We investigate the mechanisms by which inertial particles dispersed at semidilute conditions cause significant drag-reduction in a turbulent channel flow at ${\mathrm{Re}}_{\tau }=180$. We consider a series of four-way-coupled Euler-Lagrange simulations where particles having friction Stokes number ${\mathrm{St}}^{+}=6$ or 30 are introduced at progressively increasing mass loading from $M=0.2$ to 1.0. The simulations show that ${\mathrm{St}}^{+}=30$ particles cause large drag-reduction by up to 19.74% at $M=1.0$, whereas ${\mathrm{St}}^{+}=6$ particles cause large drag increase by up to 16.92% at $M=1.0$. To reveal the mechanisms underpinning drag-reduction or drag-increase, we investigate the stress distribution within the channel and the impact of the dispersed particles on the near-wall coherent structures. We find a distinctive feature of drag-reducing particles which consists in the formation of extremely long clusters, called ropes. These structures align preferentially with the low-speed streaks and contribute to their stabilization and suppression of bursting. Despite the additional stresses due to the particles, the modulation of the near-wall coherent structures leads to a greater reduction of Reynolds shear stresses and partial relaminarization of the near-wall flow. In the case of the drag-increasing particles with ${\mathrm{St}}^{+}=6$, a reduction in Reynolds shear stresses is also observed, however, this reduction is insufficient to overcome the additional particle stresses which leads to drag increase.

We investigate the underlying physics behind the change in amplitude modulation coefficient in noncanonical wall-bounded flows in the framework of the inner-outer interaction model (IOIM) [Baars et al., Phys. Rev. Fluids 1, 054406 (2016)]. The IOIM captures the amplitude modulation effect, and here we focus on extending the model to noncanonical flows. An analytical relationship between the amplitude modulation coefficient and IOIM parameters is derived, which is shown to capture the increasing trend of the amplitude modulation coefficient with an increasing Reynolds number in a smooth-wall dataset. This relationship is then applied to classify and interpret the noncanonical turbulent boundary layer results reported in previous works. We further present the case study of a turbulent boundary layer after a rough-to-smooth change. Both single-probe and two-probe hotwire measurements are performed to acquire streamwise velocity time series in the recovering flow on the downstream smooth wall. An increased coherence between the large-scale motions and the small-scale envelope in the near-wall region is attributed to the stronger footprints of the overenergetic large-scale motions in the outer layer, whereas the near-wall cycle and its amplitude sensitivity to the superposed structures are similar to that of a canonical smooth-wall flow. These results indicate that the rough-wall structures above the internal layer interact with the near-wall cycle in a similar manner as the increasingly energetic structures in a high-Reynolds number smooth-wall boundary layer.

We investigate the response of the free liquid surface in a partially filled circular cylindrical container undergoing a planar elliptic and time-periodic orbit while maintaining fixed its orientation. For small forcing amplitudes and deep liquid layers, we quantify the effect of the orbit's aspect ratio on the surface dynamics in the vicinity of the fluid system's lowest natural frequency ${\omega }_0$. We provide experimental evidence of the existence of a frequency range where stable swirling can be either co- or counterdirected with respect to the container's direction of motion. Our findings are then rationalized by an inviscid weakly nonlinear model, amended with heuristic damping.

When two bubbles submerged in a liquid are brought closely together, the intermediate liquid film separating the bubbles begins to drain. Once the film ruptures, the bubbles coalesce and form a neck that expands with time. The dynamics of the neck growth are well understood in the context of pure, Newtonian liquids. Yet much less is known about the dynamics of this singularity when the surrounding liquid contains long flexible polymers, which provide viscoelastic characteristics to the liquid's properties. Here we experimentally study the coalescence of bubbles surrounded by polymer solutions. In contrast to drop coalescence, and in spite of the singular stretching of polymers, we find that the presence of the dissolved polymers does not at all affect the coalescence dynamics at early times. The polymer elasticity is found to slow down the flow only during the later stages of coalescence. These observations are interpreted using an asymptotic solution of the Oldroyd-B model, which predicts a strong stress singularity near the extremity of the neck. However, the polymer stress turns out to diverge only in the azimuthal direction, which can explain why elastic effects remain subdominant during the initial stages of coalescence.

