Flow-induced Diffusion Research Articles

Flow-induced diffusion in a packed lattice of squirmers – ERRATUM

Flow-induced diffusion in a packed lattice of squirmers – ERRATUM

Flow-induced diffusion in a packed lattice of squirmers

Mass transport in suspensions of swimming microorganisms is one of the most important factors for the colonisation and growth of microorganisms. Hydrodynamic interactions among swimming microorganisms play an important role in mass transport, especially in highly concentrated suspensions. To elucidate the influence of highly concentrated cells on mass transport, we numerically simulated mass transport in lattices of squirmers that were fixed in space and oriented in the same direction. The effects of different volume fractions, Péclet numbers ( $Pe$ ) and lattice configurations on mass transport were quantified by tracking Lagrangian material points that move with background flow with Brownian diffusivity. Although the flow field became periodic in space and each streamline basically extended in one direction, the motion of tracer particles became diffusive over long durations due to Brownian motion and cross-flows. Flow-induced diffusion was anisotropic and significantly enhanced over Brownian diffusion in the longitudinal direction. We also investigated mass transport in random configurations of squirmers to reproduce more general conditions. Similar enhanced diffusion was also observed in the random configurations, indicating that the flow-induced diffusion appears regardless of the configurations. The present flow-induced diffusion did not follow $Pe$ dependency of the conventional Taylor dispersion due to the cross-flows. The time and velocity scales were proposed, which enabled us to predict the flow-induced diffusivity from the data of the flow field and Brownian diffusivity without solving the mass conservation equation. The findings reported here improve our understanding of the transport phenomena in packed suspensions of swimming microorganisms.

On Mathematical Analysis of Active Drug Transport Coupled With Flow-Induced Diffusion in Blood Vessels.

Blood vessels are flow-induced diffusive molecular channels equipped with transport mechanisms across their walls for conveying substances between the organs in the body. Mathematical modeling of the blood vessel as a molecular transport channel can be used for the characterization of the underlying processes and higher-level functions in the circulatory system. Besides, the mathematical model can be utilized for designing and realizing nano-scale molecular communication systems for healthcare applications including drug delivery systems. In this paper, a continuous-time Markov chain framework is proposed to simply model active transport mechanisms e.g. transcytosis, across the single-layered endothelial cells building the inner vessel wall. Correspondingly, a general homogeneous boundary condition over the vessel wall is introduced. Coupled with the derived boundary condition, the flow-induced diffusion problem in an ideal vessel structure with a cylindrical shape is accurately formulated which takes into account variation in all three dimensions. The corresponding concentration Green's function is analytically derived in terms of a convergent infinite series. Particle-based simulation results confirm the proposed analysis. Also, the effects of system parameters on the concentration Green's function are examined.

On Flow-Induced Diffusive Mobile Molecular Communication: First Hitting Time and Performance Analysis

This paper investigates the problem of flow-induced diffusive molecular communication under various mobility conditions, such as: 1) both transmitter (TX) and receiver (RX) nanomachines are mobile; 2) TX is mobile and RX is fixed; and 3) TX is fixed and RX is mobile. In particular, a 1-D environment with a point TX and a fully absorbing point RX is considered. Closed-form expressions for the probability density function (PDF) of the first hitting time under the aforementioned mobile scenarios are derived, by characterizing the movement of the nanomachines and information molecules using Brownian motion with positive drift. The derived PDF expressions are validated through particle-based simulations. Based on these results, the performance of molecular communication with on-off keying (OOK) modulation in flow-induced diffusive channels is investigated. In particular, closed-form expressions for the probabilities of detection and false alarm with likelihood ratio test (LRT)-based decision rule, probability of error, and the achievable rate in the presence of inter-symbol interference, counting errors, and noise from the other sources are derived. Simulation results are presented to verify the theoretical results and to yield insights into the system performance for different mobility conditions.

Self-fibering growth in the soot-templated CVD coating of silica on mesh for efficient oil/water separation

A comprehensive study of SiO2 grown by chemical vapor deposition is conducted on soot coated copper mesh, from which an excellent superhydrophobic-superoleophilic filter mesh is demonstrated using the structure of nano-fibered network. A dynamical model of “flow-guided dehydration” including the microscopic interplay between “flow-induced diffusion” and dehydration is presented. Furthermore, we present a device based on tubular separator to purify oily wastewater that is very much like tap-water delivering in daily life, which does not cause the problem of water blockage.

