Anisotropic diffusion in confined colloidal dispersions: The evanescent diffusivity

We employ an analogy to traditional dynamic light scattering to describe the inhomogeneous and anisotropic diffusion of colloid particles near a solid boundary measured via evanescent wave dynamic light scattering. Following this approach, we generate new expressions for the short-time self- and collective diffusivities of colloidal dispersions with arbitrary volume fraction. We use these expressions in combination with accelerated Stokesian dynamics simulations to calculate the diffusivities in the limit of large and small scattering wave numbers for evanescent penetration depths ranging from four particle radii to one-fifth of a particle radius and volume fractions from 10% to 40%. We show that at high volume fractions, and larger penetration depths, the boundaries have little effect on the dynamics of the suspension parallel to the wall since, to a first approximation, the boundary acts hydrodynamically much as another nearby particle. However, near and normal to the wall, the diffusivity shows a strong dependence on penetration depth for all volume fractions. This is due to the lubrication interactions between the particles and the boundary as the particle moves relative to the wall. These results are novel and comprehensive with respect to the range of penetration depth and volume fraction and provide a complete determination of the effect of hydrodynamic interactions on colloidal diffusion adjacent to a rigid boundary

Simulation of hydrodynamically interacting particles near a no-slip boundary

The dynamics of spherical particles near a single plane wall are computed using an extension of the Stokesian dynamics method that includes long-range many-body and pairwise lubrication interactions between the spheres and the wall in Stokes flow. Extra care is taken to ensure that the mobility and resistance tensors are symmetric, positive, and definite—something which is ineluctable for particles in low-Reynolds-number flows. We discuss why two previous simulation methods for particles near a plane wall, one using multipole expansions and the other using the Rotne-Prager tensor, fail to produce symmetric resistance and mobility tensors. Additionally, we offer some insight on how the Stokesian dynamics paradigm might be extended to study the dynamics of particles in any confining geometry

Particle motion between parallel walls: Hydrodynamics and simulation

The low-Reynolds-number motion of a single spherical particle between parallel walls is determined from the exact reflection of the velocity field generated by multipoles of the force density on the particle’s surface. A grand mobility tensor is constructed and couples these force multipoles to moments of the velocity field in the fluid surrounding the particle. Every element of the grand mobility tensor is a finite, ordered sum of inverse powers of the distance between the walls. These new expressions are used in a set of Stokesian dynamics simulations to calculate the translational and rotational velocities of a particle settling between parallel walls and the Brownian drift force on a particle diffusing between the walls. The Einstein correction to the Newtonian viscosity of a dilute suspension that accounts for the change in stress distribution due to the presence of the channel walls is determined. It is proposed how the method and results can be extended to computations involving many particles and periodic simulations of suspensions in confined geometries

Tracer diffusion in active suspensions

We study the diffusion of a Brownian probe particle of size $R$ in a dilute dispersion of active Brownian particles (ABPs) of size $a$, characteristic swim speed $U_0$, reorientation time $\tau_R$, and mechanical energy $k_s T_s = \zeta_a U_0^2 \tau_R /6$, where $\zeta_a$ is the Stokes drag coefficient of a swimmer. The probe has a thermal diffusivity $D_P = k_B T/\zeta_P$, where $k_B T$ is the thermal energy of the solvent and $\zeta_P$ is the Stokes drag coefficient for the probe. When the swimmers are inactive, collisions between the probe and the swimmers sterically hinder the probe's diffusive motion. In competition with this steric hindrance is an enhancement driven by the activity of the swimmers. The strength of swimming relative to thermal diffusion is set by $Pe_s = U_0 a /D_P$. The active contribution to the diffusivity scales as $Pe_s^2$ for weak swimming and $Pe_s$ for strong swimming, but the transition between these two regimes is nonmonotonic. When fluctuations in the probe motion decay on the time scale $\tau_R$, the active diffusivity scales as $k_s T_s /\zeta_P$: the probe moves as if it were immersed in a solvent with energy $k_s T_s$ rather than $k_B T$.Comment: 5 pages, 3 figures, submitted for publication. Please contact authors regarding supplemental informatio

Out of Step, Out of Office: Electoral Accountability and House Members’ Voting

Does a typical House member need to worry about the electoral ramifications of his roll-call decisions? We investigate the relationship between incumbents’ electoral performance and roll-call support for their party—controlling for district ideology, challenger quality, and campaign spending, among other factors—through a series of tests of the 1956–1996 elections. The tests produce three key findings indicating that members are indeed accountable for their legislative voting. First, in each election, an incumbent receives a lower vote share the more he supports his party. Second, this effect is comparable in size to that of other widely recognized electoral determinants. Third, a member’s probability of retaining office decreases as he offers increased support for his party, and this relationship holds for not only marginal, but also safe members

