Phoretic Effects Research Articles

Clustering induces switching between phoretic and osmotic propulsion in active colloidal rafts

Active particles driven by chemical reactions are the subject of intense research to date due to their rich physics, being intrinsically far from equilibrium, and their multiple technological applications. Recent attention in this field is now shifting towards exploring the fascinating dynamics of active and passive mixtures. Here we realize active colloidal rafts, composed of a single catalytic particle encircled by several shells of passive microspheres, and assembled via light-activated chemophoresis. We show that the cluster propulsion mechanism transits from diffusiophoretic to diffusioosmotic as the number of colloidal shells increases. Using the Lorentz reciprocal theorem, we demonstrate that in large clusters self-propulsion emerges by considering the hydrodynamic flow via the diffusioosmotic response of the substrate. The dynamics in our active colloidal rafts are governed by the interplay between phoretic and osmotic effects. Thus, our work highlights their importance in understanding the rich physics of active catalytic systems.

Network Effects Lead to Self-Organization in Metabolic Cycles of Self-Repelling Catalysts.

Mixtures of particles that interact through phoretic effects are known to aggregate if they belong to species that exhibit attractive self-interactions. We study self-organization in a model metabolic cycle composed of three species of catalytically active particles that are chemotactic toward the chemicals that define their connectivity network. We find that the self-organization can be controlled by the network properties, as exemplified by a case where a collapse instability is achieved by design for self-repelling species. Our findings highlight a possibility for controlling the intricate functions of metabolic networks by taking advantage of the physics of phoretic active matter.

Self-Regulatory Micro- and Macroscale Patterning of ATP-Mediated Nanobioconjugate.

Directional interactions and the assembly of a nanobioconjugate in clusters at a specific location are important for patterning and microarrays in biomedical research. Herein, we report that self-assembly and spatial control in surface patterning of the surfactant-functionalized nanoparticles can be governed in micro- and macroscale environments by two factors, synergistic enzyme-substrate-nanoparticle affinity and the phoretic effect. First, we show that aggregation of cationic gold nanoparticles (GNP) can be modulated by multivalent anionic nanoparticle binding of an adenosine-based nucleotide and enzyme, alkaline phosphatase. We further demonstrate two different types of their autonomous aggregation pattern: (i) by introducing an enzyme gradient that modulates the synergistic nonequilibrium interactivity of the nanoparticle, nucleotide, and enzyme both in microfluidic conditions and at the macroscale; and (ii) the surface deposition pattern from evaporating droplets via the coffee ring effect. Here, temporal control over the width and site of the patterning area inside the microfluidic channel under catalytic and noncatalytic conditions has also been demonstrated. Finally, we show a change in capillary phoresis parameters responsible for the coffee ring due to introduction of ATP-loaded GNP in the blood serum, showing applicability in low-cost disease diagnostics. Overall, an enzyme-actuated surface nanobiopatterning method has been demonstrated that has potential application in controlled micro- and macroscale area patterning with a diverse cascade catalytic surface and spatiotemporal multisensory-based application.

Active thermophoresis and diffusiophoresis

Thermophoresis and diffusiophoresis respectively refer to the directed drift of suspended particles in solutions with external thermal and chemical gradients, which have been widely used in the manipulation of mesoscopic particles. We here study a phoretic-like motion of a passive colloidal particle immersed in inhomogeneous active baths, where the thermal and chemical gradients are replaced separately by activity and concentration gradients of the active particles. By performing simulations, we show that the passive colloidal particle experiences phoretic-like forces that originate from its interactions with the inhomogeneous active fluid, and thus drifts along the gradient field, leading to an accumulation. The results are similar to the traditional phoretic effects occurring in passive colloidal suspensions, implying that the concepts of thermophoresis and diffusiophoresis could be generalized into active baths.

