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We analyze the interaction between a self-diffusiophoretic spherical Janus motor and an inert spherical cargo particle in an axisymmetric configuration in the Stokes regime. To study the different configurations of the two spheres and their motions, we develop an analog to the twin multipole approach to numerically determine the axisymmetric stream function for the flow field. We verify the validity and accuracy of this approach using existing literature and COMSOL Multiphysics. We study the effects of the size of the Janus cap, the relative ratio of sizes of the two spheres, and their separation distance on their interactions. For the case of a stationary cargo, we identify the existence of a distinct regime where the Janus motor hovers at a finite separation distance from the cargo and summarize the results using a phase diagram. In the presence of a freely moving cargo, we analyze the steady terminal velocities of the Janus motor and the cargo to identify distinct conditions at which the two spheres can translate with equal velocities while maintaining a finite separation distance.

Peptide surfactants (PEPS) are studied to capture and retain rare earth elements (REEs) at air-water interfaces to enable REE separations. Peptide sequences, designed to selectively bind REEs, depend crucially on the position of ligands within their binding loop domain. These ligands form a coordination sphere that wraps and retains the cation. We study variants of lanthanide binding tags (LBTs) designed to complex strongly with Tb$^{3+}$. The peptide LBT$^{5-}$ (with net charge -5) is known to bind Tb$^{3+}$ and adsorb with more REE cations than peptide molecules, suggesting that undesired non-specific Coulombic interactions occur. Rheological characterization of interfaces of LBT$^{5-}$ and Tb$^{3+}$ solutions reveal the formation of an interfacial gel. To probe whether this gelation reflects chelation among intact adsorbed LBT$^{5-}$:Tb$^{3+}$ complexes or destruction of the binding loop, we study a variant, LBT$^{3-}$, designed to form net neutral LBT$^{3-}$:Tb$^{3+}$ complexes. Solutions of LBT$^{3-}$ and Tb$^{3+}$ form purely viscous layers in the presence of excess Tb$^{3+}$, indicating that each peptide binds a single REE in an intact coordination sphere. We introduce the variant RR-LBT$^{3-}$ with net charge -3 and anionic ligands outside of the coordination sphere. We find that such exposed ligands promote interfacial gelation. Thus, a nuanced requirement for interfacial selectivity of PEPS is proposed: that anionic ligands outside of the coordination sphere must be avoided to prevent the non-selective recruitment of REE cations. This view is supported by simulation, including interfacial molecular dynamics simulations, and interfacial metadynamics simulations of the free energy landscape of the binding loop conformational space.

Hypothesis: The collective dynamics and self-assembly of colloids floating at a fluid/fluid interface is a balance between deterministic lateral interaction forces, viscous resistance to colloid motion along the surface and thermal (Brownian) fluctuations. As the colloid size decreases, thermal forces become important and can affect the self assembly into ordered patterns and crystal structures that are the starting point for various materials applications. Numerics: Langevin dynamic simulations involving two particles straddling a liquid/liquid interface with a high viscosity contrast are presented to describe the lateral interfacial assembly of particles in Brownian and non-Brownian dominated regimes. These simulations incorporate capillary attraction, electrostatic repulsion, thermal fluctuations and HI between particles (including the effect of the particle immersion depth). Simulation results are presented for neutrally wetted particles which form a contact angle of 90 degrees at the interface. Findings: Clustering, fractal growth and particle ordering are observed at critically large values of the Pe numbers, while smaller Pe numbers exhibit higher probabilities of yielding states in which particles remain uncorrelated in space and more widely separated.

Quasi-2D experiments of a submerged sediment layer creeping downward were performed, varying the channel tilt and a porous flow under the respective thresholds for yielding. Logarithmic decay rates of the deformation are observed, with the rate increasing with both control parameters. A new dimensionless parameter, $P^*$, accounting for both mean porous flow and gravity force effects on particle motion, allows a collapse of all the deformation results on a single curve. Two distinct creep regimes are identified, and correspond to a systematic change of the void size distribution as $P^*$ increases.

