Determining phoretic mobilities with Onsager's reciprocal relations: Electro- and thermophoresis revisited

Accumulation and Stretching of DNA Molecules in Temperature-Induced Concentration Gradients

Temperature fields provide a noninvasive approach for manipulating individual macromolecules in solution. Utilizing thermophoresis and other secondary effects resulting from the inhomogeneous distribution of crowding agents, one may gain valuable insights into the interactions of molecular mixtures. In this report, we examine the steady-state concentration distribution and dynamics of DNA molecules in a poly(ethylene glycol) (PEG)/water solution when exposed to localized temperature gradients generated by optical heating of a thin chrome layer at a liquid-solid boundary. This allowed us to experimentally investigate the interplay between DNA thermophoresis and PEG-induced entropic depletion effects. Our quantitative analysis demonstrates that the depletion effects dominate over DNA thermophoresis, causing the DNA polymers to migrate toward the heat source. Additionally, we explore the transient stretching of individual DNA molecules in thermally induced PEG gradients and estimate the contributing forces.

Thermophoresis beyond Local Thermodynamic Equilibrium

We measure the thermophoresis of polysterene beads over a wide range of temperature gradients and find a pronounced nonlinear phoretic characteristic. The transition to the nonlinear behavior is marked by a drastic slowing down of thermophoretic motion and is characterized by a Péclet number of order unity as corroborated for different particle sizes and salt concentrations. The data follow a single master curve covering the entire nonlinear regime for all system parameters upon proper rescaling of the temperature gradients with the Péclet number. For low thermal gradients, the thermal drift velocity follows a theoretical linear model relying on the local-equilibrium assumption, while linear theoretical approaches based on hydrodynamic stresses, ignoring fluctuations, predict significantly slower thermophoretic motion for steeper thermal gradients. Our findings suggest that thermophoresis is fluctuation dominated for small gradients and crosses over to a drift-dominated regime for larger Péclet numbers in striking contrast to electrophoresis.

Thermophoretic motion of a charged single colloidal particle

We calculate the thermophoretic drift of a charged single colloidal particle with hydrodynamically slipping surface immersed in an electrolyte solution in response to a small temperature gradient. Here we rely on a linearized hydrodynamic approach for the fluid flow and the motion of the electrolyte ions while keeping the full nonlinearity of the Poisson-Boltzmann equation of the unperturbed system to account for possible large surface charging. The partial differential equations are transformed into a coupled set of ordinary differential equations in linear response. Numerical solutions are elaborated for parameter regimes of small and large Debye shielding and different hydrodynamic boundary conditions encoded in a varying slip length. Our results are in good agreement with predictions from recent theoretical work and successfully describe experimental observations on thermophoresis of DNA. We also compare our numerical results with experimental data on polystyrene beads.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

A review of shaped colloidal particles in fluids: anisotropy and chirality

This review treats asymmetric colloidal particles moving through their host fluid under the action of some form of propulsion. The propulsion can come from an external body force or from external shear flow. It may also come from externally-induced stresses at the surface, arising from imposed chemical, thermal or electrical gradients. The resulting motion arises jointly from the driven particle and the displaced fluid. If the objects are asymmetric, every aspect of their motion and interaction depends on the orientation of the objects. This orientation in turn changes in response to the driving. The objects' shape can thus lead to a range of emergent anisotropic and chiral motion not possible with isotropic spherical particles. We first consider what aspects of a body's asymmetry can affect its drift through a fluid, especially chiral motion. We next discuss driving by injecting external force or torque into the particles. Then we consider driving without injecting force or torque. This includes driving by shear flow and driving by surface stresses, such as electrophoresis. We consider how time-dependent driving can induce collective orientational order and coherent motion. We show how a given particle shape can be represented using an assembly of point forces called a Stokeslet object. We next consider the interactions between anisotropic propelled particles, the symmetries governing the interactions, and the possibility of bound pairs of particles. Finally we show how the collective hydrodynamics of a suspension can be qualitatively altered by the particles' shapes. The asymmetric responses discussed here are broadly relevant also for swimming propulsion of active micron-scale objects such as microorganisms.

