Session R34: Micro/Nano scale Flows: General

A Heteroscedastic Gaussian Process Regression Workflow for Materials Property Prediction in Molecular Simulations

The field of computational materials science faces various challenges in data processing, including dealing with high-dimensional phase spaces, multi-parameter vectors, and error analysis. In particular, uncertainty quantification of models that fit large materials datasets has become crucial for making informed engineering decisions. Gaussian Process Regression (GPR) has gained popularity in this task compared to physical-based parametric models due to its flexibility and ability to naturally predict errors. In this talk, we focus on the self-diffusion coefficient dataset generated through Green-Kubo and Einstein's Relation during the post-processing of the molecular-dynamics (MD) dataset. We present a heteroscedastic GPR workflow for predicting the fluid self-diffusion coefficient. This workflow evaluates the mean and variance for fluid diffusivity as a function of density. Unlike the standard GPR framework, the proposed approach adapts local uncertainties into the model, making it more flexible in reflecting the non-constant variance nature of the MD dataset. We also show the extensions of the GPR model on the higher dimensional MD dataset for multiple features like the temperature and pressure.   

Sedimentation of Microscale Particles near Corrugated Wall Using Method of Fundamental Solutions

Sedimentation of particles along the corrugated surface under action of gravity is obtained by meshless Method of Fundamental Solutions (MFS).  This physical situation is found often in biological systems and microfluidic devices. The Stokes equations with no-slip boundary conditions are solved using the Green’s function for Stokeslets.  In the present study, the velocity of a moving particle is not known and becomes a part of the MFS solution. This requires an adjustment of the matrix of MFS linear system to include the unknown particle velocity and incorporate the balance of hydrodynamic and gravity forces acting on the particle in the MFS. Combination of regularization of Stokeslets and placement of Stokeslets outside flow domain is implemented to ensure accuracy and stability of computations. Comparison has been made to prior published approximate analytical and experimental results to verify the effectiveness of this methodology to predict the trajectory of particle including its deviation from vertical trajectory and select the optimal set of computational parameters. The developed methodology is applied to sedimentation of two spherical particles in proximity for which case the analytical solution is not available. The MFS results show that particles in tandem deviate from trajectory of a single particle where the forward particle is moving farther away from vertical corrugated wall and the back particle is shifted closer to the wall.    

Can microtubule diffusiophoresis be present during spindle formation?

Microtubules (MT) form the mitotic spindle assembly during mitosis in eukaryotic cells, and a concentration gradient of the protein Ran (in its GTP bound form – RanGTP) plays an important role during this process. As microtubules are negatively charged and concentration gradients of various species are ubiquitous in cells, we asked whether diffusiophoresis of microtubules can be present in such an environment. In this study, we first demonstrate migration of MTs in BRB80 buffer (which contains PIPES, EGTA, and MgCl₂) under MgCl₂ gradients and quantify the diffusiophoretic behavior by comparing with a multi-ion model of diffusiophoresis and diffusioosmosis. Then, we further study the diffusiophoresis of MT under various concentration gradients of relevant biological solutes (ATP, GTP, and RanQ69L) and unravel diffusiophoresis in more complex chemical environments.   

Theoretical and numerical models of depth-confined Brinkman flow

Highly depth-confined flows are a common feature of microfluidic devices. We study flows that are highly confined in the depth direction, which are often referred to as Brinkman flows. We seek a novel theoretical solution approach to depth-confined flows by the construction of an outer solution that satisfies the Brinkman equations and an inner solution that is valid near the boundaries. We use combined theoretical and numerical methods to investigate several basic cases including the flow past a depth-confined cylinder, lid-driven cavity flow, and flow over a backward-facing step. We close the theoretical flow solution using matching boundary conditions between the inner and outer flows. The resulting theoretical approach is general across a wide-range of microfluidic devices where the channel height is the smallest dimension, and significantly reduces the computational resources needed to model the system by reducing such flows to 2D flow problems. We performed 3D numerical simulations using OpenFOAM to validate our 2D theoretical formulation and provide more physical insights into the method.   