Self-phoretic Brownian dynamics simulations

A realistic and effective model to simulate phoretic Brownian dynamics swimmers based on the general form of the thermophoretic force is here presented. The collective behavior of self-phoretic dimers is investigated with this model and compared with two simpler versions, allowing the understanding of the subtle interplay of steric interactions, propulsion, and phoretic effects. The phoretic Brownian dynamics method has control parameters which can be tuned to closely map the properties of experiments or simulations with explicit solvent, in particular those performed with multiparticle collision dynamics. The combination of the phoretic Brownian method and multiparticle collision dynamics is a powerful tool to precisely identify the importance of hydrodynamic interactions in systems of self-phoretic swimmers.Graphic

Contribution of Phoretic and Electrostatic Effects to the Collection Efficiency of Submicron Aerosol Particles by Raindrops

This article presents an experimental study, performed in the BERGAME setup, dedicated to studying the collection of submicron aerosol particles by raindrops. The initial aim was to focus on the influence of the electrical charges of raindrops on the efficiency with which they collect aerosol particles. However, in the relative humidity range considered in this article (26–36%), measurements highlight a first-order role of phoretic effect for submicron aerosol particles. Indeed, measurements highlight a 100% increase in the collection efficiency for each percentage decrease in the atmospheric relative humidity. Phoretic effects are known to play a role in collection by drops; however, none of the models found in the literature predicts the same magnitude as the one presently measured. Characterization of the aerosol trajectories around the drop, accelerated to terminal velocity, seems to show a coupling between phoretic effects and rear capture. This interaction, already suggested by Grover et al., is a line of explanation for such a sharp unpredicted increase of the collection efficiency with moisture decrease.

Experimental study of drop shape and wake effects on particle scavenging for non-evaporating drops using ultrasonic levitation

Single drop particle scavenging was experimentally measured for a non-evaporating drop using an ultrasonic levitation technique. This technique enabled measurements of scavenging efficiency, E, for individual drops, and allowed for control of drop axis ratio, α, drop shape oscillations, and Reynolds number, Re, independently from drop diameter. Non-evaporating drops were used which resulted in essentially zero temperature and vapor concentration difference between the drop surface and the surrounding air, virtually eliminating the possibility of confounding phoretic effects. Plots of E versus Stokes number, Stk, became independent of α when Stk was calculated using the Sauter mean diameter (as opposed to the equivolume diameter). Furthermore, E was shown to be insensitive to both Re and drop shape oscillations, suggesting that wake effects do not have a measurable impact on E. Finally, a method was developed to relate E for spherical drops, which are assumed for existing scavenging model predictions, to E for arbitrarily deformed drops, such as those occurring in rain. Of note, these are the first measurements of droplet scavenging using ultrasonic levitation.

Stratification in Drying Films Containing Bidisperse Mixtures of Nanoparticles.

Large scale molecular dynamics simulations for bidisperse nanoparticle suspensions with an explicit solvent are used to investigate the effects of evaporation rates and volume fractions on the nanoparticle distribution during drying. Our results show that "small-on-top" stratification can occur when Pe sϕ s ≳ c with c ∼ 1, where Pe s is the Péclet number and ϕ s is the volume fraction of the smaller particles. This threshold of Pe sϕ s for "small-on-top" is larger by a factor of ∼α2 than the prediction of the model treating solvent as an implicit viscous background, where α is the size ratio between the large and small particles. Our simulations further show that when the evaporation rate of the solvent is reduced, the "small-on-top" stratification can be enhanced, which is not predicted by existing theories. This unexpected behavior is explained with thermophoresis associated with a positive gradient of solvent density caused by evaporative cooling at the liquid/vapor interface. For ultrafast evaporation the gradient is large and drives the nanoparticles toward the liquid/vapor interface. This phoretic effect is stronger for larger nanoparticles, and consequently the "small-on-top" stratification becomes more distinct when the evaporation rate is slower (but not too slow such that a uniform distribution of nanoparticles in the drying film is produced), as thermophoresis that favors larger particles on the top is mitigated. A similar effect can lead to "large-on-top" stratification for Pe sϕ s above the threshold when Pe s is large but ϕ s is small. Our results reveal the importance of including the solvent explicitly when modeling evaporation-induced particle separation and organization and point to the important role of density gradients brought about by ultrafast evaporation.

