Loading...
7 results
Search Results
Now showing 1 - 7 of 7
- Maximum thermodynamic power coefficient of a wind turbinePublication . Tavares, Jose; Patricio, PedroAccording to the centenary Betz-Joukowsky law, the power extracted from a wind turbine inopen flow cannot exceed 16/27 of the wind transported kinetic energy rate. This limit is usuallyinterpreted as an absolute theoretical upper bound for the power coefficient of all wind turbines,but it was derived in the special case of incompressible fluids. Following the same steps of Betzclassical derivation, we model the turbine as an actuator disk in a one dimensional fluid flowbut consider the general case of a compressible reversible fluid, such as air. In doing so, we areobliged to use not only the laws of mechanics but also and explicitly the laws of thermodynamics.We show that the power coefficient depends on the inlet wind Mach numberM0,andthatitsmaximum value exceeds the Betz-Joukowsky limit. We have developed a series expansion forthe maximum power coefficient in powers of the Mach number M0that unifies all the cases (compressible and incompressible) in the same simple expression: 𝜂max= 16∕27 + 8∕243M20.
- Smoluchowski equations for linker-mediated irreversible aggregationPublication . Tavares, Jose; Antunes, Goncalo C.; Dias, Cristóvão; da Gama, M. M. Telo; Araujo, NunoWe developed a generalized Smoluchowski framework to study linker-mediated aggregation, where linkers and particles are explicitly taken into account. We assume that the bonds between linkers and particles are irreversible, and that clustering occurs through limited diffusion aggregation. The kernel is chosen by analogy with single-component diffusive aggregation but the clusters are distinguished by their number of particles and linkers. We found that the dynamics depends on three relevant factors, all tunable experimentally: (i) the ratio of the diffusion coefficients of particles and linkers; (ii) the relative number of particles and linkers; and (iii) the maximum number of linkers that may bond to a single particle. To solve the Smoluchoski equations analytically we employ a scaling hypothesis that renders the fraction of bondable sites of a cluster independent of the size of the cluster, at each instant. We perform numerical simulations of the corresponding lattice model to test this hypothesis. We obtain results for the asymptotic limit, and the time evolution of the bonding probabilities and the size distribution of the clusters. These findings are in agreement with experimental results reported in the literature and shed light on unexplained experimental observations.
- Percolation in binary mixtures of linkers and particles: Chaining vs branchingPublication . Gouveia, M.; Dias, Cristóvão; Tavares, JoseEquilibrium gels of colloidal particles can be realized through the introduction of a second species, a linker that mediates the bonds between colloids. A gel forming binary mixture whose linkers can self-assemble into linear chains while still promoting the aggregation of particles is considered in this work. The particles are patchy particles with f(C) patches of type C and the linkers are patchy particles with 2 patches of type A and f(B) patches of type B. The bonds between patches of type A (AA bonds) promote the formation of linear chains of linkers. Two different ways (model A and model B) of bonding the linkers to the particles-or inducing branching-are studied. In model A, there is a competition between chaining and branching, since the bonding between linkers and particles takes place through AC bonds only. In model B, the linkers aggregate to particles through bonds BC only, making chaining and branching independent. The percolation behavior of these two models is studied in detail, employing a generalized Flory-Stockmayer theory and Monte Carlo simulations. The self-assembly of linkers into chains reduces the fraction of particles needed for percolation to occur (models A and B) and induces percolation when the fraction of particles is high (model B). Percolation by heating and percolation loops in temperature-composition diagrams are obtained when the formation of chains is energetically favorable by increasing the entropic gain of branching (model A). Chaining and branching are found to follow a model dependent relation at percolation, which shows that, for the same composition, longer chains require less branching for percolation to occur.
- Building up DNA, bit by bit: a simple description of chain assemblyPublication . Foffi, Riccardo; SCIORTINO, Francesco; Tavares, Jose; Teixeira, PauloWe simulate the assembly of DNA copolymers from two types of short duplexes (short double strands with a single-stranded overhang at each end), as described by the oxDNA model. We find that the statistics of chain lengths can be well reproduced by a simple theory that treats the association of particles into ideal (i.e., non-interacting) clusters as a reversible chemical reaction. The reaction constants can be predicted either from SantaLucia's theory or from Wertheim's thermodynamic perturbation theory of association for spherical patchy particles. Our results suggest that theories incorporating very limited molecular detail may be useful for predicting the broad equilibrium features of copolymerisation.
- Remnants of the disappearing critical point(s) in patchy fluids with distinct interaction patchesPublication . Tavares, Jose; Teixeira, PauloWe investigate the disappearance of the critical points of a model consisting of particles decorated with two patches of type A and a variable number (n) of patches of type B (2AnB patchy particles), in which only AA and AB bonds can form. This has been shown to exhibit a very rich phase behavior including one, two, or no liquid-vapor critical points, depending on two parameters: the ratio of the volumes available to each type of bond and the ratio of the bond strengths. We apply Wertheim's theory in the limit of strong AA bonds to a lattice version of the model [Almarza et al., J. Chem. Phys. 137, 244902 (2012)] and show that the critical point does not always vanish at zero density and temperature, in contrast with results for particles decorated with only one type of patch. We uncover two remnants of the critical points-the lines of maximum and ideal compressibility-that survive even when no critical points are present.
- Phase behavior of a binary mixture of patchy colloids: Effect of particle size and gravityPublication . Braz Teixeira, Rodrigo; de las Heras, Daniel; Tavares, Jose; Gama, MargaridaWe study theoretically the effect of size difference and that of gravity in the phase behavior of a binary mixture of patchy particles. The species, 2A and 3B, have two A and three B patches, respectively, and only bonds between patches A and B (AB bonds) are allowed. This model describes colloidal systems where the aggregation of particles (3B) is mediated and controlled by a second species, the linkers (2A) to which they bind strongly. Thermodynamic calculations are performed using Wertheim’s perturbation theory with a hard sphere reference term that accounts for the difference in the size of the two species. Percolation lines are determined employing a generalized Flory–Stockmayer theory, and the effects of gravity are included through a local density approximation. The bulk phase diagrams are calculated, and all the stacking sequences generated in the presence of gravity are determined and classified in a stacking diagram. The relative size of the particles can be used to control the phase behavior of the mixture. An increase in the size of particles 3B, relative to the size of the linkers 2A, is found to promote mixing while keeping the percolating structures and, in certain cases, leads to changes in the stacking sequence under gravity.
- Bouncing on a slopePublication . Rostamian, Rouben; Soane, Ana Maria; Tavares, JoseWe analyze the motion of a point-mass projectile shot uphill above a slanted surface, which bounces from it without loss of energy. We show that consecutive bounces occur in equal time intervals and obtain an explicit formula for the number of uphill bounces before the motion reverses and the projectile heads downhill. Additionally, we show that the projectile rises to the same height above the surface on each bounce, and we determine the necessary and sufficient conditions under which it will retrace its path upon reversal.