Modeling electrochemical systems with weakly imposed Dirichlet boundary conditions

Finite element modeling of charged species transport has enabled analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck equations coupled with the Navier-Stokes equation, with a key quantity of interest being the current at the system boundaries. Accurately computing the current flux is challenging due to the small critical dimension of the boundary layers (small Debye layer) that require fine mesh resolution at the boundaries. We resolve this challenge by using the Dirichlet-to-Neumanntransformation to weakly impose the Dirichlet conditions for the Poisson-Nernst-Planck equations. The results obtained with weakly imposed Dirichlet boundary conditions showed excellent agreement with those obtained when conventional boundary conditions with highly resolved mesh we reemployed. Furthermore, the calculated current flux showed faster mesh convergence using weakly imposed conditions compared to the conventionally imposed Dirichlet boundary conditions. We illustrate the approach on canonical 3D problems that otherwise would have been computationally intractable to solve accurately. This approach substantially reduces the computational cost of model-ing electrochemical systems.Comment: 24 pages, 14 figure

Direct numerical simulation of electrokinetic transport phenomena: variational multi-scale stabilization and octree-based mesh refinement

Finite element modeling of charged species transport has enabled the analysis, design, and optimization of a diverse array of electrochemical and electrokinetic devices. These systems are represented by the Poisson-Nernst-Planck (PNP) equations coupled with the Navier-Stokes (NS) equation. Direct numerical simulation (DNS) to accurately capture the spatio-temporal variation of ion concentration and current flux remains challenging due to the (a) small critical dimension of the electric double layer (EDL), (b) stiff coupling, large advective effects, and steep gradients close to boundaries, and (c) complex geometries exhibited by electrochemical devices. In the current study, we address these challenges by presenting a direct numerical simulation framework that incorporates: (a) a variational multiscale (VMS) treatment, (b) a block-iterative strategy in conjunction with semi-implicit (for NS) and implicit (for PNP) time integrators, and (c) octree based adaptive mesh refinement. The VMS formulation provides numerical stabilization critical for capturing the electro-convective instabilities often observed in engineered devices. The block-iterative strategy decouples the difficulty of non-linear coupling between the NS and PNP equations and allows using tailored numerical schemes separately for NS and PNP equations. The carefully designed second-order, hybrid implicit methods circumvent the harsh timestep requirements of explicit time steppers, thus enabling simulations over longer time horizons. Finally, the octree-based meshing allows efficient and targeted spatial resolution of the EDL. These features are incorporated into a massively parallel computational framework, enabling the simulation of realistic engineering electrochemical devices. The numerical framework is illustrated using several challenging canonical examples

An Electrokinetic Separation Route to Source Dialysate from Excess Fluid in Blood

To improve the health of patients with end-stage renal disease, there is a clear need for slow, continuous hemodialysis, and the primary barrier to a wearable device is the requirement of a large reservoir of dialysate. We describe an electrokinetic means of producing dialysate from the excess fluid extant in the peripheral blood of patients undergoing therapy. A critical feature of this process is the retention of essential components of blood, especially serum albumin. In progress toward this goal, we demonstrate the separation of charged from neutral species in blood plasma at a branched microchannel junction by ion concentration polarization (ICP). Further, we introduce a method that reduces the opportunity for damage to proteins and prevents electrode biofouling. The present approach results in as high as 99.7% retention of albumin and successful separation of neutral metabolites and excess fluid to be utilized as a precursor to dialysate

Dual-channel bipolar electrode focusing: simultaneous separation and enrichment of both anions and cations

In this paper we show that a microelectrochemical cell comprising two parallel microchannels spanned by a single bipolar electrode can be used to simultaneously enrich and separate both anions and cations within a single microchannel. This is possible because reduction and oxidation of water at the cathodic and anodic poles of the bipolar electrode, respectively, lead to ion depletion zones. Specifically, TrisH + is neutralized by OH 2 at the cathodic pole, while acetate buffer is neutralized by H + at the anodic pole. This action creates a local electric field gradient having both positive and negative components, and hence positive and negative ions follow their respective field gradients leading to separation. In the presence of an opposing counter-flow (pressure driven flow in this case), enrichment also occurs. In addition to separation and enrichment in a single channel, it is also possible to simultaneously enrich cations in one microchannel and anions in the other. Enrichment is achieved by controlling experimental parameters, including the type of buffer and the direction and magnitude of the opposing counter-flow

