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We quantify the macrotransport of chemotactic and diffusiophoretic colloids, demonstrating how hydrodynamic flows could tune the colloid spreading.

The gravitational settling of oil droplets solubilizing in an aqueous micellar solution contained in a capillary channel is investigated. The motion of these active droplets reflects a competition between gravitational and Marangoni forces, the latter due to interfacial tension gradients generated by differences in filled- micelle concentrations along the oil-water interface. This competition is studied by varying the surfactant concentration, the density difference between the droplet and the continuous phase, and the viscosity of the continuous phase. The Marangoni force enhances the settling speed of an active droplet when compared to the Hadamard-Rybczynski prediction for a (surfactant free) droplet settling in Stokes flow. The Marangoni force can also induce lateral droplet motion, suggesting that the Marangoni and gravitational forces are not always aligned. The decorrelation rate (𝛼) of the droplet motion, measured as the initial slope of the velocity autocorrelation and indicative of the extent to which the Marangoni and gravitational forces are aligned during settling, is examined as a function of the droplet size: correlated motion (small values of 𝛼) is observed at both small and large droplet radii, whereas significant decorrelation can occur between these limits. This behavior of active droplets settling in a capillary channel is in marked contrast to that observed in a dish, where the decorrelation rate increases with the droplet radius before saturating at large values of droplet radius. A simple relation for the crossover radius at which the maximal value of 𝛼 occurs for an active settling droplet is proposed.

A theoretical framework is presented to describe the electrochemical response of ionic conductors for use as strain and temperature sensors. This framework can be used to design sensors for in bioelectronics and soft robotics applications.

Chemically active, or autophoretic, particles that isotropically emit or absorb solute molecules undergo spontaneous self-propulsion when their activity is increased beyond a critical P\'{e}clet number ($Pe$). Here, we conduct numerical computations, using a spectral-element based method, of a rigid, spherical autophoretic particle in unsteady rectilinear translation. The particle can be freely suspended (or `unforced') or subject to an external force field (or `forced'). The motion of an unforced particle progresses through four regimes as $Pe$ is increased: quiescent, steady, stirring, and chaos. The particle is stationary in the quiescent regime, and the solute profile is isotropic about the particle. At $Pe=4$ the fore-aft symmetry in the solute profile is broken, resulting in its steady self-propulsion. Our computations indicate that the self-propulsion speed scales linearly with $Pe-4$ near the onset of self-propulsion, as has been predicted in previous studies. A further increase in $Pe$ gives rise to the stirring regime at $Pe\approx27$, where the fluid undergoes recirculation, while the particle remains essentially stationary. As $Pe$ is increased even further, the particle dynamics are marked by chaotic oscillations at $Pe\approx55$ and higher, which we characterize in terms of the mean square displacement and velocity autocorrelation of the particle. Our results for an autophoretic particle under a weak external force are in good agreement with recent asymptotic predictions (Saha, Yariv, and Schnitzer, J. Fluid Mech., vol. 916, A47, 2021). Additionally, we demonstrate that the strength and temporal scheduling of the external force may be tuned to modulate the chaotic dynamics at large $Pe$., Comment: 21 pages, 13 figures

Understanding the chemo-mechanical mechanisms that direct the motion of self-propulsive colloids is important for the development of active materials and exploration of dynamic, collective phenomena. Here, we demonstrate that the adsorption of solid particles on the surface of solubilizing oil droplets can significantly enhance the droplets' self-propulsion speeds. We investigate the relationship between the self-propulsion of bromodecane oil droplets containing silica particles of varying concentration in Triton X-100 surfactant, noting up to order of magnitude increases in propulsion speeds. Using fluorescently labeled silica, we observe packing of the particles at the oil-water interfaces of the rear pole of the moving droplets. For bromodecane oil droplets in Triton X-100, the highest droplet speeds were achieved at approximately 40% particle surface coverage of the droplet interface. We find particle-assisted propulsion enhancement in ionic surfactants and different oil droplet compositions as well, demonstrating the breadth of this effect. While a precise mechanism for the propulsion enhancement remains unclear, the simple addition of silica particles to droplet oil-water interfaces provides a straightforward route to tune active droplet dynamics.

