Session J34: Micro/Nano Particles: Diffusion

Microscopic 3D tracking of DEHS particles — determination of the mean square displacement

Particles suspended in a medium move randomly, i.e. the Brownian motion. The Brownian motion is difficult to measure, in particular the ballistic regime of the motion of a Brownian particle (at very short time scales t<<τ_p). However, even at larger time-scales, at t>>τ_p, referred to as the diffusive regime, the mean square displacement (MSD) of the particles is challenging to capture, since it is still small. Conducting particle MSD measurements in a gas rather than in a liquid is advantageous, since the MSD values in gases are about one order of magnitude larger. For this study, we employ particle imaging to determine the movement of di(2-ethylhexyl) sebacate (DEHS) seeding particles with an average diameter of around 0.35 micrometer in a confined, microscopic domain. More specifically, the 3D particle tracking velocimetry (3D-PTV) technique is used, where the spatial particle location is triangulated from at least two different views. The particle displacements are determined by means of particle tracking, using time-resolved or double-frame recordings. Unlike other microscopic single camera 3D particle imaging approaches, which require fluorescent seeding particles (and are therefore restricted to liquid flow analyses) to remove background reflections from the interfaces of the confined measurement domains, 3D-PTV uses a different approach: The issue of light reflections on the channel surfaces is overcome by a forward-scattering illumination set-up, where the camera views are at an off-axis angle of around 30° relative to the laser beam. In this way, the laser intensity can be relatively low, while the sub-micrometer DEHS seeding particles are still detectable on the sensor. Thus, microscopic 3D-PTV enables us to measure the mean square displacement of DEHS particles in air, yielding a 3D analysis of the random particle movements.   

Rational Design of Two-Dimensional Colloidal Banding

Diffusiophoresis, i.e. the movement of particles in response to concentration gradient of a solute, causes particles to accumulate in regions due to a concentration gradient. This phenomenon is known as colloidal banding. Existing literature has largely focused on how particles respond to one-dimensional solute gradients. Here, we study colloidal banding in response to two-dimensional solute gradients generated by sources and sinks. First, we investigate colloidal banding in a dipole configuration, i.e., one source and one sink. We find that two timescales govern colloidal banding: the inter-dipole diffusion and the source/sink flux decay timescales. We observe that the balance of two timescales result in an optimum separation distance which maximizes particle enrichment. The optimum separation distance is governed by the partition coefficients and relative diffusivities of solute in the bulk solution and the source/sink regions. In a system with four sources and sinks, geometric asymmetry provides additional control over the attained banding structure, leading to further enriched configurations. In summary, our findings allow for rational design of two-dimensional source and sink configurations to control banding in diffusiophoretic particles.   

Over-time measurement of solution viscosity change using quantification of Brownian motion through Particle Diffusometry

Real-time viscosity measurement techniques have been used to analyze the transition of hydrogels from a liquid state to a gel state. Measuring real-time changes in viscosity can be done through passive rheometry with the addition of tracer particles. Particle Diffusometry quantifies the Brownian motion of sub-micron-sized fluorescent particles by computing diffusion coefficients via statistical averaging. Herein, we demonstrate a method to study viscosity change over time using Particle Diffusometry on polyacrylamide hydrogel formation for a temporally and spatially resolved rheometry technique. We used synthetic images of particles undergoing a decreasing sigmoidal trend for the simulation of the viscosity change of the solution. For the experiment, polyacrylamide hydrogel was initiated using the point light source from the microscope. Using a diffusion gradient plane through PD, we confirmed a radial gel formation from the center of the imaging window. Also, by varying the initiator concentration, we observed the time-varying onset of hydrogel formation. This work establishes the groundwork for quantifying over time changes in Brownian motion.   