The clustering (preferential concentration) and collision of particles in turbulent flows is a significant process in nature, such as in the precipitation process of atmospheric clouds. We perform direct numerical simulation (DNS) to study the clustering of small, heavy, monodisperse particles subject to collision-coagulation in turbulent flow [i.e., colliding particles always coagulate (coalesce) into larger ones]. The simulations do not include gravitational effects and hydrodynamic interactions among particles. We find that collision-coagulation causes the radial distribution function (RDF) of the particles to decrease strongly at particle separation distances $r$ close to the particle diameter $d$. However, we observe that the RDF does not decrease indefinitely but approaches a finite value in the limit of $r\to d$. We study how the properties of this “depletion zone” relates to the particle Stokes number (St), particle diameter, and the Reynolds number of the turbulent flow. A collision-induced modulation factor ${\gamma }_c$ is defined to represent the degree of RDF depletion due to collision-coagulation. In the region where ${\gamma }_c\left(r\right)$ is a quasi-power-law, we find that the effective power-law exponent ${\tilde{c}}_1$ depends only weakly on St in the regime of $\text{St}\ll 1$, but increases significantly for larger St and peaks at around $\text{St}\approx 0.7$. The same qualitative trend is also observed for the limiting values of ${\gamma }_c$ at $r\to d$. We find that the overall trend of ${\tilde{c}}_1$ with respect to St is qualitatively similar to that of the classical power-law exponent $c_1$ appearing in the RDF of noncolliding particles, except that ${\tilde{c}}_1$ is barely changed at small St and the magnitude of the trend is much weaker. A complementary investigation on the Stokes number trend of the full RDF in the depletion zone is performed. The slope of the RDF appears to be constant for $\text{St}\ll 1$ but changes as St becomes large. The location of the RDF's peak is found to be St-dependent. We found that the depletion zone is insensitive to the flow Reynolds number and that ${\gamma }_c$ of different ${\text{Re}}_{\lambda }$ overlap. As the particle diameter $d$ changes, the reduction of the RDF occurs on scales that shift accordingly, and always starting at around $2.4d–3d$. We also find that the shape of ${\gamma }_c\left(r\right)$ is independent of changes in $d$.

Magnetorotational instability (MRI) is considered as the most likely mechanism driving angular momentum transport in astrophysical disks. However, despite many efforts, a direct and conclusive experimental evidence of MRI in laboratory is still missing. Recently performing one-dimensional linear analysis of the standard version of MRI (SMRI) in a Taylor-Couette (TC) flow between two rotating coaxial cylinders threaded by an axial magnetic field, we showed that SMRI can be detected in the upcoming DRESDYN-MRI experiment based on a cylindrical magnetized TC flow of liquid sodium. In this follow-up study, also related to the DRESDYN-MRI experiments, we focus on the nonlinear evolution and saturation properties of SMRI and analyze its scaling behavior with respect to various parameters of the basic TC flow using a pseudospectral code. We conduct a detailed analysis over the extensive ranges of magnetic Reynolds number $\mathrm{Rm}\in [8.5,37.1]$, Lundquist number $\mathrm{Lu}\in [1.5,15.5]$, and Reynolds number, $\mathrm{Re}\in [{10}^3,{10}^5]$. We focus on the small magnetic Prandtl number, $\mathrm{Pm}\ll 1$, regime down to $\mathrm{Pm}\sim {10}^{-4}$, aiming ultimately for those very small values typical of liquid sodium used in the experiments. In the saturated state, the magnetic energy of SMRI and associated normalized torque due to perturbations exerted on the cylinders, which characterizes angular momentum transport, both increase with $\mathrm{Rm}$ for fixed $(\mathrm{Lu},\mathrm{Re})$, while for fixed $(\mathrm{Lu},\mathrm{Rm})$, the magnetic energy decreases and torque increases with increasing $\mathrm{Re}$. We also study the scaling of the magnetic energy and torque in the saturated state as a function of $\mathrm{Re}$ and find a power-law dependence of the form ${\mathrm{Re}}^{-0.6...-0.5}$ for the magnetic energy and ${\mathrm{Re}}^{0.4...0.5}$ for the torque at all sets of $(\mathrm{Lu},\mathrm{Rm})$ and sufficiently high $\mathrm{Re}\ge 4000$. We also explore the dependence on Lundquist number and angular velocity of the cylinders. The scaling laws derived here will be instrumental in the subsequent analysis of more realistic finite-length TC flows and comparison of numerical results with those obtained from the DRESDYN-MRI experiments in order to conclusively and unambiguously identify SMRI in the laboratory.