Phoresis in turbulent flows

Phoresis, the drift of particles induced by scalar gradients in a flow, can result in an effective compressibility, bringing together or repelling particles from each other. Here, we ask whether this effect can affect the transport of particles in a turbulent flow. To this end, we study how the dispersion of a cloud of phoretic particles is modified when injected in the flow, together with a blob of scalar, whose effect is to transiently bring particles together, or push them away from the center of the blob. The resulting phoretic effect can be quantified by a single dimensionless number. Phenomenological considerations lead to simple predictions for the mean separation between particles, which are consistent with results of direct numerical simulations. Using the numerical results presented here, as well as those from previous studies, we discuss quantitatively the experimental consequences of this work and the possible impact of such phoretic mechanisms in natural systems.

Phoretic Self-Propulsion

It is well-known that micro- and nanoparticles can move by phoretic effects in response to externally imposed gradients of scalar quantities such as chemical concentration or electric potential. A class of active colloids can propel themselves through aqueous media by generating local gradients of concentration and electrical potential via surface reactions. Phoretic active colloids can be controlled using external stimuli and can mimic collective behaviors exhibited by many biological swimmers. Low–Reynolds number physicochemical hydrodynamics imposes unique challenges and constraints that must be understood for the practical potential of active colloids to be realized. Here, we review the rich physics underlying the operation of phoretic active colloids, describe their interactions and collective behaviors, and discuss promising directions for future research.

Dry deposition of particles to canopies—A look back and the road forward

AbstractThe so‐called accumulation‐size range of airborne particles is the center of a continuing disagreement about the formulation of dry deposition. Some contemporary meteorological and air quality models use theoretical developments based on early wind tunnel and other controlled experiments, while other models consider the bulk properties of the underlying surface and the ability of atmospheric turbulence to deliver particles to it. This dichotomy arose when the first micrometeorological measurements of particle deposition velocities became available, yielding numbers exceeding the highest expectations of the then‐current models based on assumptions about inertial impaction and interception. The model predictions had previously been shown to be in accord with theoretical treatments of filtration. A common reaction was to distrust the field experimental results, but the experimental findings were supported by subsequent studies. The difference between model predictions and field measurements appears greatest for densely vegetated canopies. Ongoing research is investigating factors that could give rise to the discrepancy, e.g., turbulence intermittency, leaf orientation, leaf morphology, leaf flutter, electrical charges, and a number of phoretic effects. In the meantime, many investigators are faced with a decision as to whether to make use of parameterized field results or theoretical descriptions of behaviors that are not yet well examined. Here the history of the ongoing disagreement is reviewed, and some possible resolutions are presented.

Dry deposition velocities of submicron aerosols on water surfaces: Laboratory experimental data and modelling approach

This article presents new experimental values of deposition velocities of submicron and hygroscopic aerosols of uranine with the objective to analyze dry deposition mechanisms of submicron aerosols on water surfaces in function of wind, water current and differences between air and water temperatures. A special attention is paid to phoretic effects which have been poorly considered by previous experimental studies. Experiments were performed in a laboratory wind tunnel for different conditions precisely characterized in function of aerosol size distribution, air turbulence, water current, water surface deformations, air and water temperatures and relative humidity. The experimental results do not allow detecting any effects of water current nor water surface deformation. The deposition velocity dimensionless with the friction velocity varies according to a V curve as a function of the air-water temperature difference. The minimum of this curve (≈ 2.0×10−5) is reached when the air-water temperature difference is equal to −7.5°C. To analyse these experimental results, appropriate models of hygroscopicity growth, diffusiophoresis and thermophoresis are implemented in the Slinn resistance model (Slinn & Slinn, 1980). Comparisons between experimental and modelling results confirm that the dry deposition velocity of submicron aerosol over water surface is mainly influenced by the turbulent diffusion and show that the influence of hygroscopicity growth is negligible. Furthermore, it is shown that adding the diffusiophoresis and thermophoresis velocities in the deposition layer transfer coefficient greatly improves the agreement between the experimental deposition velocity and the model. Particularly, these results reveal the important role of the thermophoresis when the air-water temperature difference becomes lower than -3°C.

