Electrical Conductivity of a Stretching Viscoelastic Filament.

Long polymeric chains highly stretched and aligned with the flow confer a strong mechanical anisotropy on a viscoelastic solution. The electrically-driven transport of free ions under such conditions is far from being understood. In this paper, we determine experimentally whether the above-mentioned deviation from isotropy affects the electric charge transport across the liquid. To this end, we measure the electrical conductivity in the flow (stretching) direction of the cylindrical liquid filament formed in the elasto-capillary thinning that arises during the breakup of a viscoelastic liquid bridge. First, we examine the behavior of monodisperse solutions of polyethylene oxide (PEO) in a mixture of glycerine and water. For all the concentrations and molecular weights considered, the filament conductivity remains practically the same as the isotropic conductivity measured under hydrostatic conditions. However, we observe a decrease in the electric current at the end of elasto-capillary regime which may partially be attributed to the reduction of the liquid conductivity. Then, we measure the conductivity of bidisperse solutions of PEO with very different molecular weights. In this case, a significant decrease in conductivity is observed as the filament radius decreases. This constitutes the first experimental evidence of ion mobility reduction in stretching viscoelastic filaments, a relevant effect in applications such as electrospinning.

Numerical model to predict and compare the hypotensive efficacy and safety of minimally invasive glaucoma surgery devices.

PURPOSE: To predict and compare the hypotensive efficacy of three minimally-invasive glaucoma surgery (MIGS) implants through a numerical model. METHODS: Post-implant hypotensive efficacy was evaluated by using a numerical model and a computational fluid dynamics simulation. Three different devices were compared: the XEN 45 stent (tube diameter, 45 µm), the XEN 63 stent (63 µm) and the PreserFlo microshunt (70 µm). The influence of the filtration bleb pressure (Bp) and tube diameter, length, and position within the anterior chamber (AC) on intraocular pressure (IOP) were evaluated. RESULTS: Using baseline IOPs of 25, 30 and 50 mmHg, respectively, the corresponding computed post-implant IOPs for each device were as follows: XEN 45: 17 mmHg (29% decrease), 19 mmHg (45%) and 20 mmHg (59%) respectively; XEN 63: 13 mmHg (48%), 13 mmHg (62%), and 13 mmHg (73%); PreserFlo: 12 mmHg (59%), 13 mmHg (73%) and 13 mmHg (73%). At a baseline IOP of 35 mmHg with an increase in the outflow resistance within the Bp from 5 to 17 mmHg, the hypotensive efficacy for each device was reduced as follows: XEN45: 54% to 37%; XEN 63: 74% to 46%; and PreserFlo: 75% to 47%. The length and the position of the tube in the AC had only a minimal (non-significant) effect on IOP (<0.1 mmHg). CONCLUSIONS: This hydrodynamic/numerical model showed that implant diameter and bleb pressure are the two most pertinent determinants of hypotensive efficacy. In distinction, tube length and position in the AC do not significantly influence IOP.

Experimental Analysis of the Extensional Flow of Very Weakly Viscoelastic Polymer Solutions.

We study with ultra-high-speed imaging the thinning of the filament formed during the breakup of a pendant droplet of very weakly viscoelastic polymer solutions of polyvinylpyrrolidone (PVP) and polyethylene oxide (PEO). In the latter case, we consider two molecular weights: 10 5 g/mol (PEO100K) and 2 × 10 6 g/mol (PEO2M). The results allow us to measure with high reproducibility extensional relaxation times of the order of 10 µ s. Despite the noticeable differences between PVP and PEO100K, very similar values are obtained for the range of concentrations where the linear elasto-capillary is established. For PEO2M, the extensional relaxation time depends on the concentration even for values significantly smaller than the overlap one. The prediction c low for the concentration below which the linear elasto-capillary regime cannot be reached qualitatively agrees with the results for PVP and PEO2M, while it underestimates the critical concentration for PEO100K. The results for PEO2M are consistent with those reported in the literature for higher concentrations.

Computational simulation of aqueous humour dynamics in the presence of a posterior-chamber versus iris-fixed phakic intraocular lens.

