Multiphase microfluidics: droplets, wetting dynamics and transport in complex media

A distributed-order time fractional derivative model for simulating bimodal sub-diffusion in heterogeneous media

<title>Abstract</title> Diffusion in a "rough" potential parameterized by a reaction coordinate q is analyzed for systems that exhibit a coarse-scale structure with barrier height ΔU and period ℓ, superimposed with fine-scale "roughness" of barrier height ΔU′ and small period ℓ′ ≪ ℓ. Numerical solution of the Smoluchowski equation and analytical predictions identify distinct dynamical regimes as a function of the distance |Δq| = |q − q_E| from the stable equilibrium at q = q_E. The physical diffusivity D, set by dissipative effects, can be rescaled to an effective diffusivity D′ that accounts for the fine-scale roughness. This rescaling is strictly valid when |Δq| &lt; Δq_I ∝ (ΔU′/ℓ′ − ΔU/ℓ). Farther than a critical distance Δq_II ∝ ΔU/ℓ, the coarse-scale barriers control activated transport and the dynamics follow Kramers-like escape with an effective diffusivity D′ inferred from the reaction-coordinate trajectory. Closer to equilibrium, the coarse-scale structure induces two diffusive regimes separated by a crossover at Δq_III ∝ 1/ℓ: an initial regime with approximately constant D′ and a near-equilibrium regime where D′ decreases over time for |Δq| &lt; Δq_III. The effective diffusivity obtained here is sensitive to the estimation method used from time series, which depends solely on the fine-scale energy barrier. These results have implications for activated transport in complex media, including protein folding landscapes, colloidal stabilization, and self-assembly.

Scalable simulation of coupled adsorption and transport of methane in confined complex porous media with density preconditioning

Magnetically directing particles for medical applications requires moving particles through the viscoelastic materials of the body. An understanding of how particle transport proceeds through such materials, and how such transport processes differ from transport through purely viscous materials, is critical for improving and optimizing transport goals. In this chapter we review broad classes of particle surface modifications for enhancing transport through tissues, as well as recent literature on motion through biological polymers, magnetic fields for inducing transport and recent advances in nonspherical particle interactions with biopolymers.

Fractional diffusion equations have been widely used to accurately describe anomalous solute transport in complex media. This paper proposes a local meshless method named the generalized finite difference method (GFDM), to solve a class of multidimensional space fractional diffusion equations (SFDEs) in a finite domain. In the GFDM, the spatial derivative terms are expressed as linear combinations of neighboring-node values with different weighting coefficients using the moving least-square approximation. An explicit formula for the SFDE is then obtained. The numerical solution is achieved by solving a sparse linear system. Four numerical examples are provided to verify the effectiveness of the proposed method. Numerical analysis indicates that the relative errors of prediction results are stable and less than 1% (0.001–1%). The method can also be applied for irregular grids with acceptable accuracy.

Collective effects in atom-light interaction is of great importance for cold-atom-based quantum devices or fundamental studies on light transport in complex media. Here we discuss and compare three different approaches to light scattering by dilute cold atomic ensembles. The first approach is a coupled-dipole model, valid at low intensity, which includes cooperative effects, like superradiance, and other coherent properties. The second one is a random-walk model, which includes classical multiple scattering and neglects coherence effects. The third approach is a crude approximation only based on the attenuation of the excitation beam inside the medium, the so-called "shadow effect". We show that in the case of a low-density sample, the random walk approach is an excellent approximation for steady-state light scattering, and that the shadow effect surprisingly gives rather accurate results at least up to optical depths on the order of 15.

Lattice Boltzmann model for incompressible flows through porous media with time-fractional effects

Diffusion in a "rough" potential parameterized by a reaction coordinate q is relevant to a wide spectrum of problems ranging from protein folding and charge transport in complex media to colloidal stabilization and self-assembly. This work studies the case of a potential having a coarse-scale structure with characteristic energy barrier ΔU and period ℓ and fine-scale "roughness" of magnitude ΔU' ≲ ΔU and small period ℓ' ≪ ℓ. The numerical solution of the Smoluchowski equation and analytical predictions from Kramers theory document distinct regimes at different distances |Δq| = |q - qE| from stable equilibrium at q = qE. The physical diffusivity D prescribed by dissipative effects can be observed farther than a distance |Δq'| ∝ (ΔU'/ℓ' + ΔU/ℓ). Rescaling the physical diffusivity to account for the fine-scale "roughness" is strictly valid when |Δq| < ΔqI ∝ (ΔU'/ℓ' - ΔU/ℓ). Farther than a critical distance ΔqII ∝ ΔU/ℓ, the diffusion process is free of coarse-scale metastable states, which facilitates determining the effective diffusivity D' from the reaction coordinate trajectory. Closer to equilibrium, the coarse-scale structure induces two diffusive regimes: nearly logarithmic evolution for ΔqII > |Δq| > ΔqIII and exponential decay over time for |Δq| < ΔqIII ∝ 1/ℓ. The effective diffusivity derived in this work is sensitive to the coarse- and fine-scale energy barriers and periods and for ℓ'/ℓ → 0 and ΔU'/kBT ≫ 1 agrees closely with mean first-passage time estimates currently employed, which depend solely on the fine-scale energy barrier.