Reducing spurious flow in simulations of electrokinetic phenomena

A numerical investigation of analyte size effects in nanopore sensing systems

We investigate the ionic current modulation in DNA nanopore translocation setups by numerically solving the electrokinetic mean-field equations for an idealized model. Specifically, we study the dependence of the ionic current on the relative length of the translocating molecule. Our simulations show a significantly smaller ionic current for DNA molecules that are shorter than the pore at low salt concentrations. These effects can be ascribed to the polarization of the ion cloud along the DNA that leads to an opposing electric dipole field. Our results for DNA shine light on the observed discrepancy between infinite pore models and experimental data on various sized DNA complexes.

Tunability of Interactions between the Core and Shell in Rattle-Type Particles Studied with Liquid-Cell Electron Microscopy

Yolk-shell or rattle-type particles consist of a core particle that is free to move inside a thin shell. A stable core with a fully accessible surface is of interest in fields such as catalysis and sensing. However, the stability of a charged nanoparticle core within the cavity of a charged thin shell remains largely unexplored. Liquid-cell (scanning) transmission electron microscopy is an ideal technique to probe the core-shell interactions at nanometer spatial resolution. Here, we show by means of calculations and experiments that these interactions are highly tunable. We found that in dilute solutions adding a monovalent salt led to stronger confinement of the core to the middle of the geometry. In deionized water, the Debye length κ-1 becomes comparable to the shell radius Rshell, leading to a less steep electric potential gradient and a reduced core-shell interaction, which can be detrimental to the stability of nanorattles. For a salt concentration range of 0.5-250 mM, the repulsion was relatively long-ranged due to the concave geometry of the shell. At salt concentrations of 100 and 250 mM, the core was found to move almost exclusively near the shell wall, which can be due to hydrodynamics, a secondary minimum in the interaction potential, or a combination of both. The possibility of imaging nanoparticles inside shells at high spatial resolution with liquid-cell electron microscopy makes rattle particles a powerful experimental model system to learn about nanoparticle interactions. Additionally, our results highlight the possibilities for manipulating the interactions between core and shell that could be used in future applications.

An extensible lattice Boltzmann method for viscoelastic flows: complex and moving boundaries in Oldroyd-B fluids

 Most biological fluids are viscoelastic, meaning that they have elastic properties in addition to the dissipative properties found in Newtonian fluids. Computational models can help us understand viscoelastic flow, but are often limited in how they deal with complex flow geometries and suspended particles. Here, we present a lattice Boltzmann solver for Oldroyd-B fluids that can handle arbitrarily shaped fixed and moving boundary conditions, which makes it ideally suited for the simulation of confined colloidal suspensions. We validate our method using several standard rheological setups and additionally study a single sedimenting colloid, also finding good agreement with the literature. Our approach can readily be extended to constitutive equations other than Oldroyd-B. This flexibility and the handling of complex boundaries hold promise for the study of microswimmers in viscoelastic fluids.

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.

Toward Understanding of Self-Electrophoretic Propulsion under Realistic Conditions: From Bulk Reactions to Confinement Effects

Active matter concerns itself with the study of particles that convert energy into work, typically motion of the particle itself. This field saw a surge of interest over the past decade, after the first micrometer-sized, man-made chemical motors were created. These particles served as a simple model system for studying in a well-controlled manner complex motion and cooperative behavior as known from biology. In addition, they have stimulated new efforts in understanding out-of-equilibrium statistical physics and started a revolution in microtechnology and robotics. Concentrated effort has gone into realizing these ambitions, and yet much remains unknown about the chemical motors themselves. The original designs for self-propelled particles relied on the conversion of the chemical energy of hydrogen peroxide into motion via catalytic decomposition taking place heterogeneously over the surface of the motor. This sets up gradients of chemical fields around the particle, which allow it to autophorese. That is, the interaction between the motor and the heterogeneously distributed solute species can drive fluid flow and the motor itself. There are two basic designs: the first relies on redox reactions taking place between the two sides of a bimetal, for example, a gold-platinum Janus sphere or nanorod. The second uses a catalytic layer of platinum inhomogeneously vapor-deposited onto a nonreactive particle. For convenience's sake, these can be referred to as redox motors and monometallic half-coated motors, respectively. To date, most researchers continue to rely on variations of these simple, yet elegant designs for their experiments. However, there is ongoing debate on the exact way chemical energy is transduced into motion in these motors. Many of the experimental observations on redox motors were successfully modeled via self-electrophoresis, while for half-coated motors there has been a strong focus on self-diffusiophoresis. Currently, there is mounting evidence that self-electrophoresis provides the dominant contribution to the observed speeds of half-coated motors, even if the vast majority of the reaction products are electroneutral. In this Account, we will summarize the most common electrophoretic propulsion model and discuss its strengths and weaknesses in relation to recent experiments. We will comment on the possible need to go beyond surface reactions and consider the entire medium as an "active fluid" that can create and annihilate charged species. This, together with confinement and collective effects, makes it difficult to gain a detailed understanding of these swimmers. The potentially dominant effect of confinement is highlighted on the basis of a recent study of an electro-osmotic pump that drives fluid along a substrate. Detailed analysis of this system allows for identification of the electro-osmotic driving mechanism, which is powered by micromolar salt concentrations. We will discuss how our latest numerical solver developments, based on the lattice Boltzmann method, should enable us to study collective behavior in systems comprised of these and other electrochemical motors in realistic environments. We conclude with an outlook on the future of modeling chemical motors that may facilitate the community's microtechnological ambitions.

