Hydrodynamic instability and flow reduction in polymer brush coated channels.

A polymer brush is a passive medium. At equilibrium the knowledge of its chemical composition and thickness is enough for a full system characterization. However, when the brush is exposed to fluid flow it reveals a much more intriguing nature, in which filamentous protrusions and the way they interact among themselves and with the surrounding fluid are of outmost importance. Here we investigate such a rich behavior via numerical simulations. We focus on the brush hydrodynamic response at low Reynolds numbers, observing a significant fluid flow reduction inside a polymer-brush coated channel. We find that the reduction of the flow inside the channel is significantly larger than what would happen if the brush effect consisted only in reducing the effective channel width. This amplified reduction is understood as being due to the morphological instability of the brush-liquid interface which is shown to have an elastic origin: the mechanical stress acting on the brush due to the imposed flow is partially released by the interface modulation. In turn, this modulation dissipates more energy than a flat interface in the surrounding fluid, causing a reduction of flow velocity. Our results and interpretations provide an explanation for recent experimental measurements.

Surface wave excitations and backflow effect over dense polymer brushes.

Polymer brushes are being increasingly used to tailor surface physicochemistry for diverse applications such as wetting, adhesion of biological objects, implantable devices and much more. Here we perform Dissipative Particle Dynamics simulations to study the behaviour of dense polymer brushes under flow in a slit-pore channel. We discover that the system displays flow inversion at the brush interface for several disconnected ranges of the imposed flow. We associate such phenomenon to collective polymer dynamics: a wave propagating on the brush surface. The relation between the wavelength, the amplitude and the propagation speed of the flow-generated wave is consistent with the solution of the Stokes equations when an imposed traveling wave is assumed as the boundary condition (the famous Taylor's swimmer).

Universality classes for unstable crystal growth.

Universality has been a key concept for the classification of equilibrium critical phenomena, allowing associations among different physical processes and models. When dealing with nonequilibrium problems, however, the distinction in universality classes is not as clear and few are the examples, such as phase separation and kinetic roughening, for which universality has allowed to classify results in a general spirit. Here we focus on an out-of-equilibrium case, unstable crystal growth, lying in between phase ordering and pattern formation. We consider a well-established 2+1-dimensional family of continuum nonlinear equations for the local height h(x,t) of a crystal surface having the general form ∂_{t}h(x,t)=-∇·[j(∇h)+∇(∇^{2}h)]: j(∇h) is an arbitrary function, which is linear for small ∇h, and whose structure expresses instabilities which lead to the formation of pyramidlike structures of planar size L and height H. Our task is the choice and calculation of the quantities that can operate as critical exponents, together with the discussion of what is relevant or not to the definition of our universality class. These aims are achieved by means of a perturbative, multiscale analysis of our model, leading to phase diffusion equations whose diffusion coefficients encapsulate all relevant information on dynamics. We identify two critical exponents: (i) the coarsening exponent, n, controlling the increase in time of the typical size of the pattern, L∼t^{n}; (ii) the exponent ß, controlling the increase in time of the typical slope of the pattern, M∼t^{ß}, where M≈H/L. Our study reveals that there are only two different universality classes, according to the presence (n=1/3, ß=0) or the absence (n=1/4, ß>0) of faceting. The symmetry of the pattern, as well as the symmetry of the surface mass current j(∇h) and its precise functional form, is irrelevant. Our analysis seems to support the idea that also space dimensionality is irrelevant.

Coarsening scenarios in unstable crystal growth.

Crystal surfaces may undergo thermodynamical as well as kinetic, out-of-equilibrium instabilities. We consider the case of mound and pyramid formation, a common phenomenon in crystal growth and a long-standing problem in the field of pattern formation and coarsening dynamics. We are finally able to attack the problem analytically and get rigorous results. Three dynamical scenarios are possible: perpetual coarsening, interrupted coarsening, and no coarsening. In the perpetual coarsening scenario, mound size increases in time as L~t(n), where the coarsening exponent is n=1/3 when faceting occurs, otherwise n=1/4.