A field trial was conducted at Sakha Experimental Research Station, Kafr El-Sheikh Governorate, Egypt during the two successive winter seasons of 2018/2019 and 2019/2020 to calibrate and validate the AquaCrop model (Version 5). Two cultivars of canola (Serw4 and Serw6) were sown to study the influence of two irrigation regimes (50 and 70% of soil moisture depletion SMD). Then, AquaCrop model was calibrated using the dataset of 1st season and validated using the 2nd season dataset by different statistical indicators i.e. coefficient of determination (R2) and degree of agreement (d). Also, the simulation of climate change impact on canola yields was done. Results show that mostly, irrigation at 50% depletion from soil moisture gives higher values of seed and biomass yields (Mg ha-1) and canola water productivity compared to 70% depletion from soil moisture. This trend is found with both canola cultivars but the Serw4 records values better than Serw6. Also, results show that AquaCrop model (Version 5) is able to simulate well seed and biomass yield of canola cultivars as well as canola water productivity under different irrigation treatments at the studied region, where, values of R2 and d record a robust agreement among predicted and observed values. As for the simulation of climate change influence, the findings indicate that increasing temperature leads to increasing the reduction percentage of seed yield of different canola cultivars, and the reduction percentage with Serw6 was more than Serw4.

This work models the behavior of a liquid-particle suspension on the surface of a tablet during the pharmaceutical film-coating process. The model uses the “mixture modeling” approach and the lubrication approximation method to simulate how the suspension moves and dries on the surface of a tablet, considering how important physical properties of the suspension, such as the density and viscosity, change when the carrier fluid evaporates. The model also accounts for the absorption of the coating suspension inside the core of the porous tablet, yielding the tablet water content, a key quantity characterizing the coating process. The numerical results, obtained with the gPROMS Modelbuilder platform, agree with experimental data taken from the literature and Volume-Of-Fluid CFD simulations.

Hypothesis Electric fields enhance surfactant transport to oil-water interfaces when the surfactant forms charged aggregates in the oil phase. Hence, transport under electric fields could be used to detect charged surfactant aggregates in nonpolar media. Experiments Two surfactants with different architecture were dispersed in Isopar-M. The transport of surfactants to an oil-water interface under a constant electric field was quantified using a custom-built electrified microtensiometer platform. Electrical conductivity of the oil with surfactant concentration was also measured to determine the presence of charge carriers. Findings The charging mechanism of the oil phase, and field-enhanced transport was different for the two surfactants. At low concentrations where the electrical conductivity of the surfactants is indistinguishable, dynamic interfacial tension measurements under electric fields can ascertain the presence of charge carriers in Isopar-M. The transport of ionic surfactants in the aqueous phase was unaffected by the field, confirming that the field-enhanced transport of oil-phase surfactants is due to electrophoresis of charge carriers. Moreover, the equilibrium interfacial tension was not found to change under an electric field, suggesting the adsorption isotherm is independent of the field strength. We demonstrate that dynamic interfacial tension measurements under electric fields is a sensitive technique to detect charge carriers in nonpolar fluids.

The dynamics of a two dimensional autophoretic disk is quantified as a minimal model for the chaotic trajectories undertaken by active droplets. Via direct numerical simulations, we show that the mean-square displacement of the disk in a quiescent fluid is linear at long times. Surprisingly, however, this apparently diffusive behavior is non-Brownian, owing to strong cross-correlations in the displacement tensor. The effect of a shear flow field on the chaotic motion of a 2D autophoretic disk is examined. Here, the stresslet on the disk is chaotic for weak shear flows; a dilute suspension of such disks would exhibit a chaotic shear rheology. This chaotic rheology is quenched first into a periodic state and ultimately a steady state as the flow strength is increased.

An advection-diffusion-reaction model for autologous chemotaxis of two cells in an interstitial flow is analyzed. Each cell secretes ligands uniformly over its surface; the ligands are absorbed by surface receptors anisotropically due to the flow and interaction between ligand fields around each cell. The absorption is quantified in terms of a vectorial anisotropy parameter, $\mathbit{A}$, which is proportional to the first moment of the ligand concentration field about the surface of each cell. We consider the physiologically relevant limit of a weak interstitial flow, where the P\'eclet number, $\text{Pe}$, which characterizes the relative importance of ligand transport via advection to diffusion, is small. We further assume that the cells are separated at a distance that is large compared to the sum of their radii. These conditions allow us to utilize a reciprocal theorem and the method of reflections to construct an asymptotic approximation for $\mathbit{A}$ to first order in $\text{Pe}$ for widely separated cells. We find that interactions between the cells: (i) reduce the flow-aligned ligand anisotropy around each cell and (ii) lead to a component of $\mathbit{A}$ that is perpendicular to the flow direction. The interaction is long ranged, decaying with the inverse distance between cells to leading order. We finally discuss how interactions between multiple cells could affect our findings.