In this paper, we use the scaling method to investigate the transient convective boundary layer evolving on the external surface of an isothermally heated vertical cylinder. Our numerical calculations show that a boundary layer flow develops in the vicinity of the heated surface due to the buoyancy effect. We also demonstrate that the thickness and velocity of the boundary layer flow are significantly affected by the curvature effect. Our analysis successfully determines a set of fully explicit scaling laws for the initial and steady flow states over a large parameter range, with Rayleigh numbers (Ra) of ${10}^7$ to ${10}^9$, Prandtl numbers (Pr) of 10 to 100, and aspect ratios ($A$) of 1 to 100. These scaling laws are explicit and easier to use than the previous implicit scaling laws [Phys. Rev. Fluids 7, 054101 (2022)]. The present scaling laws consist of the flat plate scaling, which accounts for the Ra and Pr number dependencies, and a dimensionless explicit curvature coefficient ${\mathrm{\Psi }}^{\prime }\left(A\right)$. When the boundary layer is much thinner than the cylinder radius, the proposed scaling laws reduce to the well-known flat boundary layer ones, and the curvature coefficient ${\mathrm{\Psi }}^{\prime }\left(A\right)$ approaches the unity. When the boundary layer thickness is close to or larger than the cylinder radius, the curvature effect becomes significant, and the curvature coefficient ${\mathrm{\Psi }}^{\prime }\left(A\right)$ accurately quantifies the curvature effect. Comparison between the scaling laws and numerical calculations shows that most fitting constants $R^2$ are approximately $0.999$, which convincingly validates the proposed scaling laws.

In this study, we perform boundary-integral simulations to understand the role of interfacial viscosity on the early stages of coalescence of two equal-sized droplets approaching under uniaxial compressional flow in the Stokes flow limit. We model the surface rheology of the droplet using the Boussinesq-Scriven constitutive relationship for a Newtonian interface. Previous studies have shown that colliding droplets at low capillary numbers $Ca\sim \mathcal{O}\left({10}^{-4}\right)$ (i.e., low impact velocities) remain almost spherical up to the point of film rupture, while droplets at large values of capillary number form a dimpled film that significantly slows down the drainage time. Here we explore how the interfacial viscosity affects the thin film formation and drainage time in a head-on collision between two droplets with capillary number values in the range ${10}^{-4}-{10}^{-2}$. We observe that the surface viscosity significantly arrests the thinning of the film between the coalescing droplets compared to a clean interface. We find that the film drainage time at a given capillary number increases upon increasing the Boussinesq parameter for total surface viscosity and is independent of the ratio of surface dilatational viscosity to the surface shear viscosity. We also explore the coupled influence of surface viscosity and Marangoni stresses on droplet coalescence. We incorporate the effect of surfactant transport by solving the time-dependent convection-diffusion equation and consider a nonlinear equation of state (Langmuir adsorption isotherm) to correlate the interfacial tension with the changes in surfactant concentration.

The dispersion of rigid elongated particles in turbulent channel flow bounded by rough walls is examined. In particular, the interplay between particle inertia, particle length, and wall roughness characteristics in determining particle spatial distribution, preferential orientation, and alignment within the flow is analyzed. The dispersion process is investigated by performing direct numerical simulations of the turbulent flow coupled with the Lagrangian tracking of the particles, modeled as prolate ellipsoids with varying aspect ratio and inertia, under dilute flow conditions. Simulations are carried out at friction Reynolds number ${\text{Re}}_{\tau }=180$ based on the channel half height in a domain confined by walls with different two-dimensional roughness characteristics. Particle elongation is varied considering different aspect ratios (ranging from $\lambda =1$ for the reference case of spherical particles to $\lambda =10$ for the longest particle set) while particle inertia is varied considering different Stokes numbers (ranging from ${\text{St}}^{+}=1$ for the least inertial particles to ${\text{St}}^{+}=100$ for the most inertial ones), for a total of 12 different particle sets. Our results show that particles are affected by the turbulent structures that form near the rough walls in a way that is biased both by elongation, namely length, and inertia. This is not observed with smooth walls: In this case, increasing particle inertia always leads to a stronger turbophoretic particle drift to the walls. Elongation is observed to have a quantitative effect on the slip velocity statistics, particularly for particles with small Stokes number. Differences induced by a change of the aspect ratio tend to vanish as particle inertia increases, since the relative translational motion between the particles and the surrounding fluid appears to be closely connected to preferential concentration phenomena. Wall roughness modifies the overall dynamics of the particles, as well as their distribution, orientation, and alignment with flow direction, especially in the near-wall region. Roughness hinders long-term wall deposition of particles and determines a more uniform spatial distribution across the channel. In the near-wall region, elongated particles tend to align with the streamwise direction even in the presence of large-scale roughness, albeit to a lesser extent compared to the case of smooth walls. A stronger effect of roughness is noticed on the alignment along the spanwise and wall-normal directions. Such alignment, as well as preferential orientation, is hampered by the strong velocity fluctuations induced by roughness and the behavior of the ellipsoidal particles resembles again that of spherical particles.

