Efficient solutions to robust, semi-implicit discretizations of the immersed boundary method

The immersed boundary method is a versatile tool for the investigation of flow-structure interaction. In a large number of applications, the immersed boundaries or structures are very stiff and strong tangential forces on these interfaces induce a well-known, severe time-step restriction for explicit discretizations. This excessive stability constraint can be removed with fully implicit or suitable semi-implicit schemes but at a seemingly prohibitive computational cost. While economical alternatives have been proposed recently for some special cases, there is a practical need for a computationally efficient approach that can be applied more broadly. In this context, we revisit a robust semi-implicit discretization introduced by Peskin in the late 1970s which has received renewed attention recently. This discretization, in which the spreading and interpolation operators are lagged. leads to a linear system of equations for the inter-face configuration at the future time, when the interfacial force is linear. However, this linear system is large and dense and thus it is challenging to streamline its solution. Moreover, while the same linear system or one of similar structure could potentially be used in Newton-type iterations, nonlinear and highly stiff immersed structures pose additional challenges to iterative methods. In this work, we address these problems and propose cost-effective computational strategies for solving Peskin`s lagged-operators type of discretization. We do this by first constructing a sufficiently accurate approximation to the system`s matrix and we obtain a rigorous estimate for this approximation. This matrix is expeditiously computed by using a combination of pre-calculated values and interpolation. The availability of a matrix allows for more efficient matrix-vector products and facilitates the design of effective iterative schemes. We propose efficient iterative approaches to deal with both linear and nonlinear interfacial forces and simple or complex immersed structures with tethered or untethered points. One of these iterative approaches employs a splitting in which we first solve a linear problem for the interfacial force and then we use a nonlinear iteration to find the interface configuration corresponding to this force. We demonstrate that the proposed approach is several orders of magnitude more efficient than the standard explicit method. In addition to considering the standard elliptical drop test case, we show both the robustness and efficacy of the proposed methodology with a 2D model of a heart valve. (C) 2009 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.

Surface Activity of the Triflate Ion at the Air/Water Interface and Properties of N,N,N-Trimethyl-N-Dodecylammonium Triflate Aqueous Solutions

The surface activity of salts added to water is Air orders of magnitude lower than that of surfactants. Sodium trifluoromethanesulfonate (NaTf) produced a change in surface tension. with concentration, Delta gamma/Delta c, of -13.2 mN.L/m.mol. This value is ca. 4-fold larger than those of simple salts and that of methanesulfonate. This unexpected surface effect suggested that positively charged micelles containing Tf could exhibit interesting properties. Dodecyltrimethylammonium triflate (DTATf) had a higher Kraft temperature (37 degrees C) and a lower cmc (5 x 10(-3)M) and degree of dissociation (0.11) than the chloride and bromide salts of DTA. Above the Kraft temperature, at a characteristic temperature t(1), the addition of NaTf above 0.05 M. to a DTATf solution induced phase separation. By increasing the temperature of the two-phase system to above t(1), a homogeneous, transparent solution was obtained at a characteristic temperature t(2). These results, together with well-known triflate properties, led us to suggest that the Tf ion pairs With DTA and that the -CF(3) group may be dehydrated in the interfacial region, resulting in new and interesting self-aggregated structures.

Application of Microelectrode Voltammetry to Study the Properties of Surfactant Solutions: Alkyltrimethylammonium Bromides

Microelectrode cyclic voltammetry (MV) has been employed to investigate the micellar properties of solutions of homologous alkyltrimethylammonium bromides, RMe(3)ABr, R = C(10), C(12), and C(14), in water and in the presence of added NaBr. The micellar self-diffusion coefficient was calculated from the limiting current for the reversible electron transfer of micelle-bound ferrocene. From the values of this property, other parameters were calculated, including the micellar hydrodynamic radius, RH, and aggregation number, N(agg); the latter was also theoretically calculated. We determined the values of the diffusion coefficient as a function of various experimental variables and observed the following trends: The diffusion coefficient decreases as a function of increasing surfactant concentration (no additional electrolyte added); it decreases as a function of increasing surfactant concentration at fixed NaBr concentration; and it shows a complex dependence (increase then decrease) on the NaBr concentration at a fixed RMe(3)ABr concentration. The value of the intermicellar interaction parameter decreases and then increases as a function of increasing NaBr concentration. These results are discussed in terms of intermicellar,interactions and the effect of NaBr on the micellar surface charge density and sphere-to-rod geometry change. The NaBr concentration required to induce the latter change increases rapidly as a function of decreasing the length of R: no geometry change was detected for C(10)Me(3)ABr. Values of N(agg) increase as I function of increasing the length of R and are in good agreement with both literature values and values that were calculated theoretically. Thus, MV is a convenient and simple technique for obtaining fundamental properties of surfactant solutions, including additive-induced changes of micellar parameters (N(agg)) and morphology changes.

