The flow of generalized Newtonian fluids with a rate-dependent viscosity through fibrous media is studied, with a focus on developing relationships for evaluating the effective fluid mobility. Three methods are used here: (i) a numerical solution of the Cauchy momentum equation with the Carreau or power-law constitutive equations for pressure-driven flow in a fiber bed consisting of a periodic array of cylindrical fibers, (ii) an analytical solution for a unit cell model representing the flow characteristics of a periodic fibrous medium, and (iii) a scaling analysis of characteristic bulk parameters such as the effective shear rate, the effective viscosity, geometrical parameters of the system, and the fluid rheology. Our scaling analysis yields simple expressions for evaluating the transverse mobility functions for each model, which can be used for a wide range of medium porosity and fluid rheological parameters. While the dimensionless mobility is, in general, a function of the Carreau number and the medium porosity, our results show that for porosities less than ε 0.65, the dimensionless mobility becomes independent of the Carreau number and the mobility function exhibits power-law characteristics as a result of the high shear rates at the pore scale. We derive a suitable criterion for determining the flow regime and the transition from a constant viscosity Newtonian response to a power-law regime in terms of a new Carreau number rescaled with a dimensionless function which incorporates the medium porosity and the arrangement of fibers.
In this work, we introduce a comprehensive machine-learning algorithm, namely, a multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of complex fluids. The physics-based neural networks developed here are informed by the underlying rheological constitutive models through the synthetic generation of low-fidelity model-based data points. The performance of these rheologically informed algorithms is thoroughly investigated and compared against classical deep neural networks (DNNs). The MFNNs are found to recover the experimentally observed rheology of a multicomponent complex fluid consisting of several different colloidal particles, wormlike micelles, and other oil and aromatic particles. Moreover, the data-driven model is capable of successfully predicting the steady state shear viscosity of this fluid under a wide range of applied shear rates based on its constituting components. Building upon the demonstrated framework, we present the rheological predictions of a series of multicomponent complex fluids made by DNN and MFNN. We show that by incorporating the appropriate physical intuition into the neural network, the MFNN algorithms capture the role of experiment temperature, the salt concentration added to the mixture, as well as aging within and outside the range of training data parameters. This is made possible by leveraging an abundance of synthetic low-fidelity data that adhere to specific rheological models. In contrast, a purely data-driven DNN is consistently found to predict erroneous rheological behavior.
We demonstrate the layer-by-layer (LbL) assembly of polyelectrolyte multilayers (PEM) on three-dimensional nanofiber scaffolds. High porosity (99%) aligned carbon nanotube (CNT) arrays are photolithographically patterned into elements that act as textured scaffolds for the creation of functionally coated (nano)porous materials. Nanometer-scale bilayers of poly(allylamine hydrochloride)/poly(styrene sulfonate) (PAH/SPS) are formed conformally on the individual nanotubes by repeated deposition from aqueous solution in microfluidic channels. Computational and experimental results show that the LbL deposition is dominated by the diffusive transport of the polymeric constituents, and we use this understanding to demonstrate spatial tailoring on the patterned nanoporous elements. A proof-of-principle application, microfluidic bioparticle capture using N-hydroxysuccinimide-biotin binding for the isolation of prostate-specific antigen (PSA), is demonstrated.
Analytical solutions are presented for velocity and temperature distributions of laminar fully developed flow of Newtonian, constant property fluids in micro/minichannels of hyperelliptical and regular polygonal cross sections. The considered geometries cover several common shapes such as ellipse, rectangle, rectangle with round corners, rhombus, star-shape, and all regular polygons. The analysis is carried out under the conditions of constant axial wall heat flux with uniform peripheral heat flux at a given cross section. A linear least squares point matching technique is used to minimize the residual between the actual and the predicted values on the boundary of the channel. Hydrodynamic and thermal characteristics of the flow are derived; these include pressure drop and local and average Nusselt numbers. The proposed results are successfully verified with existing analytical and numerical solutions from the literature for a variety of cross sections. The present study provides analytical-based compact solutions for velocity and temperature fields that are essential for basic designs, parametric studies, and optimization analyses required for many thermofluidic applications.
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