In this work we discuss a scaling law for wall friction weakening in three-dimensional, dense, fully confined granular flows made of shape anisotropic particles. Using particle-based simulations, we observe a rich variety of kinematics and wall stress profiles by varying the particle-wall friction coefficient and the cell width. We show that in this peculiar flow configuration: (i) particle shape has a negligible influence on translational velocity and granular temperature profiles while the angular motion is strongly hampered for elongated particles and (ii) the mobilization of friction at the sidewalls is affected by both particle shape and flow pattern. Associating data on wall stress and particles kinematics, we find that wall friction mobilization is well described by a scaling law based on a balance between sliding and rolling motion of the grains. We show that the proposed scaling law seems to be very robust, being independent of the main system parameters, e.g., particle-particle friction, particle-wall friction, channel width, vertical confinement, particle elongation, and flow configuration (shear driven or gravity driven). This result highlights the importance of angular motion of the particles for the understanding of the behavior at flat boundaries and may reignite the debate about the relevant variables in theories for dense granular flows.

A combination of analytical and numerical techniques is used to give a complete description of the late-time draining of a two-dimensional thin liquid film on the outer surface of a stationary horizontal circular cylinder. In this limit three regions of qualitatively different behavior emerge, namely a draining region on the upper part of the cylinder and a pendant-drop region on the lower part of the cylinder joined by a narrow inner region. In the draining region, capillarity is negligible and the film thins due to gravity. In the pendant-drop region (which, to leading order, contains all of the liquid initially on the cylinder), there is a quasistatic balance between gravity and capillarity. The matching between the draining and pendant-drop regions occurs via the inner region in which the film has a capillary-ripple structure consisting of an infinite sequence of alternating dimples and ridges. Gravity is negligible in the dimples, which are all thinner than the film in the draining region. On the other hand, gravity and capillarity are comparable in the ridges, which are all thicker than the film in the draining region. The dimples and the ridges are all asymmetric: specifically, the leading-order thickness of the dimples grows quadratically in the downstream direction but linearly in the upstream direction, whereas the leading-order film thickness in the ridges goes to zero linearly in the downstream direction but quadratically in the upstream direction. The dimples and ridges become apparent in turn as the draining proceeds, and only the first few dimples and ridges are likely to be discernible for large but finite times. However, there is likely to be a considerable period of time during which the present asymptotic solution provides a good description of the flow.

The present study reports an original physical model for simulating pulsating heat pipes (PHPs). Their high heat performance is due to the phase change over thin liquid films. The simulation of physically correct film behavior is thus crucial. The model adopts the one-dimensional approach, which is computationally efficient yet still capable of capturing major physical phenomena. The model assumes a spatially uniform film thickness, whereas both the film thickness and length can vary over time; therefore, we call it the oscillating film thickness model. It is based on the physical analysis of liquid film deposition by the receding menisci of Taylor bubbles and of contact line dynamics. Three key phenomena are addressed: (1) film deposition, (2) contact line receding due to dewetting acceleration by evaporation, and (3) mass exchange over films and contact lines. The model is evaluated by simulating the simplest, single-branch PHP, for which detailed experimental data are available. A quantitative agreement is reached. As the model includes the wetting properties, their impact on oscillations is analyzed, and a qualitative agreement with the experiment is demonstrated.