Pair interaction of catalytically active colloids: from assembly to escape

The dynamics and pair trajectories of two self-propelled (active) colloids in a quiescent fluid for both axisymmetric and asymmetric cases are reported. The autonomous motions of the colloids are due to a catalytic chemical reaction taking place asymmetrically on their surfaces that generates a concentration gradient of interactive solutes around the particles and actuates particle propulsion. A combined analytical–numerical technique was developed to solve the coupled mass conservation equation for the solute and the hydrodynamics between the colloids in the Stokes flow regime. For axisymmetric motions, the translational swimming velocities of the particles in the near field can be enhanced or weakened (compared to their motions when they are far apart) depending on the relative orientations of their active sections. Moreover, it can be shown that different surface activities of two symmetric particles, e.g. an inert versus a catalytic particle or two catalytic particles, can also lead to a propulsion where the far-field swimming velocity for the inert and the catalytic particle attenuate as${\sim}1/{\it\Delta}^{2}$and${\sim}1/{\it\Delta}^{5}$respectively,${\it\Delta}$is the non-dimensional centre-to-centre distance. For asymmetric motions, our analysis indicates two possible scenarios for pair trajectories of catalytically active particles: either the particles approach, come into contact and assemble or they interact and move away from each other (escape). It is found that the direction of particle rotations is the key factor in determining the escape or assembly scenario due to an interplay between both hydrodynamic and phoretic effects. Based on the analysis, a phase diagram is sketched for the pair trajectory of the catalytically active particles as a function of reacting surface coverages and their initial relative orientations with respect to each other. We believe this study has important implications in elucidation of collective behaviours of autophoretically self-propelled colloids and would be certainly a guide for experimentalists to design and control active systems.

Hydrodynamic simulations of self-phoretic microswimmers

A mesoscopic hydrodynamic model to simulate synthetic self-propelled Janus particles which is thermophoretically or diffusiophoretically driven is here developed. We first propose a model for a passive colloidal sphere which reproduces the correct rotational dynamics together with strong phoretic effect. This colloid solution model employs a multiparticle collision dynamics description of the solvent, and combines stick boundary conditions with colloid-solvent potential interactions. Asymmetric and specific colloidal surface is introduced to produce the properties of self-phoretic Janus particles. A comparative study of Janus and microdimer phoretic swimmers is performed in terms of their swimming velocities and induced flow behavior. Self-phoretic microdimers display long range hydrodynamic interactions with a decay of 1/r(2), which is similar to the decay of gradient fields generated by self-phoretic particle, and can be characterized as pullers or pushers. In contrast, Janus particles are characterized by short range hydrodynamic interactions with a decay of 1/r(3) and behave as neutral swimmers.

Phoretic self-propulsion: a mesoscopic description of reaction dynamics that powers motion

The fabrication of synthetic self-propelled particles and the experimental investigations of their dynamics have stimulated interest in self-generated phoretic effects that propel nano- and micron-scale objects. Theoretical modeling of these phenomena is often based on a continuum description of the solvent for different phoretic propulsion mechanisms, including, self-electrophoresis, self-diffusiophoresis and self-thermophoresis. The work in this paper considers various types of catalytic chemical reaction at the motor surface and in the bulk fluid that come into play in mesoscopic descriptions of the dynamics. The formulation is illustrated by developing the mesoscopic reaction dynamics for exothermic and dissociation reactions that are used to power motor motion. The results of simulations of the self-propelled dynamics of composite Janus particles by these mechanisms are presented.

Modified multi-component gas transport formulation with phoretic effects

The understanding of multicomponent mass transport processes is essential for modeling and optimization of many systems, such as fuel cells. The understanding of individual species behavior becomes quite significant at micro-nano scales, where average mixture models are not very accurate. Also at micro-nano scales, additional phoretic transport is present due to strong local temperature and pressure gradients, which is discussed by Chakraborty and Durst (Phys Fluids 19(8):088104-01–088104-04, 2007). To account for multicomponent mass transport, recently proposed mass transport model by Kerkhof and Geboers (AIChE J 51(1):79–121, 2005), provides a way to look into individual components. This article presents extended multicomponent mass transport equations for micro-nano scales within continuum region. The Kerkhof–Geboers theory and the modifications suggested by Chakraborty and Durst (2007) have been combined together to form a new set of equations. An extensive order of magnitude analysis has been done on the modified equations. The application of new equations to different problem situations has also been discussed. It is shown that at very small length scales and for highly diffusive transport, the phoretic transport dominates the system, thus rendering the conventional equations erroneous.

