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Register a new userValidating pore-scale models of drying using microfluidic experiments
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We present an experimental micro-model of drying porous media, based on microfluidic cells made of arrays of pillars on a regular grid, and complement these experiments with a matching two-dimensional pore-network model of drying. Disorder, or small-scale heterogeneity, was introduced into the cells by randomly varying the radii of the pillars, around their average value. The microfluidic chips were filled with a volatile oil and then dried horizontally, such that gravitational effects were excluded. The experimental and simulated drying rates and drying patterns were then compared in detail, for various levels of disorder, in order to verify the predictive capabilities of our model. The geometrical features were reproduced well, while reproducing drying rates proved to be more challenging.
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In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed to consist of four components: water, extracellular polymeric substances (EPS), active bacteria, and dead bacteria. The flow of water is modeled by the Stokes equation whereas a diffusion-convection equation is involved for the transport of nutrients. At the water/biofilm interface, nutrient transport and shear forces due to the water flux are considered. In the biofilm, the Brinkman equation for the water flow, transport of nutrients due to diffusion and convection, displacement of the biofilm components due to reproduction/dead of bacteria, and production of EPS are considered. A segregated finite element algorithm is used to solve the mathematical equations. Numerical simulations are performed based on experimentally determined parameters. The stress coefficient is fitted to the experimental data. To identify the critical model parameters, a sensitivity analysis is performed. The Sobol sensitivity indices of the input parameters are computed based on uniform perturbation by $pm 10 %$ of the nominal parameter values. The sensitivity analysis confirms that the variability or uncertainty in none of the parameters should be neglected.
We investigate the migration of particles of different geometrical shapes and sizes in a scaled-up model of a gravity-driven deterministic lateral displacement (g-DLD) device. Specifically, particles move through a square array of cylindrical posts as they settle under the action of gravity. We performed experiments that cover a broad range of orientations of the driving force (gravity) with respect to the columns (or rows) in the square array of posts. We observe that as the forcing angle increases particles initially locked to move parallel to the columns in the array begin to move across the columns of obstacles and migrate at angles different from zero. We measure the probability that a particle would move across a column of obstacles, and define the critical angle {theta}c as the forcing angle at which this probability is 1/2. We show that critical angle depends both on particle size and shape, thus enabling both size- and shape-based separations. Finally, we show that using the diameter of the inscribed sphere as the characteristic size of the particles the corresponding critical angle becomes independent of particle shape and the relationship between them is linear. This linear and possibly universal behavior of the critical angle as a function of the diameter of the inscribed sphere could provide guidance in the design and optimization of g-DLD devices used for shape-based separation.
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show that depending on the erosion law, the flow may become uniform and homogenized or become unstable and develop channels. By defining an order parameter capturing these different behaviors we show that a phase transition occurs depending on the erosion dynamics. Using a simple model, we identify quantitative criteria to distinguish these regimes and correctly predict the fate of the network, and discuss the experimental relevance of our result.
An electrokinetically-driven deterministic lateral displacement (e-DLD) device is proposed for the continuous, two-dimensional fractionation of suspensions in microfluidic platforms. The suspended species are driven through an array of regularly spaced cylindrical posts by applying an electric field across the device. We explore the entire range of orientations of the driving field with respect to the array of obstacles and show that, at specific forcing-angles, particles of different size migrate in different directions, thus enabling continuous, two-dimensional separation. We discuss a number of features observed in the kinetics of the particles, including directional locking and sharp transitions between migration angles upon variations in the direction of the force, that are advantageous for high-resolution two-dimensional separation. A simple model based on individual particle-obstacle interactions accurately describes the migration angle of the particles depending on the orientation of the driving field, and can be used to re-configure driving field depending on the composition of the samples.
The effects of viscoelasticity on the dynamics and break-up of fluid threads in microfluidic T-junctions are investigated using numerical simulations of dilute polymer solutions at changing the Capillary number ($mbox {Ca}$), i.e. at changing the balance between the viscous forces and the surface tension at the interface, up to $mbox{Ca} approx 3 times 10^{-2}$. A Navier-Stokes (NS) description of the solvent based on the lattice Boltzmann models (LBM) is here coupled to constitutive equations for finite extensible non-linear elastic dumbbells with the closure proposed by Peterlin (FENE-P model). We present the results of three-dimensional simulations in a range of $mbox{Ca}$ which is broad enough to characterize all the three characteristic mechanisms of breakup in the confined T-junction, i.e. ${it squeezing}$, ${it dripping}$ and ${it jetting}$ regimes. The various model parameters of the FENE-P constitutive equations, including the polymer relaxation time $tau_P$ and the finite extensibility parameter $L^2$, are changed to provide quantitative details on how the dynamics and break-up properties are affected by viscoelasticity. We will analyze cases with ${it Droplet ~Viscoelasticity}$ (DV), where viscoelastic properties are confined in the dispersed (d) phase, as well as cases with ${it Matrix ~Viscoelasticity}$ (MV), where viscoelastic properties are confined in the continuous (c) phase. Moderate flow-rate ratios $Q approx {cal O}(1)$ of the two phases are considered in the present study. Overall, we find that the effects are more pronounced in the case with MV, as the flow driving the break-up process upstream of the emerging thread can be sensibly perturbed by the polymer stresses.
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