PURPOSE: To compare aqueous humour (AH) dynamics in the presence of a precrystalline (Implantable Collamer Lens®; ICL) or iris-fixed (Artiflex®) phakic intraocular lens (PIOL). METHODS: By computational fluid dynamics simulation, AH flow was modelled through a peripheral iridotomy (PI) or central lens hole (both 360 µm) in the presence of an Artiflex or ICL lens, respectively. The impacts of AH flow were then determined in terms of wall shear stress (WSS) produced on the endothelium or crystalline lens. Effects were also modelled for different scenarios of pupil diameter (PD 3.5 or 5.5 mm), ICL vault (100, 350, 800 µm) and number of Artiflex iridotomies (1 or 2) and location (12 or 6 o'clock). RESULTS: For a PD of 3.5 mm, AH volumes flowing from the posterior to the anterior chamber were 37.6% of total flow through the lens hole (ICL) and 84.2% through PI (Artiflex). For an enlarged PD (5.5 mm), corresponding values were 10.3% and 81.9% respectively, so PI constitutes a very efficient way of evacuating AH. Central endothelial WSS in Pa was lower for the large vault ICL and the Artiflex (1-03 and 1.1-03 respectively) compared to the PIOL-free eye (1.6-03). Crystalline lens WSS was highest for the lowest vault ICL (1-04). CONCLUSIONS: AH flow varied according to the presence of a precrystalline or iris-fixed intraocular lens. Endothelial WSS was lower for an implanted ICL with large vault and Artiflex than in the PIOL-free eye, while highest crystalline WSS was recorded for the lowest vault ICL.

Diffusion of impurities in a granular gas.

Diffusion of impurities in a granular gas undergoing homogeneous cooling state is studied. The results are obtained by solving the Boltzmann-Lorentz equation by means of the Chapman-Enskog method. In the first order in the density gradient of impurities, the diffusion coefficient D is determined as the solution of a linear integral equation which is approximately solved by making an expansion in Sonine polynomials. In this paper, we evaluate D up to the second order in the Sonine expansion and get explicit expressions for D in terms of the coefficients of restitution for the impurity-gas and gas-gas collisions as well as the ratios of mass and particle sizes. To check the reliability of the Sonine polynomial solution, analytical results are compared with those obtained from numerical solutions of the Boltzmann equation by means of the direct simulation Monte Carlo method. In the simulations, the diffusion coefficient is measured via the mean-square displacement of impurities. The comparison between theory and simulation shows in general an excellent agreement, except for the cases in which the gas particles are much heavier and/or much larger than impurities. In these cases, the second Sonine approximation to D improves significantly the qualitative predictions made from the first Sonine approximation. A discussion on the convergence of the Sonine polynomial expansion is also carried out.

Shear viscosity for a moderately dense granular binary mixture.

The shear viscosity for a moderately dense granular binary mixture of smooth hard spheres undergoing uniform shear flow is determined. The basis for the analysis is the Enskog kinetic equation, solved first analytically by the Chapman-Enskog method up to first order in the shear rate for unforced systems as well as for systems driven by a Gaussian thermostat. As in the elastic case, practical evaluation requires a Sonine polynomial approximation. In the leading order, we determine the shear viscosity in terms of the control parameters of the problem: solid fraction, composition, mass ratio, size ratio, and restitution coefficients. Both kinetic and collisional transfer contributions to the shear viscosity are considered. To probe the accuracy of the Chapman-Enskog results, the Enskog equation is then numerically solved for systems driven by a Gaussian thermostat by means of an extension to dense gases of the well-known direct simulation Monte Carlo method for dilute gases. The comparison between theory and simulation shows, in general, an excellent agreement over a wide region of the parameter space.

Shear viscosity for a heated granular binary mixture at low density.

The shear viscosity for a heated granular binary mixture of smooth hard spheres at low density is analyzed. The mixture is heated by the action of an external driving force (Gaussian thermostat) that exactly compensates for cooling effects associated with the dissipation of collisions. The study is made from the Boltzmann kinetic theory, which is solved by using two complementary approaches. First, a normal solution of the Boltzmann equation via the Chapman-Enskog method is obtained up to first order in the spatial gradients. The mass, heat, and momentum fluxes are determined and the corresponding transport coefficients identified. As in the free cooling case [V. Garzó and J. W. Dufty, Phys. Fluids 14, 1476 (2002)], practical evaluation requires a Sonine polynomial approximation, and here it is mainly illustrated in the case of the shear viscosity. Second, to check the accuracy of the Chapman-Enskog results, the Boltzmann equation is numerically solved by means of the direct simulation Monte Carlo method. The simulation is performed for a system under uniform shear flow, using the Gaussian thermostat to control inelastic cooling. The comparison shows an excellent agreement between theory and simulation over a wide range of values of the restitution coefficients and the parameters of the mixture (masses, concentrations, and sizes).