We use perturbation methods to analyze the “asymmetric rectified electric field (AREF)” generated when an oscillating voltage is applied across a model electrochemical cell consisting of a binary, asymmetric electrolyte bounded by planar, parallel, blocking electrodes. The AREF refers to the steady component of the electric potential gradient within the electrolyte, as discovered via numerics by Hashemi Amrei et. al. (Phys Rev Lett 121(18):185504). We adopt the Poisson–Nernst–Planck framework for ion transport in dilute electrolytes, taking into account unequal ionic diffusivities. We consider the mathematically singular, and practically relevant, limit of thin Debye layers, $$1/(\kappa L) = \epsilon \rightarrow 0 $$ , where $$\kappa ^{-1}$$ is the Debye length, and L is the length of the half-cell. The dynamics of the electric potential and ionic strength in the “bulk” electrolyte (i.e., outside the Debye layers) are solved subject to effective boundary conditions obtained from consideration of the Debye-scale transport. We specifically analyze the case when the applied voltage has a frequency comparable to the inverse bulk ion diffusion time scale, $$\omega = {\mathcal {O}}(D_A/L^2)$$ , where $$D_A = 2D_+ D_-/(D_+ + D_-)$$ is the ambipolar diffusivity, and $$D_{\pm }$$ are the ionic diffusivities. In this regime, the AREF extends throughout the bulk of the cell, varying on a lengthscale proportional to $$ \sqrt{D_A /\omega }$$ , and has a magnitude of $${\mathcal {O}}(\epsilon ^2 k_B T /(L e))$$ to leading order in $$\epsilon $$ . Here, $$k_B$$ is the Boltzmann constant, T is temperature, and e is the charge on a proton. We obtain an analytical approximation for the AREF at weak voltages, $$V_0 \ll k_B T/e$$ , where $$V_0$$ is the amplitude of the voltage, for which the AREF is $${\mathcal {O}}(\epsilon ^2 V_0^2 e /(k_B T L))$$ . Our asymptotic scheme is also used to calculate a numerical approximation to the AREF that is valid up to logarithmically large voltages, $$V_0 = {\mathcal {O}}((k_B T/e)\ln (1/\epsilon ))$$ . The existence of an AREF implies that a charged colloidal particle undergoes net electrophoretic motion under the applied oscillatory voltage. Additionally, a gradient in the bulk ionic strength, caused by the difference in ionic diffusivities, leads to rectified diffusiophoretic particle motion. Here, we predict the electrophoretic and diffusiophoretic velocities for a rigid, spherical, colloidal particle. The diffusiophoretic velocity is comparable in magnitude to the electrophoretic velocity, and can thus affect particle motion in an AREF significantly.

We conduct an asymptotic analysis to derive a macrotransport equation for the long-time transport of a chemotactic/diffusiophoretic colloidal species in a uniform circular tube under a steady, laminar, pressure-driven flow and transient solute gradient. The solute gradient drives a ‘log-sensing’ advective flux of the colloidal species, which competes with Taylor dispersion due to the hydrodynamic flow. We demonstrate excellent agreement between the macrotransport equation and direct numerical solution of the full advection–diffusion equation for the colloidal species transport. In addition to its accuracy, the macrotransport equation requires times less computational runtime than direct numerical solution of the advection–diffusion equation. Via scaling arguments, we identify three regimes of the colloidal species macrotransport, which span from chemotactic/diffusiophoretic-dominated macrotransport to the familiar Taylor dispersion regime, where macrotransport is dominated by the hydrodynamic flow. Finally, we discuss generalization of the macrotransport equation to channels of arbitrary (but constant) cross-section and to incorporate more sophisticated models of chemotactic fluxes. The macrotransport framework developed here will broaden the scope of designing chemotactic/diffusiophoretic transport systems by elucidating the interplay of macrotransport due to chemotaxis/diffusiophoresis and hydrodynamic flow.

The motion of a rigid sphere in ambient simple shear flow of a Newtonian fluid between infinite parallel walls is calculated via the lattice Boltzmann method for various particle Reynolds numbers, . However, a sufficiently strong gravitational force will break the bifurcation and produce a single off-centre equilibrium position. We finally consider a neutrally buoyant sphere under the cessation or reversal of shear flow.