In this paper, we propose a modeling framework for large eddy simulations of particle-laden turbulent flows that captures the interaction between the particle and fluid phase on both the resolved and subgrid scales. Unlike the vast majority of existing subgrid-scale models, the proposed framework not only accounts for the influence of the subgrid-scale velocity on the particle acceleration but also considers the effect of the particles on the turbulent fluid flow. This includes the turbulence modulation of the subgrid scales by the particles, which is taken into account by the modeled subgrid-scale stress tensor and the effect of the unresolved particle motion on the resolved flow scales. Our modeling framework combines a recently proposed model for enriching the resolved fluid velocity with a subgrid-scale component, with the solution of a transport equation for the subgrid-scale kinetic energy. We observe very good agreement of the particle pair separation and particle clustering compared to the corresponding direct numerical simulation. Furthermore, we show that the change of subgrid-scale kinetic energy induced by the particles can be captured by the proposed modeling framework.

The asymptotic energy dissipation is connected to the third-order scaling of the longitudinal velocity increment magnitude in three-dimensional turbulence via the Kolmogorov $4/5$ law. It is shown that the third-order longitudinal absolute velocity increment scaling should not exceed unity for anomalous dissipation to occur, that is for nonvanishing average dissipation in the inviscid limit—also known as the “zeroth law” of turbulence. Conversely, if the third-order longitudinal absolute velocity increment scaling exceeds unity, then the average dissipation must asymptotically vanish and the velocity increment field will becomes symmetric at least at the level of its skewness. This Letter highlights the importance of the third-order absolute velocity increment scaling in assessing the status of the zeroth law of turbulence.

We consider the buoyancy-driven rise and interaction between two coaxially placed bubbles of equal size and constant volume that are initially stationary inside an elastoviscoplastic material. We simulate the material using the Saramito extension of the Herschel-Bulkley constitutive model, and we fit its properties to a 0.1% aqueous Carbopol solution. The interplay between plasticity, viscoelasticity, and inertia is investigated. We observe that a “bridge” of shear stresses develops, which connects the leading and the trailing bubble, decreasing the drag force on the latter and initiating their approach. The solidlike behavior of the material preserves stresses generated by the passage of the leading bubble and makes the material “softer” for the trailing bubble. At the same time the normal stresses primarily extend the bubbles, but their finite distance eventually causes the leading bubble to adopt a hydrodynamically less favorable shape that slows it down, further promoting the approach. Moreover, we examine the effect of the geometric characteristics and the material properties. Increasing the initial distance between the bubbles delays their approach, which, however, is inevitable. Increasing the radius results in a transition from the elastoplastic to a mixed elastoplastic-inertial regime and a delayed approach. Increasing elasticity or the shear and extension thinning of the material decreases the approach time. On the contrary, an increased viscosity delays their approach. Finally, varying the yield stress induces a nonmonotonic effect. Sufficiently small values of yield stress delay the approach compared to intermediate values, because it reduces the elastic response. Raising the yield stress slightly above the entrapment conditions of a single bubble, the bubbles still interact and move.

We investigate the wake structure and the three-dimensional stability of the two-dimensional von Kármán vortex street developing in the wake of a permeable circular cylinder. The flow through the porous medium, assumed homogenous and isotropic, is described by the Darcy law, with a Navier slip coupling condition at the interface with the pure fluid region. The two-dimensional and steady flow past the cylinder is initially considered. Permeability induces a downstream displacement of the recirculation region, which reduces its dimensions until it eventually disappears. Linear stability analysis shows that the flow is progressively stabilized as permeability increases. We identify a critical value of permeability beyond which the steady wake is linearly stable independently of the Reynolds number. Two-dimensional, time-dependent simulations are then carried out. A progressive downstream displacement of the region of onset of the vortex shedding is observed, together with a decrease in the oscillation frequency. Oscillations of aerodynamic forces are progressively quenched with permeability owing to the downstream displacement of the onset region of the vortex shedding. At the same time, traveling vortices are observed far downstream of the body, in opposition with the impervious case, characterized instead by the formation of two shear layers of opposite vorticity, at very large distances from the body. We perform linearized simulations for the evolution of three-dimensional perturbations on the two-dimensional von Kármán vortex street. The growth rate and the spatial structure of the perturbations are extracted from such linearized dynamics by employing a sparsity-promoting dynamic mode decomposition (SP-DMD). As permeability increases, the unsteady vortex street past the cylinder is progressively stabilized with respect to three-dimensional perturbations until the transition to three-dimensionality is prevented. We identify a critical value of the permeability beyond which the vortex shedding preserves its two-dimensionality, at least in the considered parameters space.