Chiral motion in colloidal electrophoresis

Asymmetrically charged, nonspherical colloidal particles in general perform complex rotations and oblique motions under an electric field. The interplay of electrostatic and hydrodynamic forces complicates the prediction of these motions. We demonstrate a method of calculating the body tensors that dictate translational and rotational velocity vectors arising from an external electric field. We treat insulating rigid bodies in the linear-response regime, with indefinitely small electrostatic screening length. The method represents the body as an assembly of point sources of both hydrodynamic drag and surface electric field. We demonstrate agreement with predicted electrophoretic mobility to within a few percent for several shapes with uniform and nonuniform charges. We show that even symmetric shapes can have strong chiral twisting motions. The method applies more generally to active colloidal swimmers.

Linear and angular motion of self-diffusiophoretic Janus particles

We theoretically study the active motion of self-diffusiophoretic Janus particles (JPs) using the Onsager-Casimir reciprocal relations. The linear and angular velocity of a single JP are shown to respectively result from a coupling of electrochemical forces to the fluid flow fields induced by a force and torque on the JP. A model calculation is provided for half-capped JPs catalyzing a chemical reaction of solutes at their surface by reducing the continuity equations of the reacting solutes to Poisson equations for the corresponding electrochemical fields. We find that an anisotropic surface reactivity alone is enough to give rise to active linear motion of a JP, whereas active rotation only occurs if the JP is not axisymmetric. In the absence of specific interactions with the solutes, the active linear velocity of the JP is shown to be related to the stoichiometrically weighted sum of the friction coefficients (or hydrodynamic radii) of the reacting solutes. Our reciprocal treatment further suggests that a specific interaction with the solutes is required to observe far-field diffusiophoretic interactions between JPs, which rely on an interfacial solute excess at the JP surface. Most notably, our approach applies beyond the boundary-layer approximation and accounts for both the diffusio- and electrophoretic nature of active motion.

Self-thermoelectrophoresis at low salinity

A locally heated Janus colloid can achieve motion in an electrolyte by an effect known as self-thermo(di)electrophoresis. We numerically study the self-propulsion of such a "hot swimmer" in a monovalent electrolyte using the finite-element method and analytic theory. The effect of electrostatic screening for intermediate and large Debye lengths is charted and we report on the fluid flow generated by self-thermoelectrophoresis. We obtain excellent agreement between our analytic theory and numerical calculations in the limit of high salinity, validating our approach. At low salt concentrations, we employ Teubner's integral formalism to arrive at expressions for the speed, which agree semi-quantitatively with our numerical results for conducting swimmers. This lends credibility to the remarkably high swim speed at very low ionic strength, which we numerically obtain for a fully insulating swimmer. We also report on hot swimmers with a mixed electrostatic boundary conditions. Our results should benefit the realization and analysis of further experiments on thermo(di)electrophoretic swimmers.

Particle motion driven by non-uniform thermodynamic forces

We present a complete reciprocal description of particle motion inside multi-component fluids that extends the conventional Onsager formulation of non-equilibrium transport to systems where the thermodynamic forces are non-uniform on the colloidal scale. Based on the dynamic length and time scale separation in suspensions, the particle flux is shown to be related to the volume-averaged coupling between the Stokes flow tensor and the thermodynamic force density acting on the fluid. The flux is then expressed in terms of thermodynamic quantities that can be computed from the interfacial properties and equation of state of the colloids. Our results correctly describe diffusion and sedimentation and suggest that force-free phoretic motion can occur even in the absence of interfacial interactions, provided that the thermodynamic gradients are non-uniform at the colloidal surface. In particular, we derive an explicit hydrodynamic form for the phoretic force resulting from these non-uniform gradients. The form is validated by the recovery of the Henry function for electrophoresis and the Ruckenstein term for thermophoresis.