Predicting rapid and slower soil evolution remains a scientific challenge. This process involves poorly understood aspects of disordered granular matter and dense suspension dynamics. This study presents a novel two-dimensional experiment on a small-scale chip structure; this allows the observation of the deformation at the particle scale of a large-grained sediment bed, under conditions where friction dominate over cohesive and thermal forces, and with an imposed fluid flow. Experiments are performed at conditions which span the particle resuspension criterion, and particle motion is detected and analyzed. The void size population and statistics of particle trajectories bring insight to the sediment dynamics near fluidization conditions. Specifically, particle rearrangement and net bed compaction are observed at flow rates significantly below the criterion for instability growth. Above a threshold, a large vertical channel through the bed forms. In the range of flow rates where channelization can occur, the coexistence of compacting and dilating bed scenarios is observed. The results of the study enhance our capacity for modeling of both slow dynamics and eventual rapid destabilization of sediment beds. Microfluidics channel soil-on-a-chip studies open avenues to new investigations including dissolution-precipitation, fine particles transport, or micro-organisms swimming and population growth, which may depend on mechanics of the porous media itself.

We study the effects of heterogeneity on interfacial pinning and hydrodynamic drag using molecular dynamics (MD) simulations of Janus nanospheres at a liquid/vapor interface. We construct the free energy landscape for this system, both in the continuum approximation using surfaces tensions and the flat-interface approximation and atomistically using MD and thermodynamic integration. The results of the two methods differ in detail due to interfacial distortion and finite width, as well as thermal fluctuations, and only the MD landscape is consistent with simulations of a nanosphere approaching the interface from the liquid or vapor side. When dragged along an interface, these Janus particles exhibit a velocity-dependent tilt accompanied by a weak variation in drag force, but never an enhancement of the drag force beyond the value when fully immersed. This velocity dependence arises when the interface is pinned at heterogeneities and prevents the particle from rotating, and similar behavior is observed for homogeneous but non-spherical particles. The occurrence of different particle orientations having different drag coefficients may lead to an apparent violation of the Stokes-Einstein relation.

Miniaturized, self-propelled locomotors use chemo-mechanical transduction mechanisms to convert fuel in the environment to autonomous motion. Recent experimental and theoretical studies demonstrate that these autonomous engines can passively follow the contours of solid boundaries they encounter. Boundary guidance, however, is not necessarily stable: Mechanical disturbances can cause the motor to hydrodynamically depart from the passively guided pathway. Furthermore, given the scaled-down size of micromotors (typically 100 nm -10 $\mu$m), Brownian thermal fluctuation forces are necessarily important and these stochastic forces can randomize passively-steered trajectories. Here we examine theoretically the stability of boundary guided motion of micromotors along infinite planar walls to mechanical disturbances and to Brownian forces. Our aim is to understand under what conditions this passively guided motion is stable. We choose a locomotor design in which spherical colloids are partially coated with a catalytic cap that reacts with solute to produce a product. The product is repelled from the particle surface, causing the particle to move with the inert face at the front (autonomous motion via self-diffusiophoresis). When propelled towards a planar wall, deterministic hydrodynamic studies demonstrate that these locomotors can exhibit, for large enough cap sizes, steady trajectories in which the particle either skims unidirectionally along the surface at a constant distance from the wall, or becomes stationary. We first investigate the linear hydrodynamic stability of these states by expanding the equations of motion about the states, and find that linear perturbations decay exponentially in time. We then study the effects of thermal fluctuations by formulating a Langevin equation for the particle motion which includes the Brownian stochastic force..., Comment: Changed title