Improved Detection by Ensemble-Decision Aliquot Ranking of Circulating Tumor Cells with Low Numbers of a Targeted Surface Antigen

Circulating tumor cells (CTCs) are shed from a solid tumor into the bloodstream and can seed new metastases. CTCs hold promise for cancer diagnosis and prognosis and to increase our understanding of the metastatic process. However, their low numbers in blood and varied phenotypic characteristics make their detection and isolation difficult. One source of heterogeneity among CTCs is molecular: When they leave the primary tumor, these cells must undergo a molecular transition, which increases their mobility and chance of survival in the blood. During this molecular transition, the cells lose some of their epithelial character, which is manifested by the expression of the cell surface antigen known as epithelial cell adhesion molecule (EpCAM). Some tumors shed CTCs that express high levels of EpCAM; others release cells that have a low level of the antigen. Nevertheless, many CTC isolation techniques rely on the detection of EpCAM to discriminate CTCs from other cells in the blood. We previously reported a high-throughput immunofluorescence-based technology that targets EpCAM to rank aliquots of blood for the presence or absence of a CTC. This technology, termed ensemble decision aliquot ranking (eDAR), recovered spiked-in cancer cells (taken from a model EpCAM^high cell line) from blood at an efficiency of 95%. In this paper, we evaluated eDAR for recovery of cells that have low EpCAM expression and developed an immunofluorescence labeling strategy that significantly enhances the method’s performance. Specifically, we used a cocktail of primary antibodies for both epithelial and mesenchymal antigens as well as a dye-linked secondary antibody. The cocktail allowed us to reliably detect a model EpCAM^low cell line for triple negative breast cancer, MDA-MB-231, with a recovery efficiency of 86%. Most significantly, we observed an average of 6-fold increase in the number of CTCs isolated from blood samples from breast cancer patients. These findings underscore the importance of benchmarking CTC technologies with model cell lines that express both high and low levels of EpCAM

Negative Dielectrophoretic Capture and Repulsion of Single Cells at a Bipolar Electrode: The Impact of Faradaic Ion Enrichment and Depletion

This paper describes the dielectrophoretic (DEP) forces generated by a bipolar electrode (BPE) in a microfluidic device and elucidates the impact of faradaic ion enrichment and depletion (FIE and FID) on electric field gradients. DEP technologies for manipulating biological cells provide several distinct advantages over other cell-handling techniques including label-free selectivity, inexpensive device components, and amenability to single-cell and array-based applications. However, extension to the array format is nontrivial, and DEP forces are notoriously short-range, limiting device dimensions and throughput. BPEs present an attractive option for DEP because of the ease with which they can be arrayed. Here, we present experimental results demonstrating both negative DEP (nDEP) attraction and repulsion of B-cells from each a BPE cathode and anode. The direction of nDEP force in each case was determined by whether the conditions for FIE or FID were chosen in the experimental design. We conclude that FIE and FID zones generated by BPEs can be exploited to shape and extend the electric field gradients that are responsible for DEP force

Negative Dielectrophoretic Capture and Repulsion of Single Cells at a Bipolar Electrode: The Impact of Faradaic Ion Enrichment and Depletion

This paper describes the dielectrophoretic (DEP) forces generated by a bipolar electrode (BPE) in a microfluidic device and elucidates the impact of faradaic ion enrichment and depletion (FIE and FID) on electric field gradients. DEP technologies for manipulating biological cells provide several distinct advantages over other cell-handling techniques including label-free selectivity, inexpensive device components, and amenability to single-cell and array-based applications. However, extension to the array format is nontrivial, and DEP forces are notoriously short-range, limiting device dimensions and throughput. BPEs present an attractive option for DEP because of the ease with which they can be arrayed. Here, we present experimental results demonstrating both negative DEP (nDEP) attraction and repulsion of B-cells from each a BPE cathode and anode. The direction of nDEP force in each case was determined by whether the conditions for FIE or FID were chosen in the experimental design. We conclude that FIE and FID zones generated by BPEs can be exploited to shape and extend the electric field gradients that are responsible for DEP force