Normal Inverse Gaussian Approximation for Arrival Time Difference in Flow-Induced Molecular Communications

In this paper, we consider molecular communications in one-dimensional flow-induced diffusive channels with a perfectly absorbing receiver. In such channels, the random propagation delay, until the molecules are absorbed, follows an inverse Gaussian (IG) distribution and is referred to as first hitting time. Knowing the distribution for the difference of the first hitting times of two molecules is very important if the information is encoded by a limited set of molecules and the receiver exploits their arrival time and/or order. Hence, we propose a moment matching approximation by a normal IG (NIG) distribution and we derive an expression for the asymptotic tail probability. Numerical evaluations show that the NIG approximation matches very well with the exact solution obtained by numerical convolution of the IG density functions. Moreover, the asymptotic tail probability outperforms state-of-the-art tail approximations.

Dynamics of comb-of-comb-network polymers in random layered flows.

We analyze the dynamics of comb-of-comb-network polymers in the presence of external random flows. The dynamics of such structures is evaluated through relevant physical quantities, viz., average square displacement (ASD) and the velocity autocorrelation function (VACF). We focus on comparing the dynamics of the comb-of-comb network with the linear polymer. The present work displays an anomalous diffusive behavior of this flexible network in the random layered flows. The effect of the polymer topology on the dynamics is analyzed by varying the number of generations and branch lengths in these networks. In addition, we investigate the influence of external flow on the dynamics by varying flow parameters, like the flow exponent α and flow strength W_{α}. Our analysis highlights two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The anomalous long-time dynamics is governed by the temporal exponent ν of ASD, viz., ν=2-α/2. Compared to a linear polymer, the comb-of-comb network shows a shorter crossover time (from the subdiffusive to superdiffusive regime) but a reduced magnitude of ASD. Our theory displays an anomalous VACF in the random layered flows that scales as t^{-α/2}. We show that the network with greater total mass moves faster.

Force-induced diffusion in suspensions of hydrodynamically interacting colloids

We study the influence of hydrodynamic, thermodynamic and interparticle forces on the diffusive motion of a Brownian probe driven by a constant external force through a dilute colloidal dispersion. The influence of these microscopic forces on equilibrium self-diffusivity (passive microrheology) is well known: all three act to hinder the short- and long-time self-diffusion. Here, via pair-Smoluchowski theory, we explore their influence on self-diffusion in a flowing suspension, where particles and fluid have been set into motion by an externally forced probe (active microrheology), giving rise to non-equilibrium flow-induced diffusion. The probe’s motion entrains background particles as it travels through the bath, deforming the equilibrium suspension microstructure. The shape and extent of microstructural distortion is set by the relative strength of the external force $F^{\mathit{ext}}$ to the entropic restoring force $kT/a_{\mathit{th}}$ of the bath particles, defining a Péclet number $\mathit{Pe}\equiv F^{\mathit{ext}}/(2kT/a_{\mathit{th}})$; and also by the strength of hydrodynamic interactions, set by the range of interparticle repulsion ${\it\kappa}=(a_{\mathit{th}}-a)/a$, where $kT$ is the thermal energy and $a_{\mathit{th}}$ and $a$ are the thermodynamic and hydrodynamic sizes of the particles, respectively. We find that in the presence of flow, the same forces that hinder equilibrium diffusion now enhance it, with diffusive anisotropy set by the range of interparticle repulsion ${\it\kappa}$. A transition from hindered to enhanced diffusion occurs when diffusive and advective forces balance, $\mathit{Pe}\sim 1$, where the exact value is a sensitive function of the strength of hydrodynamics, ${\it\kappa}$. We find that the hindered to enhanced transition straddles two transport regimes: in hindered diffusion, stochastic forces in the presence of other bath particles produce deterministic displacements (Brownian drift) at the expense of a maximal random walk. In enhanced diffusion, driving the probe with a deterministic force through an initially random suspension leads to fluctuations in the duration of probe–bath particle entrainment, giving rise to enhanced, flow-induced diffusion. The force-induced diffusion is anisotropic for all $\mathit{Pe}$, scaling as $D\sim \mathit{Pe}^{2}$ in all directions for weak forcing, regardless of the strength of hydrodynamic interactions. When probe forcing is strong, $D\sim \mathit{Pe}$ in all directions in the absence of hydrodynamic interactions, but the picture changes qualitatively as hydrodynamic interactions grow strong. In this nonlinear regime, microstructural asymmetry weakens while the anisotropy of the force-induced diffusion tensor increases dramatically. This behaviour owes its origins to the approach toward Stokes flow reversibility, where diffusion along the direction of probe force scales advectively while transverse diffusion must vanish.