Development and validation of a size-resolved particle dry deposition scheme for application in aerosol transport models

Abstract. A size-resolved particle dry deposition scheme is developed for inclusion in large-scale air quality and climate models where the size distribution and fate of atmospheric aerosols is of concern. The "resistance" structure is similar to what is proposed by Zhang et al. (2001), while a new "surface" deposition velocity (or surface resistance) is derived by simplification of a one-dimensional aerosol transport model (Petroff et al., 2008b, 2009). Compared to Zhang et al.'s model, the present model accounts for the leaf size, shape and area index as well as the height of the vegetation canopy. Consequently, it is more sensitive to the change of land covers, particularly in the accumulation mode (0.1–1 micron). A drift velocity is included to account for the phoretic effects related to temperature and humidity gradients close to liquid and solid water surfaces. An extended comparison of this model with experimental evidence is performed over typical land covers such as bare ground, grass, coniferous forest, liquid and solid water surfaces and highlights its adequate prediction. The predictions of the present model differ from Zhang et al.'s model in the fine mode, where the latter tends to over-estimate in a significant way the particle deposition, as measured by various investigators or predicted by the present model. The present development is thought to be useful to modellers of the atmospheric aerosol who need an adequate parameterization of aerosol dry removal to the earth surface, described here by 26 land covers. An open source code is available in Fortran90.

Derivation and verification of an aerosol dynamics expression for the below-cloud scavenging process using the moment method

An aerosol dynamics equation for the below-cloud scavenging process considering phoretic and electric charging effects in addition to the conventional mechanisms (the Brownian diffusion, interception, and impaction) is developed by using the moment method. Then, the dynamics of particle size distribution by the below-cloud scavenging process is calculated by using the developed equation and verified with the measurement data. The calculated particle size distribution changes are quite small compared to the measured changes. The calculated removal rate is smaller by 10−2–10−3 than the measured data when only the conventional mechanisms are considered. With the extended mechanisms, the scavenging coefficient increases upto 20 times, mainly for the particle size range of 0.1 μm<dp<3.0 μm. However, the difference between the calculated and measured scavenging coefficient is still large, especially, for dp<0.1 μm. Other possible scavenging mechanisms that might affect the below-cloud scavenging process such as coagulation and condensational growth of hygroscopic particles, turbulence, and updraft into cloud are discussed. It is recommended that further studies on wet scavenging process are needed.

Relative contributions of individual phoretic effect in the below-cloud scavenging process

We systematically estimate the thermophoretic and diffusiophoretic effect to the below-cloud scavenging coefficient based on the below-cloud scavenging coefficient expression derived in Bae, Jung, and Kim [(2006). Development and evaluation of an expression for polydisperse particle scavenging coefficient for the below-cloud scavenging as a function of rain intensity using the moment method. J. Aerosol Sci. 37, 1507]. The temperature difference between the ambient air temperature ( T) and raindrop surface temperature ( T s ), denoted ( T− T s ), is the most important factor to the thermophoretic effect. The scavenging coefficient by diffusiophoresis is mainly affected by T, ( T− T s ), and relative humidity ( RH). The diffusiophoresis increases with the decrease of ( T− T s ). The driving force of diffusiophoresis increases with the increase of T. As RH becomes lower, diffusiophoresis is more effective. The relative contribution of thermophoresis and diffusiophoresis shows opposite trend to the changes of both T and ( T− T s ) at all T except ( T− T s ) being 1 °C. Thermophoresis and diffusiophoresis are important to the scavenging process when particle diameter is between 0.1 and 10 μm, especially around 1 μm.

Designing phoretic micro- and nano-swimmers

Small objects can swim by generating around them fields or gradients which in turn induce fluid motion past their surface by phoretic surface effects. We quantify for arbitrary swimmer shapes and surface patterns, how efficient swimming requires both surface ‘activity’ to generate the fields, and surface ‘phoretic mobility.’ We show in particular that (i) swimming requires symmetry breaking in either or both of the patterns of ‘activity’ and ‘mobility,’ and (ii) for a given geometrical shape and surface pattern, the swimming velocity is size-independent. In addition, for given available surface properties, our calculation framework provides a guide for optimizing the design of swimmers.