ZetaSpin determines zeta potential by measuring the streaming potential generated by rotating a disk-shaped sample about its axis while submerged in the liquid. The apparatus and procedure developed for ZetaSpin in aqueous solutions was adapted for use in highly nonpolar fluids like surfactant-doped alkanes. Perhaps most unexpected is the need for up to 10 min (instead of a fraction of one second for aqueous solutions) for the electrometer to display changes in streaming potential in response to changes in rotation speed. Four tests (suggested by theory) confirm that the potential finally reported by the electrometer was indeed the streaming potential. Compared to electrophoresis, ZetaSpin does not require a value for the Debye length, avoids the complication caused by the electric-field-dependence of electrophoretic mobility and can be used with planar samples as well as colloidal particles.

Induced-charge electro-osmotic (ICEO) flow caused by an alternating electric field applied around an infinitely long, ideally polarizable, uncharged circular cylinder in a binary electrolyte with unequal cation and anion diffusion coefficients is analysed. The thin-Debye-layer and weak-field approximations are invoked to compute the time-averaged, or rectified, quadrupolar ICEO flow around the cylinder. The inequality of ionic diffusion coefficients leads to transient ion concentration gradients, or concentration polarization, in the electroneutral bulk electrolyte outside the Debye layer. Consequently, the electric potential in the bulk is non-harmonic. Further, the concentration polarization alters the electro-osmotic slip at the surface of the cylinder and generates body forces in the bulk, both of which affect the rectified ICEO flow. Predictions for the strength of the rectified flow for varying ratio of ionic diffusion coefficients are in reasonable agreement with available experimental data. Our work highlights that an inequality in ionic diffusion coefficients – which all electrolytes possess to some extent – is an important factor in modelling ICEO flows.

The interaction of surrounding drops is modeled as a temporally fluctuating electric field around a test drop. Because of the field-squared dependence, the drop deformation is larger under a fluctuating electric field than under a steady field. Consequently, drop breakup is observed at mean capillary numbers smaller than the critical capillary number for breakup under a steady field. Moreover, fluctuations drive drop breakup faster than a steady field.

An integral expression for the translational velocity of a perfectly slipping spherical particle under a time-dependent applied force in unsteady Stokes flow is derived. For example, when the ratio of particle density to fluid density is small, our analysis pertains to an inviscid bubble in a viscous fluid. We determine an explicit form of the particle velocity under an impulsive force, wherefrom the velocity autocorrelation function and mean-squared displacement of a perfectly slipping sphere undergoing Brownian motion are obtained. The above results are contrasted against the time-dependent diffusion of a rigid sphere with no hydrodynamic slip. Finally, the thermal force power spectral density is analytically calculated for a diffusing sphere with arbitrary slip length. We suggest this quantity to be suitable to infer slip length from the measurement of nondiffusive Brownian motion.

We study the pairwise interactions of drops in an applied uniform DC electric field within the framework of the leaky dielectric model. We develop three-dimensional numerical simulations using the boundary integral method and an analytical theory assuming small drop deformations. We apply the simulations and the theory to explore the electrohydrodynamic interactions between two identical drops with arbitrary orientation of the their line of centers relative to the applied field direction. Our results show complex dynamics depending on the conductivities and permittivities of the drops and suspending fluids, and the initial drop pair alignment with the applied electric field.

The authors examine the inertial lift on a neutrally-buoyant circular cylinder in confined shear flow. Through two-dimensional lattice Boltzmann simulations, it is shown that the transverse equilibrium position of the cylinder will undergo a pitchfork bifurcation above a critical Reynolds number, with the stable equilibrium position shifting away from the centerline of the channel. The study demonstrates that this critical Reynolds number is dependent on the ratio of particle size to channel width, and occurs below the transition to unsteady flow.

