Mathieu Sellier

Viscosity of α-pinene secondary organic material and implications for particle growth and reactivity

Particles composed of secondary organic material (SOM) are abundant in the lower troposphere. The viscosity of these particles is a fundamental property that is presently poorly quantified yet required for accurate modeling of their formation, growth, evaporation, and environmental impacts. Using two unique techniques, namely a “bead-mobility” technique and a “poke-flow” technique, in conjunction with simulations of fluid flow, the viscosity of the water-soluble component of SOM produced by α-pinene ozonolysis is quantified for 20- to 50-μm particles at 293–295 K. The viscosity is comparable to that of honey at 90% relative humidity (RH), similar to that of peanut butter at 70% RH, and at least as viscous as bitumen at ≤30% RH, implying that the studied SOM ranges from liquid to semisolid or solid across the range of atmospheric RH. These data combined with simple calculations or previous modeling studies are used to show the following: (i) the growth of SOM by the exchange of organic molecules between gas and particle may be confined to the surface region of the particles for RH ≤ 30%; (ii) at ≤30% RH, the particle-mass concentrations of semivolatile and low-volatility organic compounds may be overpredicted by an order of magnitude if instantaneous equilibrium partitioning is assumed in the bulk of SOM particles; and (iii) the diffusivity of semireactive atmospheric oxidants such as ozone may decrease by two to five orders of magnitude for a drop in RH from 90% to 30%. These findings have possible consequences for predictions of air quality, visibility, and climate.

Gravity-driven flow of continuous thin liquid films on non-porous substrates with topography

A range of two- and three-dimensional problems is explored featuring the gravity-driven flow of a continuous thin liquid film over a non-porous inclined flat surface containing well-defined topography. These are analysed principally within the framework of the lubrication approximation, where accurate numerical solution of the governing nonlinear equations is achieved using an efficient multigrid solver. Results for flow over one-dimensional steep-sided topographies are shown to be in very good agreement with previously reported data. The accuracy of the lubrication approximation in the context of such topographies is assessed and quantified by comparison with finite element solutions of the full Navier–Stokes equations, and results support the consensus that lubrication theory provides an accurate description of these flows even when its inherent assumptions are not strictly satisfied. The Navier–Stokes solutions also illustrate the effect of inertia on the capillary ridge/trough and the two-dimensional flow structures caused by steep topography. Solutions obtained for flow over localized topography are shown to be in excellent agreement with the recent experimental results of Decre & Baret (2003) for the motion of thin water films over finite trenches. The spread of the ‘bow wave’, as measured by the positions of spanwise local extrema in free-surface height, is shown to be well-represented both upstream and downstream of the topography by an inverse hyperbolic cosine function. An explanation, in terms of local flow rate, is given for the presence of the ‘downstream surge’ following square trenches, and its evolution as trench aspect ratio is increased is discussed. Unlike the upstream capillary ridge, this feature cannot be completely suppressed by increasing the normal component of gravity. The linearity of free-surface response to topographies is explored by superposition of the free surfaces corresponding to two ‘equal-but-opposite’ topographies. Results confirm the findings of Decre & Baret (2003) that, under the conditions considered, the responses behave in a near-linear fashion.

Flow of evaporating, gravity-driven thin liquid films over topography

The effect of topography on the free surface and solvent concentration profiles of an evaporating thin film of liquid flowing down an inclined plane is considered. The liquid is assumed to be composed of a resin dissolved in a volatile solvent with the associated solvent concentration equation derived on the basis of the well-mixed approximation. The dynamics of the film is formulated as a lubrication approximation and the effect of a composition-dependent viscosity is included in the model. The resulting time-dependent, nonlinear, coupled set of governing equations is solved using a full approximation storage multigrid method. The approach is first validated against a closed-form analytical solution for the case of a gravity-driven, evaporating thin film flowing down a flat substrate. Analysis of the results for a range of topography shapes reveal that although a full-width, spanwise topography such as a step-up or a step-down does not affect the composition of the film, the same is no longer true for th...

A computational model of hemodynamic parameters in cortical capillary networks.

The analysis of hemodynamic parameters and functional reactivity of cerebral capillaries is still controversial. To assess the hemodynamic parameters in the cortical capillary network, a generic model was created using 2D voronoi tessellation in which each edge represents a capillary segment. This method is capable of creating an appropriate generic model of cerebral capillary network relating to each part of the brain cortex because the geometric model is able to vary the capillary density. The modeling presented here is based on morphometric parameters extracted from physiological data of the human cortex. The pertinent hemodynamic parameters were obtained by numerical simulation based on effective blood viscosity as a function of hematocrit and microvessel diameter, phase separation and plasma skimming effects. The hemodynamic parameters of capillary networks with two different densities (consistent with the variation of the morphometric data in the human cortical capillary network) were analyzed. The results show pertinent hemodynamic parameters for each model. The heterogeneity (coefficient variation) and the mean value of hematocrits, flow rates and velocities of the both network models were specified. The distributions of blood flow throughout the both models seem to confirm the hypothesis in which all capillaries in a cortical network are recruited at rest (normal condition). The results also demonstrate a discrepancy of the network resistance between two models, which are derived from the difference in the number density of capillary segments between the models.