Measurements of the surface diffusivity of colloidal spheres translating along a vapor/liquid inter- face show an unexpected decrease in diffusivity, or increase in surface drag (from the Stokes-Einstein relation) when the particles situate further into the vapor phase. However, direct measurements of the surface drag from the colloid velocity due to an external force find the expected decrease with deeper immersion into the vapor. The paradoxical drag increase observed in diffusion experiments has been attributed to the attachment of the fluid interface to heterogeneities on the colloid surface, which causes the interface, in response to thermal fluctuations, to either jump or remain pinned, creating added drag. We have performed molecular dynamics simulations of the diffusivity and force experiments for a nanoparticle with a rough surface at a vapor/liquid interface to examine the effect of contact line fluctuations. The drag calculated from both experiments agree and decrease as the particle positions further into the vapor. The surface drag is smaller than the bulk liquid drag due to the partial submersion into the liquid, and the finite thickness of the interfacial zone relative to the nanoparticle size. Contact line fluctuations do not give rise to an anomalous increase in drag.

We study the diffusiophoretic self-propulsion of a colloidal catalytic particle due to a surface chemical reaction in a vicinity of a solid wall. Diffusiophoresis is a chemico-mechanical transduction mechanism in which a concentration gradient of an interacting solute produces an unbalanced force on a colloidal particle and drives it along the gradient. We consider a spherical particle with an axisymmetric reacting cap covering the polar angle range $0\le \theta\le \theta_{cap}$ in the presence of a repulsive solute, near an infinite planar wall, and solve the coupled solute concentration and Stokes equations, using a mixture of numerical and analytic arguments. The resulting particle trajectory is determined by $\theta_{cap}$ and the initial orientation of the symmetry axis with respect to the plane. At normal incidence the particle initially moves away from or towards the wall, depending on whether the cap faces towards or away, respectively, but even in the latter case the particle never reaches the wall due to hydrodynamic lubrication resistance. For other initial orientations, when $\theta_{cap}\le 115^{\circ}$ the particle either moves away immediately or else rotates along its trajectory so as to cause the active side to face the wall and the particle to rebound. For higher coverage we find trajectories where the particle skims along the wall at constant separation or else comes to rest. We provide a phase diagram giving the nature of the trajectory (repulsion, rebound, skimming or stationary) as a function of $\theta_{cap}$ and the initial orientation.

Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow that propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillary to direct the movement of bubbles in space is the fact that surfactant impurities, which are unavoidably present in the continuous phase, can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. (This can also be the case if kinetic desorption of surfactant at the back end of the bubble is much slower than convection.) For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like and bubbles translate as solid particles). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature-induced tension gradient, and can decrease to near zero the bubble's thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have be retarded by the adsorption onto the bubble surface of a surfactant impurity. Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble surface much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition, the rapid kinetic exchange and high bulk concentration maintain a saturated surface with uniform surface concentrations. This prevents retarding surface tension gradients and keeps the thermocapillary velocity high. In our reports over the first 2 years, we presented numerical simulations of the bubble motion and surfactant transport which verified theoretically the concept of remobilization, and the development of an apparatus to track and measure the velocity of rising bubbles in a glycerol/water surfactant solution. This year, we detail experimental observations of remobilization. Two polyethylene oxide surfactants were studied, C12E6 (CH3(CH2)11(OCH2)6OH) and C10E8 (CH3(CH2)4(OCH2CH2)8OH). Measurements of the kinetic exchange for these surfactants show that the one with the longer hydrophobe chain C12E6 has a lower rate of kinetic exchange. In addition, this surfactant is much less soluble in the glycerol/water mixture because of the shorter ethoxylate chain. As a result, we found that C12E6 had only a very limited ability to remobilize rising bubbles because of the limited kinetic exchange and reduced solubility. However, C10E8, with its higher solubility and more rapid exchange was found to dramatically remobilize rising bubbles. We also compared our theoretical calculations to the experimental measurements of velocity for both the non-remobilizing and remobilizing surfactants and found excellent agreement. We further observed that for C10E8 at high concentrations, which exceeded the critical micelle concentrations, additional remobilization was measured. In this case the rapid exchange of monomer between micelle and surfactant provides an additional mechanism for maintaining a uniform surface concentrations.

