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Register a new userGeneralized Taylor dispersion for translationally invariant microfluidic systems
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We consider Taylor dispersion for tracer particles in micro-fluidic planar channels with strong confinement. In this context, the channel walls modify the local diffusivity tensor and also interactions between the tracer particles and the walls become important. We provide a simple and general formula for the effective diffusion constant along the channel as well as the first non-trivial finite time correction for arbitrary flows along the channel, arbitrary interaction potentials with the walls and arbitrary expressions for the diffusion tensor. The formula are in particular amenable to a straightforward numerical implementation, rendering them extremely useful for comparison with experiments. We present a number of applications, notably for systems which have parabolically varying diffusivity profiles, to systems with attractive interactions with the walls as well as electroosmotic flows between plates with differing surface charges within the Debye-Huckel approximation.
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Particles transported in fluid flows, such as cells, polymers, or nanorods, are rarely spherical. In this study, we numerically and theoretically investigate the dispersion of an initially localized patch of passive elongated Brownian particles constrained to one degree of rotational freedom in a two-dimensional Poiseuille flow, demonstrating that elongated particles exhibit an enhanced longitudinal dispersion. In a shear flow, the rods translate due to advection and diffusion and rotate due to rotational diffusion and their classical Jefferys orbit. The magnitude of the enhanced dispersion depends on the particles aspect ratio and the relative importance of its shear-induced rotational advection and rotational diffusivity. When rotational diffusion dominates, we recover the classical Taylor dispersion result for the longitudinal spreading rate using an orientationally averaged translational diffusivity for the rods. However, in the high-shear limit, the rods tend to align with the flow and ultimately disperse more due to their anisotropic diffusivities. Results from our Monte Carlo simulations of the particle dispersion are captured remarkably well by a simple theory inspired by Taylors original work. For long times and large Peclet numbers, an effective one-dimensional transport equation is derived with integral expressions for the particles longitudinal transport speed and dispersion coefficient. The enhanced dispersion coefficient can be collapsed along a single curve for particles of high aspect ratio, representing a simple correction factor that extends Taylors original prediction to elongated particles.
In this paper, the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability(RTI, KHI and RTKHI, respectively) system is investigated using a multiple-relaxation-time discrete Boltzmann model. Both the morphological boundary length and thermodynamic nonequilibrium (TNE) strength are introduced to probe the complex configurations and kinetic processes. In the simulations, RTI always plays a major role in the later stage, while the main mechanism in the early stage depends on the comparison of buoyancy and shear strength. It is found that, both the total boundary length $L$ of the condensed temperature field and the mean heat flux strength $D_{3,1}$ can be used to measure the ratio of buoyancy to shear strength, and to quantitatively judge the main mechanism in the early stage of the RTKHI system. Specifically, when KHI (RTI) dominates, $L^{KHI} > L^{RTI}$ ($L^{KHI} < L^{RTI}$), $D_{3,1}^{KHI} > D_{3,1}^{RTI}$ ($D_{3,1}^{KHI} < D_{3,1}^{RTI}$); when KHI and RTI are balanced, $L^{KHI} = L^{RTI}$, $D_{3,1}^{KHI} = D_{3,1}^{RTI}$. A second sets of findings are as below: For the case where the KHI dominates at earlier time and the RTI dominates at later time, the evolution process can be roughly divided into two stages. Before the transition point of the two stages, $L^{RTKHI}$ initially increases exponentially, and then increases linearly. Hence, the ending point of linear increasing $L^{RTKHI}$ can work as a geometric criterion for discriminating the two stages. The TNE quantity, heat flux strength $D_{3,1}^{RTKHI}$, shows similar behavior. Therefore, the ending point of linear increasing $D_{3,1}^{RTKHI}$ can work as a physical criterion for discriminating the two stages.
Rayleigh-Taylor-instability(RTI) induced flow and mixing are of great importance in both nature and engineering scenarios. To capture the underpinning physics, tracers are introduced to make a supplement to discrete Boltzmann simulation of RTI in compressible flows. Via marking two types of tracers with different colors, the tracer distribution provides a clear boundary of two fluids during the RTI evolution. Fine structures of the flow and thermodynamic nonequilibrium behavior around the interface in a miscible two-fluid system are delineated. Distribution of tracers in its velocity phase space makes a charming pattern showing quite dense information on the flow behavior, which opens a new perspective for analyzing and accessing significantly deep insights into the flow system. RTI mixing is further investigated via tracer defined local mixedness. The appearance of Kelvin-Helmholtz instability is quantitatively captured by mixedness averaged align the direction of the pressure gradient. The role of compressibility and viscosity on mixing are investigated separately, both of which show two-stage effect. The underlying mechanism of the two-stage effect is interpreted as the development of large structures at the initial stage and the generation of small structures at the late stage. At the late stage, for a fixed time, a saturation phenomenon of viscosity is found that further increase of viscosity cannot see an evident decline in mixedness. The mixing statues of heavy and light fluids are not synchronous and the mixing of a RTI system is heterogenous. The results are helpful for understanding the mechanism of flow and mixing induced by RTI.
Investigating translationally invariant qudit spin chains with a low local dimension, we ask what is the best possible tradeoff between the scaling of the entanglement entropy of a large block and the inverse-polynomial scaling of the spectral gap. Restricting ourselves to Hamiltonians with a rewriting interaction, we find the pair-flip model, a family of spin chains with nearest neighbor, translationally invariant, frustration-free interactions, with a very entangled ground state and an inverse-polynomial spectral gap. For a ground state in a particular invariant subspace, the entanglement entropy across a middle cut scales as $log n$ for qubits (it is equivalent to the XXX model), while for qutrits and higher, it scales as $sqrt{n}$. Moreover, we conjecture that this particular ground state can be made unique by adding a small translationally-invariant perturbation that favors neighboring letter pairs, adding a small amount of frustration, while retaining the entropy scaling.
An electrokinetically-driven deterministic lateral displacement (e-DLD) device is proposed for the continuous, two-dimensional fractionation of suspensions in microfluidic platforms. The suspended species are driven through an array of regularly spaced cylindrical posts by applying an electric field across the device. We explore the entire range of orientations of the driving field with respect to the array of obstacles and show that, at specific forcing-angles, particles of different size migrate in different directions, thus enabling continuous, two-dimensional separation. We discuss a number of features observed in the kinetics of the particles, including directional locking and sharp transitions between migration angles upon variations in the direction of the force, that are advantageous for high-resolution two-dimensional separation. A simple model based on individual particle-obstacle interactions accurately describes the migration angle of the particles depending on the orientation of the driving field, and can be used to re-configure driving field depending on the composition of the samples.
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