Reconstruction of river bed topography from free surface data using a direct numerical approach in one-dimensional shallow water flow

River bed topography is of paramount importance for the study of fluvial hydraulics, flood prediction and river flow monitoring. It is therefore important to develop fast, easy-to-implement and cost-effective methods to determine underwater river topography. This paper presents a new one-step approach for reconstructing the river bed topography from known free surface data. This problem corresponds to the inverse of the classical hydrodynamic problem where the shallow water equations provide the free surface profile for a given river bed. We show in this work that instead of treating this inverse problem in the traditional partial differential equation (PDE)-constrained optimization framework, we can conveniently rearrange the governing equations for the direct problem to obtain an explicit PDE for the inverse problem. This leads to a direct solution of the inverse problem. An interesting consequence of the analysis is that the equations governing the forward and inverse problems have a very similar form, and the same discretization technique, based on an upwind conservative numerical scheme, can be used. The proposed methodology is successfully tested on a range of benchmark problems for noisy and noiseless free surface data. It was found that this solution approach creates very little amplification of noise.

Modeling the coalescence of sessile droplets

This paper proposes a simple scenario to describe the coalescence of sessile droplets. This scenario predicts a power-law growth of the bridge between the droplets. The exponent of this power law depends on the driving mechanism for the spreading of each droplet. To validate this simple idea, the coalescence is simulated numerically and a basic experiment is performed. The fluid dynamics problem is formulated in the lubrication approximation framework and the governing equations are solved in the commercial finite element software COMSOL. Although a direct comparison of the numerical results with experiment is difficult because of the sensitivity of the coalescence to the initial and operating conditions, the key features of the event are qualitatively captured by the simulation and the characteristic time scale of the dynamics recovered. The experiment consists of inducing coalescence by pumping a droplet through a substrate which grows and ultimately coalesces with another droplet resting on the substrate. The coalescence was recorded using high-speed imaging and also confirmed the power-law growth of the neck.

Substrate design or reconstruction from free surface data for thin film flows

This paper addresses two inverse problems relevant to the flow of thin liquid films on uneven surfaces. The first one consists in controlling the free surface profile by a suitable design of the substrate and the second involves the reconstruction of the substrate topography from a known free surface profile. These problems are treated in the classical lubrication approximation framework and admit, for planar flows, a surprisingly simple close-form solution, which is successfully tested on a range of problems.

An iterative algorithm for optimal mould design in high-precision compression moulding

Abstract The mould design for the manufacturing of high-precision glass parts remains a challenging task. This motivates the present study which proposes an optimization technique to identify the mould design that yields the desired glass piece profile at the end of the compression moulding process with an accuracy of the order of 1 μm. The intuitive, yet very efficient method consists in computing at each optimization loop the mismatch between the deformed and desired glass piece geometries and using this information to update the mould design. The deformed glass piece geometry is computed using the commercial finite element package ABAQUS. This package is well suited to model the multistage forming process, the complex rheology of the glass, and the varying mechanical contact between the parts involved. The feasibility of the method is demonstrated in theory by designing the required mould for a convex-concave lens, where an accuracy of the order of 1 μm is achieved.

Droplet actuation induced by coalescence: Experimental evidences and phenomenological modeling

This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of fascinating phenomena can be observed. In particular, the interaction may result in the actuation of the droplet system, i.e. its displacement over a finite length. In order to control this displacement, we consider droplets confined on a hydrophilic stripe created by plasma-treating a PDMS substrate. This controlled actuation opens up unexplored opportunities in the field of microfluidics. In order to explain the observed actuation phenomenon, we propose a simple phenomenological model based on Newton’s second law and a simple balance between the driving force arising from surface energy gradients and the viscous resistive force. This simple model is able to reproduce qualitatively and quantitatively the observed droplet dynamics.

Optimal Shape Design in Heat Transfer Based on Body-Fitted Grid Generation

This paper deals with an inverse steady-state heat transfer problem. We develop in this work a new numerical methodology to infer the shape a heated body should have for the temperature distribution on part of its boundary to match a prescribed one. This new numerical methodology solves this shape optimization problem using body-fitted grid generation to map the unknown optimal shape onto a fixed computational domain. This mapping enables a simple discretization of the Heat Equation using finite differences and allows us to remesh the physical domain, which varies at each optimization iteration. A novel aspect of this work is the sensitivity analysis, which is expressed explicitly in the fixed computational domain. This allows a very efficient evaluation of the sensitivities. The Conjugate Gradient method is used to minimize the objective function and this work proposes an efficient redistribution method to maintain the quality of the mesh throughout the optimization procedure.