Characteristics of thin cellulose ester films spin-coated from acetone and ethyl acetate solutions

Spin-coated films of cellulose acetate (CA), cellulose acetate propionate (CAP), cellulose acetate butyrate (CAB) and carboxymethylcellulose acetate butyrate (CMCAB) have been characterized by ellipsometry, atomic force microscopy (AFM) and contact angle measurements. The films were spin-coated onto silicon wafers, a polar surface. Mean thickness values were determined by means of ellipsometry and AFM as a function of polymer concentration in solutions prepared either in acetone or in ethyl acetate (EA), both are good solvents for the cellulose esters. The results were discussed in the light of solvent evaporation rate and interaction energy between substrate and solvent. The effects of annealing and type of cellulose ester on film thickness, film morphology, surface roughness and surface wettability were also investigated.

Transport coefficients, Raman spectroscopy, and computer simulation of lithium salt solutions in an ionic liquid

Lithium salt solutions of Li(CF3SO2)(2)N, LiTFSI, in a room-temperature ionic liquid (RTIL), 1-butyl-2,3-dimethyl-imidazolium cation, BMMI, and the (CF3SO2)(2)N-, bis(trifluoromethanesulfonyl)imide anion, [BMMI][TFSI], were prepared in different concentrations. Thermal properties, density, viscosity, ionic conductivity, and self-diffusion coefficients were determined at different temperatures for pure [BMMI][TFSI] and the lithium solutions. Raman spectroscopy measurements and computer simulations were also carried out in order to understand the microscopic origin of the observed changes in transport coefficients. Slopes of Walden plots for conductivity and fluidity, and the ratio between the actual conductivity and the Nernst-Einstein estimate for conductivity, decrease with increasing LiTFSI content. All of these studies indicated the formation of aggregates of different chemical nature, as it is corroborated by the Raman spectra. In addition, molecular dynamics (MD) simulations showed that the coordination of Li+ by oxygen atoms of TFSI anions changes with Li+ concentration producing a remarkable change of the RTIL structure with a concomitant reduction of diffusion coefficients of all species in the solutions.

Effect of the chain length in the structure of imidazolic ionic liquids and dimethylformamide solutions probed by Raman spectroscopy

The Raman band assigned to the nu(C=O)mode in N,N-dimethylformamide (at ca. 1660 cm(-1)) was used as a probe to study a group of ionic liquids 1-alkyl-3-methylimidazolium bromide ([C(n)Mlm]Br) with different alkyl groups (n = 2, 4, 6, 8 and 10 carbons) in binary equimolar binary mixtures with dimethylformamide. Due to the high electric dipole moment of the group C=O, there is a substantial coupling between adjacent molecules in the solution, and the corresponding Raman band involves both vibrational and reorientational modes. Different chain lengths of the ILs lead to different extents of the uncoupling of adjacent molecules of dimethylformamide, resulting in different shifts for this band in the mixtures. Information about the organization of ionic liquids in solution was obtained and a model of aggregation for these systems is proposed. (C) 2010 Elsevier B.V. All rights reserved.

Wettability of Aqueous Rhamnolipids Solutions Produced by Pseudomonas aeruginosa LBI

The wetting behavior of rhamnolipids produced by Pseudomonas aeruginosa LBI strain grown on waste oil substrate and sodium dodecyl sulfate (SDS) on glass, polyethylene terephthalate (PET), poly(vinyl chloride) (PVC), poly(epsilon-caprolactone) (PCL) and polymer blend (PVC-PCL) was investigated by the measuring contact angle of sessile drops, to determine the wetting characteristics of rhamnolipids. The comparison of the wetting profiles showed that at low SDS and rhamnolipid concentrations, the contact angle increased and when the concentration of the surfactant increased further, the contact angle decreased. The blend surface (PVC-PCL) showed better wettability than the homopolymers themselves and the blend changed the surface hydrophobicity of the polymer, making it more hydrophilic. The rhamnolipids produced by the LBI strain exhibited superior wetting abilities than the chemical surfactant SDS one. This is the first work that evaluates the wetting properties of rhamnolipids on polymer blends.

Electrocombustion of humic acid and removal of algae from aqueous solutions

This paper reports experiments involving the electrochemical combustion of humic acid (HA) and removal of algae from pond water. An electrochemical flow reactor with a boron-doped diamond film anode was used and constant current experiments were conducted in batch recirculation mode. The mass transfer characteristics of the electrochemical device were determined by voltammetric experiments in the potential region of water stability, followed by a controlled current experiment in the potential region of oxygen evolution. The average mass transfer coefficient was 5.2 x 10(-5) m s(-1). The pond water was then processed to remove HA and algae in the conditions in which the reaction combustion occurred under mass transfer control. To this end, the mass transfer coefficient was used to estimate the initial limiting current density applied in the electrolytic experiments. As expected, all the parameters analyzed here-solution absorbance at 270 nm, total phenol concentration and total organic carbon concentration-decayed according to first-order kinetics. Since the diamond film anode successfully incinerated organic matter, the electrochemical system proved to be predictable and programmable.