We examine the problem of determining the particle-phase velocity variance and rhe-ology of sheared gas-solid suspensions at small Reynolds numbers and finite Stokes numbers. Our numerical simulations take into account the Stokes flow interactions among particles except for pairs of particles with a minimum gap width comparable to or smaller than the mean free path of the gas molecules for which the usual lubrication approximation breaks down and particle collisions occur in a finite time. The simulation results are compared to the predictions of two theories. The first is an asymptotic theory for large Stokes number St and nearly elastic collisions, i.e. St [Gt ] 1 and 0 ≤ 1 - e [Lt ] 1, e being the coefficient of restitution. In this limit, the particle velocity distribution is close to an isotropic Maxwellian and the velocity variance is determined by equating the energy input in shearing the suspension to the energy dissipation by inelastic collisions and viscous effects. The latter are estimated by solving the Stokes equations of motion in suspensions with the hard-sphere equilibrium spatial and velocity distribution while the shear energy input and energy dissipation by inelastic effects are estimated using the standard granular flow theory (i.e. St = ∞). The second is an approximate theory based on Grad's moments method for which St and 1 – e are O(1). The two theories agree well with each other at higher values of volume fraction ϕ of particles over a surprisingly large range of values of St. For smaller ϕ however, the two theories deviate significantly except at sufficiently large St. A detailed comparison shows that the predictions of the approximate theory based on Grad's method are in excellent agreement with the results of numerical simulations.
Kinetic theory and numerical simulations are used to explore the dynamics of a dilute gas–solid suspension subject to simple shear flow. The particles experience a Stokes drag force and undergo solid-body interparticle collisions. Two qualitatively different steady-state behaviours are possible: an ignited state, in which the variance of the particle velocity is very large; and a quenched state, in which most of the particles follow the local fluid velocity. Theoretical results for the ignited state are obtained by perturbing from a Maxwell distribution, while predictions for the quenched state result from consideration of the collision of particles that initially move with the fluid. A composite theory, which includes effects of collisions driven by both the mean shear and the velocity fluctuations, predicts the existence of multiple steady states. Dynamic simulations and calculations using the direct-simulation Monte Carlo method confirm the result that, for certain volume fractions and shear rates, either the quenched or ignited state can be achieved depending on the initial velocity variance.Simulations are also performed for particles experiencing a nonlinear drag force. Both the theory of rapid granular flow, which neglects drag, and our theory for the ignited state with linear drag predict that the particle velocity variance can grow without bound as ϕ → 0, where ϕ is the volume fraction. The nonlinear drag force eliminates the divergence and leads to a particle velocity variance that will always decrease with decreasing volume fraction in the limit ϕ → 0.
Restrained molecular dynamics simulations were performed to study the interaction forces of a protein with the self-assembled monolayers (SAMs) of S(CH2)4(EG)4OH, S(CH2)11OH, and S(CH2)11CH3 in the presence of water molecules. The force-distance curves were calculated by fixing the center of mass of the protein at several separation distances from the SAM surface. Simulation results show that the relative strength of repulsive force acting on the protein is in the decreasing order of OEG-SAMs > OH-SAMs > CH3-SAMs. The force contributions from SAMs and water molecules, the structural and dynamic behavior of hydration water, and the flexibility and conformation state of SAMs were also examined to study how water structure at the interface and SAM flexibility affect the forces exerted on the protein. Results show that a tightly bound water layer adjacent to the OEG-SAMs is mainly responsible for the large repulsive hydration force.
A ring-shaped stain is frequently left on a substrate by a drying drop containing colloids as a result of contact line pinning and outward flow. In this work, however, different patterns are observed for drying drops containing small solutes or polymers on various hydrophilic substrates. Depending on the surface activity of solutes and the contact angle hysteresis (CAH) of substrates, the pattern of the evaporation stain varies, including a concentrated stain, a ringlike deposit, and a combined structure. For small surface-inactive solutes, the concentrated stain is formed on substrates with weak CAH, for example, copper sulfate solution on silica glass. On the contrary, a ringlike deposit is developed on substrates with strong CAH, for example, a copper sulfate solution on graphite. For surface-active solutes, however, the wetting property can be significantly altered and the ringlike stain is always visible, for example, Brij-35 solution on polycarbonate. For a mixture of surface-active and surface-inactive solutes, a combined pattern of a ringlike and concentrated stain can appear. For various polymer solutions on polycarbonate, similar results are observed. Concentrated stains are formed for weak CAH such as sodium polysulfonate, and ring-shaped patterns are developed for strong CAH such as poly(vinyl pyrrolidone). The stain pattern is actually determined by the competition between the time scales associated with contact line retreat and solute precipitation. The suppression of the coffee-ring effect can thus be acquired by the control of CAH.
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