A parameter identification problem in stochastic homogenization

In porous media physics, calibrating model parameters through experiments is a challenge. This process is plagued with errors that come from modelling, measurement and computation of the macroscopic observables through random homogenization -- the forward problem -- as well as errors coming from the parameters fitting procedure -- the inverse problem. In this work, we address these issues by considering a least-square formulation to identify parameters of the microscopic model on the basis on macroscopic observables. In particular, we discuss the selection of the macroscopic observables which we need to know in order to uniquely determine these parameters. To gain a better intuition and explore the problem without a too high computational load, we mostly focus on the one-dimensional case. We show that the Newton algorithm can be efficiently used to robustly determine optimal parameters, even if some small statistical noise is present in the system

Electroosmotic flow of biorheological micropolar fluids through microfluidic channels

An analysis is presented in this work to assess the influence of micropolar nature of fluids in fully developed flow induced by electrokinetically driven peristaltic pumping through a parallel plate microchannel. The walls of the channel are assumed as sinusoidal wavy to analyze the peristaltic flow nature. We consider that the wavelength of the wall motion is much larger as compared to the channel width to validate the lubrication theory. To simplify the Poisson Boltzmann equation, we also use the Debye-Hückel linearization (i.e. wall zeta potential ≤ 25mV). We consider governing equation for micropolar fluid in absence of body force and couple effects however external electric field is employed. The solutions for axial velocity, spin velocity, flow rate, pressure rise and stream functions subjected to given physical boundary conditions are computed. The effects of pertinent parameters like Debye length and Helmholtz-Smoluchowski velocity which characterize the EDL phenomenon and external electric field, coupling number and micropolar parameter which characterize the micropolar fluid behavior, on peristaltic pumping are discussed through the illustrations. The results show that peristaltic pumping may alter by applying external electric fields. This model can be used to design and engineer the peristalsis-lab-on-chip and micro peristaltic syringe pumps for biomedical applications

From cellulose to kerogen: molecular simulation of a geological process

The process by which organic matter decomposes deep underground to form petroleum and its underlying kerogen matrix has so far remained a no man's land to theoreticians, largely because of the geological (Myears) timescale associated with the process. Using reactive molecular dynamics and an accelerated simulation framework, the replica exchange molecular dynamics method, we simulate the full transformation of cellulose into kerogen and its associated fluid phase under prevailing geological conditions. We observe in sequence the fragmentation of the cellulose crystal and production of water, the development of an unsaturated aliphatic macromolecular phase and its aromatization. The composition of the solid residue along the maturation pathway strictly follows what is observed for natural type III kerogen and for artificially matured samples under confined conditions. After expulsion of the fluid phase, the obtained microporous kerogen possesses the structure, texture, density, porosity and stiffness observed for mature type III kerogen and a microporous carbon obtained by saccharose pyrolysis at low temperature. As expected for this variety of precursor, the main resulting hydrocarbon is methane. The present work thus demonstrates that molecular simulations can now be used to assess, almost quantitatively, such complex chemical processes as petrogenesis in fossil reservoirs and, more generally, the possible conversion of any natural product into bio-sourced materials and/or fuel

Fluid-driven metamorphism of the continental crust governed by nanoscale fluid flow

The transport of fluids through the Earth’s crust controls the redistribution of elements to form mineral and hydrocarbon deposits, the release and sequestration of greenhouse gases, and facilitates metamorphic reactions that influence lithospheric rheology. In permeable systems with a well-connected porosity, fluid transport is largely driven by fluid pressure gradients. In less permeable rocks, deformation may induce permeability by creating interconnected heterogeneities, but without these perturbations, mass transport is limited along grain boundaries or relies on transformation processes that self-generate transient fluid pathways. The latter can facilitate large-scale fluid and mass transport in nominally impermeable rocks without large-scale fluid transport pathways. Here, we show that pervasive, fluid-driven metamorphism of crustal igneous rocks is directly coupled to the production of nanoscale porosity. Using multi-dimensional nano-imaging and molecular dynamics simulations, we demonstrate that in feldspar, the most abundant mineral family in the Earth’s crust, electrokinetic transport through reaction-induced nanopores (<100 nm) can potentially be significant. This suggests that metamorphic fluid flow and fluid-mediated mineral transformation reactions can be considerably influenced by nanofluidic transport phenomena