Analytical and numerical study of Joule heating effects on electrokinetically pumped continuous flow PCR chips

Alternating Current Electroosmotic Flow of Maxwell Fluid in a Parallel Plate Microchannel with Sinusoidal Roughness

The EOF of a viscoelastic Maxwell fluid driven by an alternating pressure gradient and electric field in a parallel plate microchannel with sinusoidal roughness has been investigated within the Debye-Hückel approximation based on boundary perturbation expansion and separation of variables. Perturbation solutions were obtained for the potential distribution, the velocity and the mean velocity, and the relation between the mean velocity and the roughness. There are significant differences in the velocity amplitudes of the Newtonian and Maxwell fluids. It is shown here that the velocity distribution of the viscoelastic fluid is significantly affected by the roughness of the walls, which leads to the appearance of fluctuations in the fluid. Also, the velocity is strongly dependent on the phase difference θ of the roughness of the upper and lower plates. As the oscillation Reynolds number ReΩ increases, the velocity profile and the average velocity um(t) of AC EOF oscillate rapidly but the velocity amplitude decreases. The Deborah number De plays a similar role to ReΩ, which makes the AC EOF velocity profile more likely to oscillate. Meanwhile, phase lag χ (representing the phase difference between the electric field and the mean velocity) decreases when G and θ are increased. However, for larger λ (e.g., λ > 3), it almost has no phase lag χ.

A Reduced Order Model for Whole-Chip Thermal Analysis of Microfluidic Lab-on-a-Chip Systems

This paper presents a Krylov subspace projection-based Reduced Order Model (ROM) for whole microfluidic chip thermal analysis, including conjugate heat transfer. Two key steps in the reduced order modeling procedure are described in detail, including (1) the acquisition of a 3D full-scale computational model in the state-space form to capture the dynamic thermal behavior of the entire microfluidic chip; and (2) the model order reduction using the Block Arnoldi algorithm to markedly lower the dimension of the full-scale model. Case studies using practically relevant thermal microfluidic chip are undertaken to establish the capability and to evaluate the computational performance of the reduced order modeling technique. The ROM is compared against the full-scale model and exhibits good agreement in spatiotemporal thermal profiles (<0.5% relative error in pertinent time scales) and over three orders-of-magnitude acceleration in computational speed. The salient model reusability and real-time simulation capability renders it amenable for operational optimization and in-line thermal control and management of microfluidic systems and devices.

Electrokinetic transport in microchannels with random roughness

We present a numerical framework to model the electrokinetic transport in microchannels with random roughness. The three-dimensional microstructure of the rough channel is generated by a random generation-growth method with three statistical parameters to control the number density, the total volume fraction, and the anisotropy characteristics of roughness elements. The governing equations for the electrokinetic transport are solved by a high-efficiency lattice Poisson-Boltzmann method in complex geometries. The effects from the geometric characteristics of roughness on the electrokinetic transport in microchannels are therefore modeled and analyzed. For a given total roughness volume fraction, a higher number density leads to a lower fluctuation because of the random factors. The electroosmotic flow rate increases with the roughness number density nearly logarithmically for a given volume fraction of roughness but decreases with the volume fraction for a given roughness number density. When both the volume fraction and the number density of roughness are given, the electroosmotic flow rate is enhanced by the increase of the characteristic length along the external electric field direction but is reduced by that in the direction across the channel. For a given microstructure of the rough microchannel, the electroosmotic flow rate decreases with the Debye length. It is found that the shape resistance of roughness is responsible for the flow rate reduction in the rough channel compared to the smooth channel even for very thin double layers, and hence plays an important role in microchannel electroosmotic flows.