Microgravity technologies often require aqueous phases to spread over nonwetting hydrophobic solid/surfaces. At a hydrophobic surface, the air/hydrophobic solid tension is low, and the solid/aqueous tension is high. A large contact angle forms as the aqueous/air tension acts together with the solid/air tension to balance the large solid/aqueous tension. The aqueous phase, instead of spreading, is held in a meniscus by the large angle. Surfactants facilitate the wetting of water on hydrophobic surfaces by adsorbing on the water/air and hydrophobic solid/water interfaces and lowering the surface tensions of these interfaces. The tension reductions decrease the contact angle, which increases the equilibrium wetted area. Hydrocarbon surfactants (i.e. amphiphiles with a hydrophobic chain of methylene groups attached to a large polar group to give aqueous solubility) do not reduce significantly the contact angles of the very hydrophobic surfaces such as parafilm or polyethylene. Trisiloxane surfactants (amphiphiles with a hydrophobe consisting of methyl groups linked to a trisiloxane backbone in the form of a disk ((CH3)3-Si-O-Si-O-Si(CH3)3)) and an extended ethoxylate (-(OCH2CH2)n-) polar group in the form of a chain with seven or eight units) can significantly reduce the contact angle of water on a very hydrophobic surface and cause rapid and complete (or nearly complete) spreading (lermed superspreading). The overall goal of the research described in this proposal is to establish and verify a theory for how trisiloxanes cause superspreading, and then use this knowledge as a guide to developing more general hydrocarbon based surfactant systems which superspread and can be used in microgravity. We propose that the trisiloxane surfactants superspread when the siloxane adsorbs, the hydrophobic disk parts of the molecule adsorb onto the surface removing the surface water. Since the cross sectional area of the disk is larger than that of the extended ethoxylate chain, the disks can form a space filling mat on the surface which removes a significant amount of the surface water. The water adjacent to the hydrophobic solid surface is of high energy due to incomplete hydrogen bonding; its removal significantly lowers the tension and reduces the contact angle. Hydrocarbon surfactants cannot remove as much surface water because their large polar groups prevent the chains from cohering lengthwise. In our report last year we presented a poster describing the preparation of model very hydrophobic surfaces which are homogeneous and atomically smooth using self assembled monolayers of octadecyl trichlorosilane (OTS). In this poster we will use these surfaces as test substrates in developing hydrocarbon based surfactant systems which superspread. We studied a binary hydrocarbon surfactant systems consisting of a very soluble large polar group polyethylene oxide surfactant (C12E6 (CH3(CH2)11(OCH2CH2)6OH) and a long chain alcohol dodecanol. By mixing the alcohol with this soluble surfactant we have found that the contact angle of the mixed system on our test hydrophobic surfaces is very low. We hypothesize that the alcohol fills in the gaps between adjacent adsorbed chains of the large polar group surfactant. This filling in removes the surface water and effects the decrease in contact angle. We confirm this hypothesis by demonstrating that at the air/water interface the mixed layer forms condensed phases while the soluble large polar group surfactant by itself does not. We present drop impact experiments which demonstrate that the dodecanol/C12E6 mixture is effective in causing impacting drops to spread on the very hydrophobic model OTS surfaces.