Mesoscopic modelling and simulation of soft matter

The deformability of soft condensed matter often requires modelling of hydrodynamical aspects to gain quantitative understanding. This, however, requires specialised methods that can resolve the multiscale nature of soft matter systems. We review a number of the most popular simulation methods that have emerged, such as Langevin dynamics, dissipative particle dynamics, multi-particle collision dynamics, sometimes also referred to as stochastic rotation dynamics, and the lattice-Boltzmann method. We conclude this review with a short glance at current compute architectures for high-performance computing and community codes for soft matter simulation.

Microfluidic pumping by micromolar salt concentrations

An ion-exchange-resin-based microfluidic pump is introduced that utilizes trace amounts of ions to generate fluid flows. We show experimentally that our pump operates in almost deionized water for periods exceeding 24 h and induces fluid flows of μm s^-1 over hundreds of μm. This flow displays a far-field, power-law decay which is characteristic of two-dimensional (2D) flow when the system is strongly confined and of three-dimensional (3D) flow when it is not. Using theory and numerical calculations we demonstrate that our observations are consistent with electroosmotic pumping driven by μmol L^-1 ion concentrations in the sample cell that serve as 'fuel' to the pump. Our study thus reveals that trace amounts of charge carriers can produce surprisingly strong fluid flows; an insight that should benefit the design of a new class of microfluidic pumps that operate at very low fuel concentrations.

Ionic screening and dissociation are crucial for understanding chemical self-propulsion in polar solvents

Polar solvents like water support the bulk dissociation of themselves and their solutes into ions, and the re-association of these ions into neutral molecules in a dynamic equilibrium, e.g., H₂O₂ ⇌ H⁺ + HO₂^-. Using continuum theory, we study the influence of these association-dissociation reactions on the self-propulsion of colloids driven by surface chemical reactions (chemical swimmers). We find that association-dissociation reactions should have a strong influence on swimmers' behaviour, and therefore should be included in future modelling. In particular, such bulk reactions should permit charged swimmers to propel electrophoretically even if all species involved in the surface reactions are neutral. The bulk reactions also significantly modify the predicted speed of chemical swimmers propelled by ionic currents, by up to an order of magnitude. For swimmers whose surface reactions produce both anions and cations (ionic self-diffusiophoresis), the bulk reactions produce an additional reactive screening length, analogous to the Debye length in electrostatics. This in turn leads to an inverse relationship between swimmer radius and swimming speed, which could provide an alternative explanation for recent experimental observations on Pt-polystyrene Janus swimmers [S. Ebbens et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2012, 85, 020401]. We also use our continuum theory to investigate the effect of the Debye screening length itself, going beyond the infinitely-thin-screening-length approximation used by previous analytical theories. We identify significant departures from this limiting behaviour for micron-sized swimmers under typical experimental conditions and find that the approximation fails entirely for nanoscale swimmers.

Selective Trapping of DNA Using Glass Microcapillaries

We show experimentally that an inexpensive glass microcapillary can accumulate λ-phage DNA at its tip and deliver the DNA into the capillary using a combination of electro-osmotic flow, pressure-driven flow, and electrophoresis. We develop an efficient simulation model based on the electrokinetic equations and the finite-element method to explain this phenomenon. As a proof of concept for the generality of this trapping mechanism we use our numerical model to explore the effect of the salt concentration, the capillary surface charge, the applied voltage, the pressure difference, and the mobility of the analyte molecules. Our results indicate that the simple microcapillary system has the potential to capture a wide range of analyte molecules based on their electrophoretic mobility that extends well beyond our experimental example of λ-phage DNA. Our method for separation and preconcentration of analytes therefore has implications for the development of low-cost lab-on-a-chip devices.