Search citation statements
Paper Sections
Citation Types
Year Published
Publication Types
Relationship
Authors
Journals
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.
The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared with diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is the generalized Taylor dispersion theory. In contrast, the dynamics and transport in orientation space remains less developed. In this work we develop a rotational Taylor dispersion theory that characterizes the long-time orientational transport of a spheroidal particle in linear flows that is constrained to rotate in the velocity-gradient plane. Similar to Taylor dispersion in position space, the orientational distribution of axisymmetric particles in linear flows at long times satisfies an effective advection–diffusion equation in orientation space. Using this framework, we then calculate the long-time average angular velocity and dispersion coefficient for both simple shear and extensional flows. Analytic expressions for the transport coefficients are derived in several asymptotic limits including nearly spherical particles, weak flow and strong flow. Our analysis shows that at long times the effective rotational dispersion is enhanced in simple shear and suppressed in extensional flow. The asymptotic solutions agree with full numerical solutions of the derived macrotransport equations and results from Brownian dynamics simulations. Our results show that the interplay between flow-induced rotations and Brownian diffusion can fundamentally change the long-time transport dynamics.
The study of diffusion in complex confined environments has received great attention in the field of condensed matter physics. The emergence of colloidal systems provides an excellent experimental model system for the quantitative study of the confined diffusion of microscopic particles. When the shape of colloidal particles changes from spherical to ellipsoidal, the system exhibits anisotropic diffusion dynamics. Recent studies have found that rough surfaces, another important physical parameter of colloids, can lead to unusual rotational dynamics in spherical colloidal systems. However, due to the lack of a suitable experimental system, little is known about the effect of rough surfaces on the confined diffusion of ellipsoidal colloidal particles. In this paper, rough colloidal sphere, rough colloidal ellipsoid and smooth colloidal ellipsoid are prepared, and then monolayer colloidal samples are prepared to study the confined diffusion of these two types of ellipsoids in a dense packing of the rough sphere colloids. By calculating the mean square displacement, intermediate self-scattering function, and orientation correlation function of the ellipsoids, we quantitatively characterized the diffusion dynamics of rough and smooth ellipsoids in varying concentrations of rough spheres. The results indicate that the translational and rotational diffusion of both rough and smooth ellipsoids slow down as the concentration of rough spheres increases. This is due to the confinement of the ellipsoid by the surrounding spheres. At low stacking fractions of spheres, smooth and rough ellipsoids show similar translational and rotational diffusion. However, as the stacking fraction of spheres increases, the advection diffusion of rough and smooth ellipsoids differs significantly. The advection diffusion of rough ellipsoids is significantly slower than that of smooth ellipsoids. This is because the rough surface strongly inhibits rotation, meaning that the rotational diffusion of the rough ellipsoid is significantly slower than that of the smooth ellipsoid. By extracting the diffusion coefficients for translation and rotation from the ellipsoid's long-time mean-square displacements, we found that at Φ = 0.60 and 0.65, the diffusion coefficients of rough ellipsoids are smaller than those of smooth ellipsoids. The translational diffusion coefficient of the rough ellipsoid is notably smaller than that of the smooth ellipsoid. However, the rotation diffusion coefficient of the rough ellipsoid does not significantly differ from that of the smooth ellipsoid. This suggests that rough surfaces primarily impact translational diffusion, strongly suppressing the translational diffusion of the ellipsoid. By calculating the displacement probability distribution for ellipsoidal motion, we found that at Φ = 0.65, the rough ellipsoid's translational displacements have a relatively narrow distribution. This suggests that the particles' translational motion is suppressed by the rough surface. However, the distributions of rotation displacement for both are very similar, indicating that the rough surface has less impact on particle rotation. At Φ = 0.74, the rough surface suppresses both the translation and rotation of the ellipsoid, resulting in a narrower displacement distribution compared to the smooth ellipsoid. These findings suggest that rough surfaces significantly impede ellipsoidal diffusion, with effects on translational and rotational motions not occurring simultaneously. This study marks a significant advancement in understanding the role of rough surfaces of colloidal particles in confined diffusion and provides an experimental basis for explaining the diffusion laws of rough materials.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
customersupport@researchsolutions.com
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.
Copyright © 2025 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.