Coastal wetland area change for two freshwater diversions in the Mississippi River Delta

Coastal systems around the globe are being re-integrated with adjacent river systems to restore the natural hydrologic connection to riparian wetlands. The Mississippi River sediment diversions or river reconnections are one such tool to combat high rates of wetland loss in coastal Louisiana, USA by providing freshwater, sediment, and nutrients. There has been some disagreement in the published literature whether re-establishing river reconnection is slowing or contributing to coastal wetland loss. This issue is due to the difficulties in the application of remote sensing in low-relief environments where water level changes could indicate either land loss or simply temporary submergence. We analyzed land change at the receiving areas of two existing freshwater river diversions, Davis Pond and Caernarvon, which have been intermittently receiving river water for up to 2+ decades. This study provides a robust analysis of wetland land change rates in proximity these river diversions including years before river reconnection. Our analyses indicate a net land gain since river reconnection operations began at Davis Pond Diversion (+3.42 km2; range: +2.02–4.81 km2) and no statistically significant change at the Caernarvon Diversion. The Davis Pond wetland results are corroborated with data from a decadal field study documenting increased inorganic sedimentation in the soil. It is clear from this study and others, that river reconnection can increase or, in the case of Caernarvon, have no statistical effect on the land change in these systems due to differences in vegetation, hydroperiod, sediment delivery and external factors including hurricane impacts. Our remote sensing analysis was compared with a global water area change analysis mapping tool which also supported our findings

Fluctuation-dissipation in active matter

In a colloidal suspension at equilibrium, the diffusive motion of a tracer particle due to random thermal fluctuations from the solvent is related to the particle’s response to an applied external force, provided this force is weak compared to the thermal restoring forces in the solvent. This is known as the fluctuation-dissipation theorem (FDT) and is expressed via the Stokes-Einstein-Sutherland (SES) relation D = k_BT/ζ, where D is the particle’s self-diffusivity (fluctuation), ζ is the drag on the particle (dissipation), and k_BT is the thermal Boltzmann energy. Active suspensions are widely studied precisely because they are far from equilibrium—they can generate significant nonthermal internal stresses, which can break the detailed balance and time-reversal symmetry—and thus cannot be assumed to obey the FDT a priori. We derive a general relationship between diffusivity and mobility in generic colloidal suspensions (not restricted to near equilibrium) using generalized Taylor dispersion theory and derive specific conditions on particle motion required for the FDT to hold. Even in the simplest system of active Brownian particles (ABPs), these conditions may not be satisfied. Nevertheless, it is still possible to quantify deviations from the FDT and express them in terms of an effective SES relation that accounts for the ABPs conversion of chemical into kinetic energy

Fluctuation-dissipation in active matter

In a colloidal suspension at equilibrium, the diffusive motion of a tracer particle due to random thermal fluctuations from the solvent is related to the particle’s response to an applied external force, provided this force is weak compared to the thermal restoring forces in the solvent. This is known as the fluctuation-dissipation theorem (FDT) and is expressed via the Stokes-Einstein-Sutherland (SES) relation D = k_BT/ζ, where D is the particle’s self-diffusivity (fluctuation), ζ is the drag on the particle (dissipation), and k_BT is the thermal Boltzmann energy. Active suspensions are widely studied precisely because they are far from equilibrium—they can generate significant nonthermal internal stresses, which can break the detailed balance and time-reversal symmetry—and thus cannot be assumed to obey the FDT a priori. We derive a general relationship between diffusivity and mobility in generic colloidal suspensions (not restricted to near equilibrium) using generalized Taylor dispersion theory and derive specific conditions on particle motion required for the FDT to hold. Even in the simplest system of active Brownian particles (ABPs), these conditions may not be satisfied. Nevertheless, it is still possible to quantify deviations from the FDT and express them in terms of an effective SES relation that accounts for the ABPs conversion of chemical into kinetic energy

Colloidal diffusion and hydrodynamic screening near boundaries

The hydrodynamic interactions between colloidal particles in small ensembles are measured at varying distances from a no-slip surface over a range of inter-particle separations. The diffusion tensor for motion parallel to the wall of each ensemble is calculated by analyzing thousands of particle trajectories generated by blinking holographic optical tweezers and by dynamic simulation. The Stokesian Dynamics simulations predict similar particle dynamics. By separating the dynamics into three classes of modes: self, relative and collective diffusion, we observe qualitatively different behavior depending on the relative magnitudes of the distance of the ensemble from the wall and the inter-particle separation. A simple picture of the pair-hydrodynamic interactions is developed, while many-body-hydrodynamic interactions give rise to more complicated behavior. The results demonstrate that the effect of many-body hydrodynamic interactions in the presence of a wall is much richer than the single particle behavior and that the multiple-particle behavior cannot be simply predicted by a superposition of pair interactions