The nonlinear viscoelasticity of a dilute suspension of Brownian spheroids subject to an oscillatory shear deformation is calculated numerically. This is achieved by determining the suspension microstructure, parameterized via the orientation distribution function. Specifically, the long-time periodic orientation distribution function is obtained via a numerical solution to the Fokker–Planck equation by combining a finite-difference approximation in space with a Fourier series in time. From an ensemble average of the particle stresslet, weighted by the orientation distribution function, the entire stress tensor and relevant birefringence parameters, namely, the average orientation angle and linear dichroism, are calculated; this is done over a range of the Weissenberg number ( W i) and the Deborah number ( D e), or dimensionless strain-rate amplitude and oscillation frequency, respectively. Detailed calculations are presented for prolate spheroids of aspect ratio r = 20; however, our methodology is general and can be applied to spheroids of arbitrary aspect ratio. We provide results in four viscoelastic regimes: linear viscoelastic ( W i ≪ 1), quasilinear viscoelastic ( W i > 1 and W i / D e ≪ 1), quasisteady viscoelastic ( D e → 0), and finally, the nonlinear viscoelastic regime ( W i ≳ 1 and W i / D e ≳ 1), which is our main emphasis. In this last regime, where the nonlinear and unsteady viscoelasticity of the material is probed, multiple overshoots are observed in the shear stress and first normal stress difference. The mechanistic origin of these overshoots can be understood from the periodic orientation dynamics (i.e., Jeffery orbits) of a particle under steady shear in the absence of Brownian rotation ( W i → ∞). This is achieved by simultaneously analyzing the microstructure, shear stress, first normal stress difference, and birefringence parameters specifically at W i = 20 and D e = 1. For these values of W i , D e, and r, the period of a Jeffery orbit is comparable to the period of an oscillation cycle, allowing sufficient time for a single Jeffery orbit (and subsequent overshoot) to occur during an oscillation cycle. We contrast this behavior to recent work by Khair [J. Fluid. Mech. 791, R5 (2016)] on nearly spherical particles, for which many more overshoots are observed during an oscillation cycle, due to the shorter period of the Jeffery orbit. We briefly provide results for oblate spheroids of aspect ratio r = 0.05 and compare to the results for r = 20. Finally, we comment on the relevance of the present micro-mechanical analysis to the nonlinear viscoelasticity of other complex fluid materials.

Slender-body theory is utilized to derive an asymptotic approximation to the hydrodynamic drag on an axisymmetric particle that is held fixed in an otherwise uniform stream of an incompressible Newtonian fluid at moderate Reynolds number. The Reynolds number, $Re$ , is based on the length of the particle. The axis of rotational symmetry of the particle is collinear with the uniform stream. The drag is expressed as a series in powers of $1/\text{ln}(1/\unicode[STIX]{x1D716})$ , where $\unicode[STIX]{x1D716}$ is the small ratio of the characteristic width to length of the particle; the series is asymptotic for $Re\ll O(1/\unicode[STIX]{x1D716})$ . The drag is calculated through terms of $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ , thereby extending the work of Khayat & Cox (J. Fluid Mech., vol. 209, 1989, pp. 435–462) who determined the drag through $O[1/\text{ln}^{2}(1/\unicode[STIX]{x1D716})]$ . The calculation of the $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ term is accomplished via the generalized reciprocal theorem (Lovalenti & Brady, J. Fluid Mech., vol. 256, 1993, pp. 561–605). The first dependence of the inertial contribution to the drag on the cross-sectional profile of the particle is at $O[1/\text{ln}^{3}(1/\unicode[STIX]{x1D716})]$ . Notably, the drag is insensitive to the direction of travel at this order. The asymptotic results are compared to a numerical solution of the Navier–Stokes equations for the case of a prolate spheroid. Good agreement between the two is observed at moderately small values of $\unicode[STIX]{x1D716}$ , which is surprising given the logarithmic error associated with the asymptotic expansion.

Asymptotic approximations are derived for the hydrodynamic force on a rigid, axisymmetric slender particle executing longitudinal or transverse oscillation in unsteady Stokes flow. The slender particle has an aspect ratio , where is the half-length of the particle, and is its characteristic cross-sectional width. It is assumed that the particle has zero thickness at its ends. The frequency of oscillation is parameterized by the complex quantity , where is the kinematic viscosity, is the particle angular oscillation frequency (units of radians per second) and . Asymptotic approximations for the force are obtained in three distinguished limits for longitudinal oscillations: (i) a ‘low-frequency’ regime with and fixed; (ii) a ‘moderate-frequency’ regime with and ; and (iii) a ‘high-frequency’ regime with and . The acceleration reaction is a leading-order contributor to the force in this last regime, whereas it is subdominant at moderate frequency. For transverse oscillation we construct asymptotic approximations in the low and moderate-frequency regimes. Here, the acceleration reaction here plays a leading-order role at moderate frequency; hence, a ‘high frequency’ regime in this case simply corresponds to the limiting behaviour for . Our asymptotic predictions are in good agreement with the numerically computed frequency-dependent force on a prolate spheroid ( ) for longitudinal and transverse oscillations by Lawrence and Weinbaum (J. Fluid Mech., vol. 189, 1988, pp. 463–489) and Pozrikidis (Phys. Fluids, vol. 1, 1989a, pp. 1508–1520), respectively.

