Macrotransport theory for diffusiophoretic colloids and chemotactic microorganisms

Chu, Henry; Garoff, Stephen; Tilton, Robert D.; Khair, Aditya S.

doi:10.1017/jfm.2021.322

Cited by 16 publications

(41 citation statements)

References 79 publications

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“…To model the transport of chemotactic/diffusiophoretic colloids under an imposed hydrodynamic flow, one must solve the following set of coupled solute and colloid advection–diffusion–reaction equations 10–19,21,24,29–36 where C is the colloid concentration, D s is the constant, intrinsic solute diffusivity, Γ is the colloid decay rate constant††We focus on inert ( Γ = 0) or decaying colloids ( Γ > 0), which are the applicable regimes of the key macrotransport eqn (3) of this work. Eqn (3) may not be applicable to replicating colloids, Γ < 0.…”

Section: Introductionmentioning

confidence: 99%

“…24,41 However, to demonstrate the key physics of chemotactic/diffusiophoretic transport, here we proceed with our discussion in terms of eqn (1) and (2), and we refer readers to our previous work for the justifications of adopting eqn (1) and (2). 36 In eqn (1) and (2), vector notation is used to represent two or higher spatial dimensions of the transport. Solving these equations numerically is in general very costly because of the separation of time and length scales in the system.…”

Section: Introductionmentioning

confidence: 99%

“…To model the two-dimensional chemotactic/diffusiophoretic colloid transport in a circular tube and circumvent this high computational cost, recently we have developed a reduced-order, one-dimensional “macrotransport” equation for the colloid evolution 36 ‡‡The macrotransport equation is readily generalizable to channels of other geometries. This is discussed in Section 5 and in ref.…”

Section: Introductionmentioning

confidence: 99%

“…This is discussed in Section 5 and in ref. 36.This is accompanied by the familiar macrotransport equation derived by Taylor for the solute 42 where D s,Taylor and D c,Taylor are the Taylor dispersion coefficients for the solute and colloid, respectively; R is the radius of the tube; u z is the axial component of the chemotactic/diffusiophoretic flow; the steady, pressure-driven laminar flow v is directed along the axial direction z ; and overbar denotes a cross-sectional averaged quantity with r and θ being the radial and angular coordinate, respectively. Eqn (3) and (4) were derived by an asymptotic analysis of the long-time transport of the solute and the colloids.…”

Section: Introductionmentioning

confidence: 99%

“…The coupling between the hydrodynamic flow and radial diffusion gives rise to an enhanced axial diffusion, or Taylor dispersion, 42,43 In our previous work, we have demonstrated that the macrotransport equations recover the two-dimensional transport accurately with O (10 3 ) times less computational runtime. 36…”

Section: Introductionmentioning

confidence: 99%

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Section: Introductionmentioning

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confidence: 99%

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confidence: 99%

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confidence: 99%

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Diffusioosmosis-driven dispersion of colloids: a Taylor dispersion analysis with experimental validation

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Diffusiophoresis refers to the movement of colloidal particles in the presence of a concentration gradient of a solute and enables directed motion of colloidal particles in geometries that are inaccessible, such as dead-end pores, without imposing an external field. Previous experimental reports on dead-end pore geometries show that, even in the absence of mean flow, colloidal particles moving through diffusiophoresis exhibit significant dispersion. Existing models of diffusiophoresis are not able to predict the dispersion and thus the comparison between the experiments and the models is largely qualitative. To address these quantitative differences between the experiments and models, we derive an effective one-dimensional equation, similar to a Taylor dispersion analysis, that accounts for the dispersion created by diffusioosmotic flow from the channel sidewalls. We derive the effective dispersion coefficient and validate our results by comparing them with direct numerical simulations. We also compare our model with experiments and obtain quantitative agreement for a wide range of colloidal particle sizes. Our analysis reveals two important conclusions. First, in the absence of mean flow, dispersion is driven by the flow created by diffusioosmotic wall slip such that spreading can be reduced by decreasing the channel wall diffusioosmotic mobility. Second, the model can explain the spreading of colloids in a dead-end pore for a wide range of particle sizes. We note that, while the analysis presented here focuses on a dead-end pore geometry with no mean flow, our theoretical framework is general and can be adapted to other geometries and other background flows.

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Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

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Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang, Hesse & Wang (J. Fluid Mech., vol. 828, 2017, pp. 733–752) have investigated the temporal evolution of moments using the Laplace transform method. Owing to difficulties introduced by the adsorption–desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form that is valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption–desorption condition, based on which higher-order statistics including skewness and kurtosis can be explicitly explored in practice. Also extended is Gill's generalised dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic reactive process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption–desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

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Macrotransport theory for diffusiophoretic colloids and chemotactic microorganisms

Abstract: Abstract

Cited by 16 publications

References 79 publications

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows

Diffusioosmosis-driven dispersion of colloids: a Taylor dispersion analysis with experimental validation

Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

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