasi-periodic motion. In this work, a manifold-constrained finite volume algorithm is developed to evaluate efficiently the ensemble-averaged stresslet contributions of ellipsoidal particles interacting with a background flow field and subject to thermal fluctuations. Non-Newtonian rheological properties are quantified, and the shapes of maximally viscosifying ellipsoids under geometrical constraints will be discussed (with some unexpected results).

Howard A. **Stone**^{1}

^{1}Department of Mechanical and Aerospace Engineering, Princeton University

Monday 20 May 4:00-4:20 pm

We describe two low-Reynolds-number flow problems that utilize methods made popular by Howard Brenner. In particular, we illustrate the motion of a sphere translating approximately parallel to a soft substrate and calculate the drift speed normal to the substrate using the reciprocal theorem. Also, we study the motion of particles near patterned boundaries and show that three dimensional helical trajectories are possible. If there is time, as a last example, I discuss an evaporation problem involving *N* droplets, and show how a
19th-century approach, which would likely have made Howard Brenner happy, appears to be more effective than
modern (mostly numerical) studies of the problem.

Tsung-Lin Hsieh^{1}, Stephen Garoff^{2} and Robert D. **Tilton**^{1}

^{1}Department of Chemical Engineering, Carnegie Mellon University

^{2}Department of Physics, Carnegie Mellon University

Tuesday 21 May 11:20-11:40 am

Synergistic component interactions underlie the macroscopic properties of many complex fluids and may be put to use when formulating such fluids for commercial applications. If a mixture of surfactants produces a greater surface tension reduction than either of the individual surfactants at the same concentration as the total surfactant concentration in the mixture, then that system exhibits surface tension synergism. This presentation considers the possibility of solutal Marangoni transport synergism, wherein the rate of Marangoni transport induced by a surfactant mixture at some total concentration exceeds the rate induced by either individual surfactant at the same concentration. Here, Marangoni transport is initiated by localized deposition of a surfactant solution at the air/water interface, and the migration of surface tracer particles is used to track its progress. Whereas surface tension synergism is a strictly thermodynamic phenomenon, "Marangoni synergism" requires a favorable combination of thermodynamic and dynamic phenomena. A combination of experimentation and numerical transport modeling reveals that surface tension synergism is a necessary but insufficient condition for Marangoni synergism to occur. The intrinsic adsorption and desorption kinetics determine whether surface tension synergism will lead to Marangoni synergism.

Salvatore **Torquato**^{1}

^{1}Department of Chemistry, Department of Physics, Princeton Materials Institute
and Program in Applied & Computational Mathematics, Princeton University

Monday 20 May 2:30-2:50 pm

A variety of performance demands are being placed on material systems, including desirable mechanical, thermal, electrical, optical, acoustic and flow properties. I will review the emerging field of disordered hyperuniform heterogeneous media and their novel multifunctional characteristics. Disordered hyperuniform media are exotic amorphous states of matter that are characterized by an anomalous suppression of large-scale volume-fraction fluctuations compared to those in "garden-variety" disordered materials. Such unusual media can have advantages over their periodic counterparts, such as unique or nearly optimal, direction-independent physical properties and robustness against defects. It will be shown that disordered hyperuniform composites and porous media can be endowed with a broad spectrum of extraordinary physical properties, including photonic, phononic, transport, chemical and mechanical characteristics that are only beginning to be discovered.

Ehud **Yariv**^{1} and Michael Siegel^{2}

^{1}Department of Mathematics, Technion — Israel Institute of Technology

^{2}Department of Mathematical Sciences, New Jersey Institute of Technology

Tuesday 21 May 11:40 am — 12:00 pm

Motivated by recent experiments, we address the motion of a superhydrophobic particle through an otherwise quiescent liquid. In these problems the superhydrophobic effect is naturally quantified by the enhancement of the Stokes mobility. We focus upon what may be the simplest problem in that class, namely the rotation of an infinite circular cylinder whose boundary is periodically decorated by a finite number of infinite grooves, with the goal of calculating the rotational mobility. The associated two-dimensional flow problem is defined by two geometric parameters, namely the number *N* of grooves and the solid fraction. Using matched asymptotic expansions we analyze the large-*N* limit (and arbitrary solid fraction), obtaining an approximation for the hydrodynamic mobility. Comparison with Fourier-series solutions suggests that the approximation is in fact exact. Making use of conformal mapping techniques we show that the preceding approximation indeed holds for all *N*.

Alexander **Zinchenko**^{1}

^{1}Department of Chemical and Biological Engineering, University of Colorado Boulder

Tuesday 21 May 4:50-5:10 pm

Steady-state sedimentation of a Newtonian, non-wetting deformable drop on an inclined
wall in another liquid at zero Reynolds number is numerically simulated in a broad
range of parameters (tilt *θ*, Bond number, and drop-to-medium viscosity
ratio *λ*), with particular emphasis on the most challenging combinations of small
tilt with high *λ*, when the drop surface glides extremely close to the solid wall
on a lubricating film; the drop shape varies broadly from almost spherical to pancaked
with a large near-contact spot. The first 3D boundary-integral (BI) studies [1,2] of
this problem based on half-space Green function were severely limited to
generic values of *θ* and *λ* = *O*(1);
at small tilts and *λ* ≫ 1, divergence
of BI iterations on the way to steady state could not be overcome with standard drop-surface
resolutions. A novel, multipole-accelerated BI algorithm employing the system of
mesh nodes and their mirror images in the lower half-space is presented, together
with a novel and universal high-order near-singularity subtraction in the
double-layer BI, for successful long-time simulations with *O*(3 × 10^{5}) boundary
elements. The steady-state drop speed, geometry of the dimpled lubrication space and different modes of drop motion (sliding, tank-treading, rolling with slip) are studied in
detail for *θ* down to 7.5 deg. and *λ* up to 300. Qualitative comparisons
with the asymptotic theory [3] and limitations on the analytical studies are also discussed.

[1] A.J. Griggs, A.Z. Zinchenko and R.H. Davis. Gravity-driven motion of a deformable drop or bubble near an inclined plane at low Reynolds number. *Int. J. Multiphase Flow* **34**, 408-418 (2008).

[2] A.J. Griggs, A.Z. Zinchenko and R.H. Davis. Creeping motion and pending breakup of drops and bubbles near an inclined wall. *Phys. Fluids* **21**, 093303 (2009)

[3] S.R. Hodges, O.E. Jensen and J.M. Rallison. Sliding, slipping, and
rolling: the sedimentation of a viscous drop down a gently inclined plane.
*J. Fluid Mech.* **512**, 95-131 (2004).