Turbulent bluff body flows exhibit large-scale, low frequency dynamics associated with symmetry breaking in the wake which compromise stability and increase surface pressure drag. Previous tomographic PIV had detailed that these instabilities were associated with the stochastic reorientation of a hairpin featuring a near-base “head” connected to counter-rotating streamwise “tails” extending downstream. To better understand the associated flow physics, a half-axisymmetric bluff body is assessed by means of particle image velocimetry and pressure measurements. By application of proper orthogonal decomposition (POD) and an assessment of spanwise phase difference using a Morlet wavelet analysis, we show that the asymmetry of the wake region is intrinsically linked to a large scale circulation reversal responsible for the switch to the opposing symmetry breaking state. The antiphase relationship across the base is established by propagation of an oblique wave in the cross-stream direction at separation and as a result, the wake becomes twisted and skewed to one side inducing an asymmetric base pressure gradient. The two most energetic modes in the near wake are halved with respect to rectilinear bistable bodies; the first shows a helical topology with lateral asymmetry and the second shows a symmetry preserving condition with two counter rotating vortices at each side. Across the switch, the unsteady second mode briefly characterizes the wake. The associated parallel shedding regime with reduced asymmetry promotes axial motion (bubble pumping) which is coupled to an optimal, low drag condition.

In this paper, we study internal wave focusing in a trapezoidal domain with one moving boundary. Using linear theory, we construct an exact analytic solution for the case of ideal uniformly stratified Boussinesq fluid, which is appropriate for developing weakly nonlinear theory. This analytical solution is compared against the results of direct numerical simulations performed with the help of the spectral element method. It is shown that the nested structure of wave beams in the ideal-fluid solution is consistent with the peculiarities of the wave-beam profiles obtained in weakly viscous numerical simulations performed in a range of Stokes numbers covering three orders of magnitude beyond the typical experimental values. Finally, we explore the role of the shape of the wave generator on the instantaneous profiles and envelopes of the wave beams.

In this paper, systematical experiments are carried out to study the distinct behavior of a buoyant cavitation bubble near a vertical rigid boundary. Under the combined influence of gravity and the rigid boundary, the bubble centroid migrates rapidly when the bubble completely collapses, and a microjet of intermediate strength subsequently penetrates the bubble in the same inclined direction. By recalling the nondimensional form of the Kelvin impulses, or the pressure anisotropy parameters, we analytically predict the angle between the jet and the horizontal direction at different experimental conditions. We further successfully establish the scaling law of the jet velocity by denoting the displacement of the bubble centroid as the characteristic length scale. The findings of this study contribute to our understanding of the nonspherical cavitation bubble dynamics under the simultaneous influence of multiple factors.

Diffusion-driven flow is a boundary layer flow that results from the combined influence of gravity and diffusion, which exists in density-stratified fluids whenever a gravitational field is not parallel to the solid boundary. In this paper, we investigate the unsteady diffusion-driven flows that emerge in a parallel-plate channel domain with a linear density stratification. We first compute the time-dependent diffusion-driven flows and perturbed density field using eigenfunction expansions under the Boussinesq approximation. In channel domain, the unsteady flow converges to a steady-state solution either monotonically or nonmonotonically (highly oscillatory), depending on the relation between the Schmidt number and the nondimensionalized stratified scalar diffusivity, while the flow in the half-space inclined plane problem exhibits oscillatory convergence for all parameters. To validate the Boussinesq approximation, we propose the quasi-Boussinesq approximation, which includes transverse density variation in the inertial term. Numerical solutions show that the relative difference between the Boussinesq and quasi-Boussinesq approximations is uniformly small. We also study the mixing of a passive tracer induced by the advection of the unsteady diffusion-driven flow and present the series representation of the time-dependent effective diffusion coefficient. For small Schmidt numbers, the effective diffusion coefficient induced by the unsteady flow solution can oscillate with an amplitude larger than the effective diffusion coefficient induced by the long-time-limiting steady-state flow. Interestingly, the unsteady flow solution can reduce the time-dependent effective diffusion coefficient temporally in some parameter regimes, below even that produced by pure molecular diffusion in the absence of a flow. However, at long times, the effective diffusion is significantly enhanced for large Péclet numbers.