The impact of probe size on measurements of diffusion in active microrheology.

We present a framework to elucidate the influence of polydispersity on flow-induced diffusion in active microrheology. A colloidal probe particle is driven through a suspension of hydrodynamically interacting background particles, where the probe may be larger or smaller than the bath particles. The thermodynamic size of the particles may be greater than their hydrodynamic size; the hydrodynamic sizes can be identical with thermodynamic sizes that differ, or vice versa, or a combination of both. The diffusive behavior is set entirely and dually by the proximity with which two particles can approach one another, and by the extent to which this minimum approach distance is occupied by the hydrodynamic size of the forced particle. We find that reducing the size of the probe reduces flow-induced diffusion when hydrodynamic interactions are weak but increases flow-induced diffusion when hydrodynamic interactions are strong-regardless of the strength of external forcing. This behavior owes its origins to a rich evolution of the dominance of hydrodynamic and entropic forces with changes in the relative hydrodynamic and thermodynamic sizes of the particles.

Dynamics of generalized Gaussian polymeric structures in random layered flows.

We develop a formalism for the dynamics of a flexible branched polymer with arbitrary topology in the presence of random flows. This is achieved by employing the generalized Gaussian structure (GGS) approach and the Matheron-de Marsily model for the random layered flow. The expression for the average square displacement (ASD) of the center of mass of the GGS is obtained in such flow. The averaging is done over both the thermal noise and the external random flow. Although the formalism is valid for branched polymers with various complex topologies, we mainly focus here on the dynamics of the flexible star and dendrimer. We analyze the effect of the topology (the number and length of branches for stars and the number of generations for dendrimers) on the dynamics under the influence of external flow, which is characterized by their root-mean-square velocity, persistence flow length, and flow exponent α. Our analysis shows two anomalous power-law regimes, viz., subdiffusive (intermediate-time polymer stretching and flow-induced diffusion) and superdiffusive (long-time flow-induced diffusion). The influence of the topology of the GGS is unraveled in the intermediate-time regime, while the long-time regime is only weakly dependent on the topology of the polymer. With the decrease in the value of α, the magnitude of the ASD decreases, while the temporal exponent of the ASD increases in both the time regimes. Also there is an increase in both the magnitude of the ASD and the crossover time (from the subdiffusive to the superdiffusive regime) with an increase in the total mass of the polymeric structure.

Shear-induced diffusion of red blood cells in a semi-dilute suspension

AbstractThe diffusion of red blood cells (RBCs) in blood is important to the physiology and pathology of the cardiovascular system. In this study, we investigate flow-induced diffusion of RBCs in a semi-dilute system by calculating the pairwise interactions between RBCs in simple shear flow. A capsule with a hyperelastic membrane was used to model an RBC. Its deformation was resolved using the finite element method, whereas fluid motion inside and outside the RBC was solved using the boundary element method. The results show that shear-induced RBC diffusion is significantly anisotropic, i.e. the velocity gradient direction component is larger than the vorticity direction. We also found that the motion of RBCs during the interaction is strongly dependent on the viscosity ratio of the internal to external fluid, and the diffusivity decreases monotonically as the viscosity ratio increases. The scaling argument also suggests that the diffusivity is proportional to the shear rate and haematocrit, if the suspension is in a semi-dilute environment and the capillary number is invariant. These fundamental findings are useful to understand transport phenomena in blood flow.

Molecular Motion in a Spreading Precursor Film

Spreading of a polymer drop on a solid substrate was monitored with molecular resolution. Three characteristic rates, i.e., the spreading rate of the precursor film D(spread)=(3.9+/-0.2)x10(3) nm(2)/s, the flow-induced diffusion rate of molecules within the film D(induced)=1.3+/-0.1 nm(2)/s, and the thermal diffusion coefficient of single molecules D(therm)</=0.10+/-0.03 nm(2)/s, were independently measured. Since D(spread)>>D(induced), the plug flow of polymer chains was identified as the main mass-transport mechanism of spreading with an insignificant contribution from the molecular diffusion.