The effective viscosity of a dilute emulsion of spherical drops containing a soluble surfactant is calculated under a linear creeping flow. It is assumed that convection of surfactant is small relative to diffusion, and thus the Peclet number, Pe, is small. We calculate the effective viscosity of the emulsion to $\mathcal {O}(Pe\phi \mu )$ , where ϕ is the small volume fraction of the dispersed drops and μ is the viscosity of the surfactant-free suspending fluid. This $\mathcal {O}(Pe\phi \mu )$ contribution is a sensitive function of the bulk and interfacial surfactant transport. Specifically, soluble surfactant molecules diffuse from the bulk to the interface and then adsorb to the interface. The ratio of the time scale for bulk diffusion to the time scale for adsorption to the interface is quantified by a Damkohler number, Da. The adsorption of surfactant to the interface may cause a significant decrease in the bulk concentration, which is known as depletion. The impact of depletion is characterized by two parameters: h, which is a dimensionless depletion depth; and k, which is the ratio of the desorption time scale to the adsorption time scale. We analytically determine how the $\mathcal {O}(Pe\phi \mu )$ contribution to the effective viscosity depends on h, k, and Da. Surprisingly, for certain regimes in the h − k − Da parameter space, we predict the effective viscosity of the emulsion to be greater than Einstein’s result for the viscosity of a suspension of rigid spheres. Large Marangoni stresses driven by convective transport of soluble surfactant molecules are responsible for this result.

This theoretical analysis quantifies the effect of coupled ionic fluxes on the charging dynamics of an electrochemical cell. We consider a model cell consisting of a concentrated, binary electrolyte between parallel, blocking electrodes, under a suddenly applied DC voltage. It is assumed that the magnitude of the applied voltage is small compared to the thermal voltage scale, RT/F, where R is the universal gas constant, T is the temperature and F is the Faraday's constant. We employ the Stefan–Maxwell equations to describe the hydrodynamic coupling of ionic fluxes that arise in concentrated electrolytes. These equations inherently account for asymmetry in the mobilities of the ions in the electrolyte. A modified set of Poisson–Nernst–Planck equations, obtained by incorporating Stefan–Maxwell fluxes into the species balances, are formulated and solved in the limit of weak applied voltages. A long-time asymptotic analysis reveals that the electrolyte dynamics occur on two distinct time scales. The first is a faster “RC” time, τRC = κ−1L/E, where κ−1 is the Debye length, L is the length of the half-cell, and E is an effective diffusivity, which characterizes the evolution of charge density at the electrode. The effective diffusivity, E, is a function of the ambi-polar diffusivity of the salt, a, as well as a cross-diffusivity, +−, of the ions. This time scale also dictates the initial exponential decay of current in the external circuit. At times longer than τRC, the external current again decays exponentially on a slower, diffusive time scale, τD ∼ L2/a, where a is the ambi-polar diffusivity of the salt. This diffusive time scale is due to the unequal ion mobilities that result in a non-uniform bulk concentration of the salt during the charging process. Finally, we propose an approach by which our theory may be used to measure the cross-diffusivity in concentrated electrolytes.

We utilize slender body theory along with a reciprocal theorem to predict the convective enhancement in heat and mass transfer from an axisymmetric particle in a Stokes flow that approaches a uniform stream at large distances. The particle can be oriented at an arbitrary angle to the flow. The Peclet number, Pe , based on the particle length is considered to be O ( 1 ) , in which case the effect of convection is not small on this scale. Specifically, we calculate the ratio Nu ( Pe ) / Nu ( 0 ) through O ( 1 / ln ( 1 / ∊ ) ) , where Nu is the Nusselt number (i.e., the normalized heat flux from the particle) and ∊ is the (small) ratio of the characteristic thickness to length of the particle. At fixed Pe , the maximum value of Nu occurs for a body whose axis of symmetry is perpendicular to the imposed flow; the minimum value occurs when the axis of symmetry is aligned with the flow.

This paper quantifies the effects of different operating conditions on the stability of the crystallization interface in the horizontal ribbon growth (HRG) process. Specifically, we perform a linear stability analysis of the base state, and we derive the profiles for thermal, solutal and flow fields with regard to small-amplitude normal mode perturbations of the base state. Within the velocity boundary layer induced by the removal of solid ribbon, a linear Couette flow is assumed; at the outer edge of the boundary layer, all perturbations are assumed to dissipate. Critical operating conditions and the unstable modes have been identified. To that end, we demonstrate that fast pulling velocity (greater than 100 mm/min), low wedge factors (the ratio of the length to the thickness of the wafer is less than 500), and insufficient heat removal (temperature gradient G l is less than 200 K/cm) lead to instabilities. A finite bandwidth of wavenumber for instability occurs for all the unstable modes.