CNN-PD: Convolutional Neural Networks for Particle Diffusometry Measurements

Measuring fluid properties (such as viscosity & temperature) on a microscale plays a vital role in areas ranging from fuel cells to pharmaceuticals. These properties can be obtained in real-time by seeding an otherwise featureless fluid with particles & monitoring the particles’ diffusion. However, existing methods such as single-particle tracking & correlation-based measurement are significantly degraded when the fluid is flowing as well as in the presence of diffusion coefficient gradients. This work provides a convolutional neural network (CNN) based alternative for diffusion coefficient measurement that averages PIV-style interrogation regions from successive frames. The averaged images used for training the CNNs can have an arbitrary number of frames (n > 1). The results show that with only two-frame averages, R² values (about 0.99) when there was no flow or a known uniform flow. Moreover, the CNNs maintained high R² (about 0.96) without retraining, even when the underlying frames had a diffusion coefficient gradient. Additionally, similar R² values were obtained for arbitrary flows with four-frame averaged images. It shows that the CNNs learn useful representations of diffusion coefficient from temporally averaged particle images & can generalize it to unseen cases.   

Optimal geometry for surface-enhanced diffusion

Molecular diffusion in bulk liquids proceeds according to Fick's law, which stipulates that the current is proportional to the conductive area. This constrains the efficiency of filtration systems in which both selectivity and permeability are valued. Numerous studies have demonstrated that interactions between the diffusing species and solid boundaries, e.g., filter pore walls, can enhance or reduce particle transport relative to bulk conditions. To our knowledge, however, only cases that preserved the monotonic relationship between particle current and conductive area are known. Here, we provide examples of the opposite: a class of surface interactions that allows both the selectivity and permeability to increase several-fold as the pore size diminishes. The example is based on the century-old theory of a charged particle interacting with an electrical double layer. The effects of diffusion and bulk flow are explored. This surprising discovery could lead to improvements in the efficiency of filtration and may improve our understanding of biological pore structures.   

Diffusiophoretic focusing of colloids in a microfluidic T-junction

Diffusiophoretic migration of colloids due to chemical gradients has been used to manipulate and guide them in simple configurations, including co-flow channels and open/dead-end pores. In these scenarios, the colloid distribution is determined by the solute and flow velocity fields. Here, we report on an unexpected particle focusing effect in a microfluidic T-junction in the presence of a solute concentration gradient between the two sides. Using experimental observations and numerical simulations, we explain the mechanism of this focusing effect as an interplay between phoretic and osmotic flows.   

Diffusiophoretic field flow fractionation in the presence of a pH gradient

Diffusiophoresis is the spontaneous motion of particles under concentration gradients of solutes. When there are electrolyte concentration gradients formed across a channel flow, particles with nonzero surface potential can undergo diffusiophoresis and accumulate toward side walls. The direction of motion depends on the mobilities of particles and the system demonstrates diffusiophoretic-driven field flow fractionation. In this study, we show a channel flow configuration where there is initially a steady-state stream of a particle suspension at a high pH. Then, we impose a concentration gradient of ions due to CO₂ dissolution from one side wall and, consequently, particles undergo diffusiophoresis. We study experimentally and theoretically the diffusion of multiple ions in the system and the pH-dependent diffusiophoretic behaviors of the particles.    

Quantifying the maximum efficiency of diffusiophoresis-driven filtration

Diffusiophoresis —the migration of particles in a fluid induced by a chemical gradient— has attracted increasing attention in recent years, with studies showing its relevance in processes ranging from fabric cleaning to particle delivery in porous materials. One of its particularly promising applications is water remediation, demonstrated using a CO2 gradient perpendicular to a flow of water contaminated with solid micro-beads [Shin et al., Nat. Commun. (2017)]. The resulting phoretic motion concentrates the solids on the channel sides and, after the particle-rich stream is diverted, results in membraneless water cleaning with an efficiency comparable to microfiltration. Here, we present a model of this effect for fully-developed species and particle concentrations, when the separation of solids is highest after the particle-free exclusion zone has reached its maximum thickness. The asymptotic theory produces quantitative predictions for the filtration efficiency as a function of three parameters that depend on the chemistry and particle properties. These results are then discussed and compared to measurements performed in microfluidic channels.   

Weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion: general theory

We study the weakly nonlinear dynamics of an isotropic chemically active particle in the limit where the Péclet number approaches its critical value, beyond which the symmetric base state is unstable and the particle exhibits symmetry-breaking spontaneous motion. The theory consists of a nonlinear amplitude equation governing the slow-time dynamics of the particle's velocity, in which unsteadiness—associated with the particle interacting with its own concentration wake over large scales—is manifested in a temporally nonlocal term that nonlinearly depends on the history of the particle's motion. Our derivation involves matching a quasi-steady particle-scale expansion with an unsteady leading-order solution for the concentration field in a large-scale region, describing diffusion from a moving point source; it additionally relies on a novel adjoint formulation that enables us to straightforwardly treat fully 3D particle motion and include the effects of general weak perturbations, which can have a leading-order effect sufficiently near the threshold. Our weakly nonlinear theory allows inexpensive numerical simulation of one or many active particles over long times scales, as well as analysis of various physical effects (see following talk by Gunnar Peng).   

Weakly nonlinear dynamics of chemically active particles near the threshold for spontaneous motion: numerical and theoretical results

A submerged isotropic active particle (or droplet) that emits/consumes a chemical and interacts with it to drive flow via diffusio-osmotic slip (or Marangoni effects) can exhibit symmetry-breaking spontaneous motion. We simulate the dynamics of the particle with a reduced-order model, derived using a weakly nonlinear expansion near the threshold for spontaneous motion, in which the particle velocity depends on a time integral over the history of the particle motion (see preceding talk by Ory Schnitzer). Various cases are studied, including the particle interacting with a force, a wall and/or other particles, resulting in linear motion, circular motion, and more exotic dynamics such as bouncing and trapping. Results from asymptotic and linear-stability analyses are also presented.   

Multimodal Analysis of Driven Nanobeams with Arbitrary Tension in a Viscous Fluid

We investigate the driven dynamics of a long and slender nanoscale beam with tension that is immersed in a viscous fluid. The beam motion is driven by a harmonic force that is applied over the spatial region near its fixed ends. We develop a multimode theoretical description that is valid for all values of tension, includes the coupling of the beam dynamics with the spatially varying drive force, and can be used for a Newtonian fluid. The fluid dynamics are modeled using the hydrodynamic function of an oscillating blade. Using our theoretical description, we quantify the dynamics over a wide range of conditions. We directly compare the theoretical predictions with experimental measurements for a beam under very high tension that is driven electrothermally and placed in air and water. We compare theory with experiment for the first several modes of oscillation which shows good agreement. For very high tension, we demonstrate the benefit of modeling the system as an oscillating string immersed in a fluid.   

Brownian Fluctuations of a Nanomechanical String Resonator Immersed in a Viscous Fluid

The precision of a measurement using a mechanical resonator is limited by Brownian motion, especially for a small resonator such as a nanoelectromechanical systems (NEMS) resonator. Here, we investigate the Brownian dynamics of a doubly-clamped nanomechanical beam under high tension immersed in a viscous fluid both theoretically and experimentally. Our beam is modeled as an oscillating cylinder so that Stokes theory can be applied to obtain an analytic form for fluid dissipation. Due to the high tension, the beam obeys the equation of motion of a fluid-loaded string, from which we find its mechanical susceptibility as a function of frequency and position along the beam. The position-dependent power spectral density (PSD) of the thermal displacement fluctuations of the beam is then obtained from the susceptibility via the fluctuation-dissipation theorem. In order to verify our theory, we use optical interferometry to measure the displacement fluctuations of a 50 μm × 900 nm × 100 nm silicon nitride beam in air and water. The PSD of the beam's displacement noise in air shows distinct peaks at the eigenfrequencies, which we integrate over frequency to obtain the modal spring constants. The experimentally-determined eigenfrequencies and spring constants are then inserted into our analytically-derived expression to predict the PSD of displacement fluctuations in water. We obtain excellent agreement between theory and experiments in water for different positions along the beam, observing broad and overlapping modal peaks.