Long-lived and unstable modes of Brownian suspensions in microchannels

We investigate the stability of the pressure-driven, low-Reynolds flow of Brownian suspensions with spherical particles in microchannels. We find two general families of stable/unstable modes: (i) degenerate modes with symmetric and anti-symmetric patterns; (ii) single modes that are either symmetric or anti-symmetric. The concentration profiles of degenerate modes have strong peaks near the channel walls, while single modes diminish there. Once excited, both families would be detectable through high-speed imaging. We find that unstable modes occur in concentrated suspensions whose velocity profiles are sufficiently flattened near the channel centreline. The patterns of growing unstable modes suggest that they are triggered due to Brownian migration of particles between the central bulk that moves with an almost constant velocity, and highly-sheared low-velocity region near the wall. Modes are amplified because shear-induced diffusion cannot efficiently disperse particles from the cavities of the perturbed velocity field.Comment: 11 pages, accepted for publication in Journal of Fluid Mechanic

Normal oscillatory modes of rotating orthotropic disks

Knowlegde on wave and oscillations theoryRadial eigenfunctions and mode shapes for rotating isotropic and orthotropic disks. The ratio of the outer radius to the inner radius of the disk is 10Componente Curricular::Educação Superior::Ciências Exatas e da Terra::Físic

Molecular Dynamics Simulation of the Adsorption and Aggregation of Ionic Surfactants at Liquid–Solid Interfaces

Structure of surfactants adsorbed on solid surfaces is a key knowledge in various technologies and applications. It is widely accepted in the literature that the surface–surfactant headgroup electrostatic interaction is a major driving force of adsorption of ionic surfactants on charged substrates. Our result shows that the adsorption of surfactants as monomers is driven by both electrostatic and nonelectrostatic interactions. Further adsorption of surfactants in aggregates is essentially driven by the tail–tail interaction. To a great extent, the substrate–tail interaction determines the structures of the adsorbed surfactant aggregates. Water and counterions influence the headgroup–substrate and tail–substrate interactions. We investigate two vastly different surfactants and substrates by molecular dynamics simulations: (1) SDS on alumina (SDS–Al₂O₃), and (2) CTAB on silica (CTAB–SiO₂). We study the adsorption of a single surfactant at the solid surface by the density profiles and free energy of adsorption. In the SDS–Al₂O₃ system, we analyze the free energy of adsorption on the substrate covered by aggregates of different sizes. We examine the configurations of surfactants and the distribution of water and ions at the liquid–solid interface as the number of adsorbed molecules on the substrate increases. In the SDS–Al₂O₃ system, the headgroup adsorption is mediated by the Na⁺ counterions; the adsorbed water molecules may be displaced by the surfactant headgroup but unlikely by the hydrocarbon tails. As a function of the surfactant adsorption, we observe single surfactants, aggregates of different morphologies, and bilayers. The CTAB–SiO₂ system combines both electrostatic attraction of the surfactant headgroup and affinity for the surfactant’s hydrocarbon tail. At low surfactant adsorption, aggregates and single surfactant molecules lie on the substrate; hemimicelles form at intermediate adsorption; and micelles form at high surfactant adsorption. Our results agree with experimental observations and indicate two different surfactant adsorption mechanisms where the tail–tail and tail–substrate interactions play a fundamental role