The deformation of a weakly conducting, ‘leaky dielectric’, drop in a density matched, immiscible weakly conducting medium under a uniform direct current (DC) electric field is quantified computationally. We exclusively consider prolate drops, for which the drop elongates in the direction of the applied field. Furthermore, for the majority of this study, we assume the drop and medium to have equal viscosities. Using axisymmetric boundary integral computations, we delineate drop deformation and breakup regimes in the $Ca_{E}-Re_{E}$ parameter space, where $Ca_{E}$ is the electric capillary number (ratio of the electric to capillary stresses); and $Re_{E}$ is the electric Reynolds number (ratio of charge relaxation to flow time scales), which characterizes the strength of surface charge convection along the interface. For so-called ‘prolate A’ drops, where the surface charge is convected towards the ‘poles’ of the drop, we demonstrate that increasing $Re_{E}$ reduces the critical capillary number for breakup. Moreover, surface charge convection is the cause of an abrupt transition in the breakup mode of a drop from end pinching, where the drop elongates and develops bulbs at its ends that eventually detach, to a breakup mode characterized by the formation of conical ends. On the contrary, the deformation of ‘prolate B’ drops, where the surface charge is convected away from the poles, is essentially unaffected by the magnitude of $Re_{E}$.

The deformation of the electric double layer around a charged colloidal particle during sedimentation or electrophoresis in a binary, symmetric electrolyte is studied. The surface potential of the particle is assumed to be small compared to the thermal voltage scale. Additionally, the Debye length is assumed to be large compared to the particle size. These assumptions enable a linearization of the electrokinetic equations. The particle appears as a point charge in this thick-double-layer limit; the distribution of charge in the diffuse cloud surrounding it is determined by a balance of advection due to the particle motion, Brownian diffusion of ions, and electrostatic screening of the particle by the cloud. The ability of advection to deform the charge cloud from its equilibrium state is parametrized by a Péclet number, Pe. For weak advection (Pe ≪ 1), the cloud is only slightly deformed. In contrast, the cloud can be completely stripped from the particle at Pe ≫ 1; consequently, electrokinetic effects on the particle motion vanish in this regime. Therefore, in sedimentation the drag limits to Stokes' law for an uncharged particle as Pe → ∞. Likewise, the particle velocity for electrophoresis approaches Huckel's result. The strongly deformed cloud at large Pe is predicted to generate a concomitant increase in the sedimentation field in a dilute settling suspension.

The linear viscoelasticity of a dilute suspension of active (self-propelled) rigid spheroidal particles is calculated under a small-amplitude oscillatory shear (SAOS) deformation. The imposed shear acts to drive the microstructure of the suspension, as parameterized by the orientational probability distribution function, out of equilibrium. The microstructure relaxes via two independent mechanisms: rotational Brownian motion and correlated tumbling; the combination of which results in an increased rate of stress relaxation, relative to a suspension that relaxes solely by either mechanism. We explicitly calculate the non-equilibrium orientational microstructure due to the SAOS deformation, rotational diffusion, and tumbling. From this, we determine the linear viscoelasticity of the suspension from the orientationally averaged stresslet, which arises from the imposed flow, rotational diffusion, and particle activity (self-propulsion). Next, we demonstrate that a modified Cox-Merz rule is applicable to a dilute, active suspension via a comparison of our linear viscoelasticity results to a theoretical prediction of the steady shear viscosity of active, slender rods (Saintillan, Exp Mech 50(9) 1275–1281, 2010). Finally, through a comparison of our results to experiments on Escherichia coli (Lopez et al., Phys Rev Lett 115(2) 028, 301, 2015), we show that the linear viscoelasticity of an active suspension can be utilized to determine the mechanism of self-propulsion (i.e., pusher or puller), and estimate the strength of self-propulsion and correlation between tumbling events.