Thermocapillary migration is a method for moving bubbles in space in the absence of buoyancy. A temperature gradient is applied to the continuous phase in which a bubble is situated, and the applied gradient impressed on the bubble surface causes one pole of the drop to be cooler than the opposite pole. As the surface tension is a decreasing function of temperature, the cooler pole pulls at the warmer pole, creating a flow which propels the bubble in the direction of the warmer fluid. A major impediment to the practical use of thermocapillarity to direct the movement of bubbles in space is the fact that surfactant impurities which are unavoidably present in the continuous phase can significantly reduce the migration velocity. A surfactant impurity adsorbed onto the bubble interface is swept to the trailing end of the bubble. When bulk concentrations are low (which is the case with an impurity), diffusion of surfactant to the front end is slow relative to convection, and surfactant collects at the back end of the bubble. Collection at the back lowers the surface tension relative to the front end setting up a reverse tension gradient. For buoyancy driven bubble motions in the absence of a thermocapillarity, the tension gradient opposes the surface flow, and reduces the surface and terminal velocities (the interface becomes more solid-like). When thermocapillary forces are present, the reverse tension gradient set up by the surfactant accumulation reduces the temperature tension gradient, and decreases to near zero the thermocapillary velocity. The objective of our research is to develop a method for enhancing the thermocapillary migration of bubbles which have been retarded by the adsorption onto the bubble surface of a surfactant impurity, Our remobilization theory proposes to use surfactant molecules which kinetically rapidly exchange between the bulk and the surface and are at high bulk concentrations. Because the remobilizing surfactant is present at much higher concentrations than the impurity, it adsorbs to the bubble much faster than the impurity when the bubble is formed, and thereby prevents the impurity from adsorbing onto the surface. In addition the rapid kinetic exchange and high bulk concentration maintain a saturated surface with a uniform surface concentrations. This prevents retarding surface tension gradients and keeps the velocity high. In our first report last year, we detailed experimental results which verified the theory of remobilization in ground based experiments in which the steady velocity of rising bubbles was measured in a continuous phase consisting of a glycerol/water mixture containing a polyethylene glycol surfactant C12E6 (CH3(CH2)11(OCH2CH2)6OH). In our report this year, we detail our efforts to describe theoretically the remobilization observed. We construct a model in which a bubble rises steadily by buoyancy in a continuous (Newtonian) viscous fluid containing surfactant with a uniform far field bulk concentration. We account for the effects of inertia as well as viscosity in the flow in the continuous phase caused by the bubble motion (order one Reynolds number), and we assume that the bubble shape remains spherical (viscous and inertial forces are smaller than capillary forces, i e. small Weber and capillary numbers). The surfactant distribution is calculated by solving the mass transfer equations including convection and diffusion in the bulk, and finite kinetic exchange the bulk and the surface. Convective effects dominate diffusive mass transfer in the bulk of the liquid (high Peclet numbers) except in a thin boundary layer near the surface. A finite volume method is used to numerically solve the hydrodynamic and mass transfer equations on a staggered grid which accounts specifically for the thin boundary layer. We present the results of the nondimensional drag as a function of the bulk concentration of surfactant for different rates of kinetic exchange, from which we develop criteria for the concentration necessary to develop a prescribed degree of remobilization. The criteria compare favorably with the experimental results.

When a fluid interface with surfactants is at rest, the interfacial stress is isotropic (as given by the equilibrium interfacial tension), and is described by the equation of state which relates the surface tension to the surfactant surface concentration. When surfactants are subjected to shear and dilatational flows, flow induced interaction of the surfactants; can create interfacial stresses apart from the equilibrium surface tension. The simplest relationship between surface strain rate and surface stress is the Boussinesq-Scriven constitutive equation completely characterized by three coefficients: equilibrium interfacial tension, surface shear viscosity, and surface dilatational viscosity Equilibrium interfacial tension and surface shear viscosity measurements are very well established. On the other hand, surface dilatational viscosity measurements are difficult because a flow which change the surface area also changes the surfactant surface concentration creating changes in the equilibrium interfacial tension that must be also taken into account. Surface dilatational viscosity measurements of existing techniques differ by five orders of magnitude and use spatially damped surface waves and rapidly expanding bubbles. In this presentation we introduce a new technique for measuring the surface dilatational viscosity by contracting an aqueous pendant drop attached to a needle tip and having and insoluble surfactant monolayer at the air-water interface. The isotropic total tension on the surface consists of the equilibrium surface tension and the tension due to the dilation. Compression rates are undertaken slow enough so that bulk hydrodynamic stresses are small compared to the surface tension force. Under these conditions we show that the total tension is uniform along the surface and that the Young-Laplace equation governs the drop shape with the equilibrium surface tension replaced by the constant surface isotropic stress. We illustrate this technique using DPPC as the insoluble surfacant monolayer and measured for it a surface dilatational viscosity in the LE phase that is 20 surface poise.