The Dynamics of a Micron Scale Beam Driven by Synthetic Noise in a Fluid

As nanotechnology rapidly advances, the role of nonlinear dynamics and the influence of dissipation will become increasingly important -- even when the dynamics are driven by molecular collisions. As a means to study this regime while using currently accessible microscale systems, we use a noisy electrothermal drive whose magnitude can be varied to explore the linear and nonlinear dynamics of a micron scale beam immersed in fluid. The electrothermal actuation is a synthetic noise force that we have tailored to generate beam dynamics that approximate Brownian driven motion. In the linear regime, we use the fluctuation-dissipation theorem to quantify the ability of the synthetic noise to generate driven Brownian dynamics. We use deterministic and stochastic numerical approaches to describe the beam dynamics that are valid in the linear and nonlinear regimes. We explore extensions of these approaches to include the variations in mass loading and damping that occur for oscillators in a viscous fluid. Theory, numerics, and experiment will be compared where possible to highlight new physical insights into the strongly driven dynamics of small elastic structures in fluid.   

Carbon nanotube wall shear stress sensors

Continued miniaturization of fluid flow devices demands ever smaller sensors. We have developed a miniature, capacitive, wall shear stress sensor made from vertically aligned carbon nanotube arrays grown from photolithographically patterned catalyst. The components that mechanically respond to flow and convert that signal to an electrical response measure 50 by 60 by 200 cubic microns and can measure wall shear stress in the range of 0.1 to 7 Pa. Sensor stiffness and response to deformation are characterized by atomic force microscopy while sensor deflection in flow is visualized by optical microscopy. Capacitance response to wall shear stress is further characterized through calibration in a flow channel. The results reveal a diverse range of ways the sensor can respond to flow, which could be leveraged to tune sensitivity or operating range for specific target applications. The design furthers efforts to miniaturize drag-based flow sensors, with applications in microfluidic systems, autonomous micro aerial vehicle control, and experiments resolving microscopic flow features.   

Kinetic description of flow detachment at a micro-step

We study the pressure-driven steady gas flow over a backward-facing step in a two-dimensional microchannel. Focusing on the near-free-molecular regime of high Knudsen numbers, the problem is analyzed asymptotically based on the Bhatnager, Gross and Krook kinetic model, and supported by numerical Discrete Velocity Method computations. The wall conditions are formulated using the Maxwell model, superposing specular and diffuse surface conditions. The asymptotic solution contains the leading-order free-molecular description and a first-order integral representation of the near-free-molecular correction. In contrast with the common view that flow detachment is a low Knudsen number phenomenon, our results indicate that flow separation at the step may occur at arbitrarily large (yet finite) Knudsen numbers in smooth (specular reflecting) channels, where the flow is driven by temperature differences between the channel inlet and outlet reservoirs. It is then shown that detachment is significantly suppressed by the imposition of density variations between the reservoirs and an increase in the channel walls accommodation coefficient towards diffuse-surface conditions. While the mass flow rate in a specular channel decreases with decreasing Knudsen in a density-driven setup (in line with the Knudsen Paradox), it increases in a temperature-driven flow. The results are obtained for arbitrary differences between the inlet and outlet reservoir equilibrium properties, and are rationalized using the linearized problem formulation.   

Diffusion into dead-end pores of non-uniform cross-sections

Understanding micron-scale fluid flows is critical to perfecting the manufacturing and use of microfluidic technologies for medical and engineering applications. Microchannels with dead-end pores are ubiquitous in natural and industrial settings, and ongoing research focuses on fluid and chemical transport in and out of these pores. In the present work, we detail a repeatable and accessible experimental protocol developed to study the passive diffusion of a dissolved solute into dead-end pores of rectangular and trapezoidal geometries. Custom microchannels with pores of specified geometries are rapidly produced using inexpensive materials and a commercial craft cutter. The experimental data is compared directly to both detailed 3D numerical simulations as well as analytical solutions of an effective 1D diffusion equation: the Fick-Jacobs equation. The role of the pore geometry on the passive diffusion process will be highlighted. Ongoing and future directions will be discussed.