A framework for determining the first nonlinear relaxation modulus of a viscoelastic fluid from a medium-amplitude oscillatory shear (MAOS) deformation is constructed. Knowledge of this “MAOS relaxation modulus” allows one to predict the weakly nonlinear stress response of a material under an arbitrary transient deformation via a memory integral expansion. Our framework is demonstrated by explicitly determining the MAOS relaxation modulus for a dilute suspension of Brownian spheroids subject to a dual-frequency oscillatory shear flow. Specifically, we first calculate the second normal stress difference for such a deformation from a corotational memory integral expansion. Second, the microstructural stress response of the model system of Brownian spheroids is determined via a regular perturbation expansion of the orientation distribution function at small dimensionless strain-rate amplitude, or Weissenberg number. An analytical expression for the MAOS relaxation modulus is resolved by comparing the second normal stress difference results of the memory integral expansion and microstructural stress calculation. Finally, using the MAOS relaxation modulus, we reconstruct the stress response of the model system for the start-up and cessation of simple shear and uniaxial extension. In summary, our work offers an approach to utilizing medium (and large) amplitude oscillatory shear results to predict stress dynamics of viscoelastic fluids in other transient, nonlinear flows.

We analytically calculate the one-dimensional advective-diffusive spreading of a point source of diffusiophoretic (DP) colloids, driven by the simultaneous diffusion of a Gaussian solute patch. The spreading of the DP colloids depends critically on the ratio of the DP mobility, M (which can be positive or negative), to the solute diffusivity, Ds. For instance, we demonstrate, for the first time, that solute-repelling colloids (M < 0) undergo long-time super-diffusive transport for M/Ds < −1. In contrast, the spreading of strongly solute-attracting colloids (M/Ds ≫ 1) can be spatially arrested over long periods on the solute diffusion timescale, due to a balance between colloid diffusion and DP under the evolving solute gradient. Further, a patch of the translating solute acts as a “shuttle” that rapidly transports the colloids relative to their diffusive timescale. Finally, we use numerical computations to show that the above behaviors persist for three-dimensional, radially symmetric DP spreading. The results presented here could guide the use of DP colloids for microscale particle sorting, deposition, and delivery.

The transport dynamics of oil-soluble surfactants to oil-water interfaces are quantified using a custom-built electrified capillary microtensiometer platform. Dynamic interfacial tension measurements reveal that surfactant transport is enhanced under a dc electric field, due to electro-migration of charge carriers in the oil toward the interface. Notably, this enhancement can be precisely tuned by altering the field strength and temporal scheduling. We demonstrate electric fields as a new parameter to manipulate surfactant transport to microscale fluid-fluid interfaces.

The impedance of dodecane doped with sorbitan trioleate (Span 85), sorbitan monooleate (Span 80) and sorbitan monolaurate (Span 20) was measured as a function of frequency using a 10 mV amplitude sinusoidal voltage applied across a parallel plate cell with a 10 μm spacing. The tested solutions varied in concentration from 1 mM to 100 mM and the frequency range was 10(-2)-10(4) Hz. Nyquist plots of all three surfactants showed the high frequency semicircle characteristic of parallel resistance and capacitance but often exhibited a second semicircle at low frequencies which was attributed to charge adsorption and desorption. The electrical conductivity of each surfactant was proportional to surfactant concentration for concentrations above 10mM. Fitting the data to models for charge migration, differential capacitance, and adsorption allowed extraction of both charge concentration and two kinetic parameters that characterize the rate of adsorption and desorption. Above 10 mM the ratio of charge carriers per surfactant molecule was 22 ppm for Span 20, 3 ppm for Span 80, and 0.2 ppm for Span 85. A higher number of charge carriers per molecule of surfactant was associated with larger micelles. The adsorption rate constants were independent of surfactant concentration while the desorption rate constants were proportional to the surfactant concentration. This dependence indicated that uncharged surfactant, whether in micelles or not, participated in the desorption of charge. Predictions of the adsorption/desorption model for large constant electric fields agreed qualitatively with data from the literature (Karvar et al., 2014).

An asymptotic solution to the Giesekus constitutive model of polymeric fluids under homogenous, oscillatory simple shear flow at large Weissenberg number, Wi≫1, and large strain amplitude, Wi/De≫1, is constructed. Here, Wi=λ*γ0*, where λ* is the polymer relaxation time and γ0* is the shear rate amplitude, and De=λ*ω* is a Deborah number, where ω* is the oscillation frequency. Under these conditions, we show that the first normal stress difference is the dominant rheological signal, scaling as G*Wi1/2, where G* is the elastic modulus. The shear stress and second normal stress difference are of order G*. The polymer stress exhibits pronounced nonlinear oscillations, which are partitioned into two temporal regions: (i) A “core region,” on the time scale of λ*, reflecting a balance between anisotropic drag and orientation of polymers in the strong flow; and (ii) a “turning region,” centered around times when the shear flow reverses, whose duration is on the hybrid time scale (λ*)2/3/(γ0*)1/3, in which flow...