We develop two models to describe ion transport in microchannels and nanochannels. For the first model, we obtain a one-dimensional (unsteady) partial differential equation governing flow and charge transport through a shallow and wide electrokinetic channel. In this model, the effects of electric double layer (EDL) on axial transport are taken into account using exact solutions of the Poisson-Boltzmann equation. The second simpler model, which is approachable analytically, assumes that the EDLs are confined to near-wall regions. Using a characteristics analysis, we showed that the latter model captures concentration polarization (CP) effects and provides useful insight into its dynamics. Two distinct CP regimes are identified: CP with propagation in which enrichment and depletion shocks propagate outward; and CP without propagation where polarization effects stay local to micro-nanochannel interfaces. The existence of each regime is found to depend on a nanochannel Dukhin number and mobility of the co-ion nondimensionalized by electroosmotic mobility. Interestingly, microchannel dimensions and axial diffusion are found to play an insignificant role in determining whether CP propagates. The steady state condition of propagating CP is shown to be controlled by channel heights, surface chemistry and co-ion mobility instead of the reservoir condition. Both models are validated against experimental results in Part II of this two paper series.

In this tutorial review aimed at researchers using nanofluidic devices, we summarize the current state of theoretical and experimental approaches to describing concentration polarization (CP) in hybrid microfluidic-nanofluidic systems. We also analyze experimental results for these systems and place them in the context of recent theoretical developments. We then extend the theory to explain the behavior of both positively and negatively charged, low-concentration, analyte species in systems with CP. We conclude by discussing several applications of CP in microfluidics.

Cell mass, volume and growth rate are tightly controlled biophysical parameters in cellular development and homeostasis, and pathological cell growth defines cancer in metazoans. The first measurements of cell mass were made in the 1950s, but only recently have advances in computer science and microfabrication spurred the rapid development of precision mass-quantifying approaches. Here we discuss available techniques for quantifying the mass of single live cells with an emphasis on relative features, capabilities and drawbacks for different applications.

We present results of a combined computational and experimental study of the propagation of concentration polarization (CP) zones in a microchannel-nanochannel system. Our computational model considers the combined effects of bulk flow, electromigration, and diffusion and accurately captures the dynamics of CP. Using wall charge inside the nanochannel as a single fitting parameter, we predict experimentally observed enrichment and depletion shock velocities. Our model can also be used to compute the existence of CP with propagating enrichment and depletion shocks based on measured ion mobility and wall properties. We present experiments where the background electrolyte consists of only a fluorescent ion and its counter ion. These results are used to validate the computational model and confirm predicted trends from an analytical model presented in the first of this two-paper series. We show experimentally that the enrichment region concentration is effectively independent of the applied current, while the enrichment and depletion shock velocities increase in proportion to current density.

Rapid antibody production in response to invading pathogens requires the dramatic expansion of pathogen-derived antigen-specific B lymphocyte populations. Whether B cell population dynamics are based on stochastic competition between competing cell fates, as in the development of competence by the bacterium , or on deterministic cell fate decisions that execute a predictable program, as during the development of the worm, remains unclear. Here, we developed long-term live-cell microscopy of B cell population expansion and multiscale mechanistic computational modeling to characterize the role of molecular noise in determining phenotype heterogeneity. We show that the cell lineage trees underlying B cell population dynamics are mediated by a largely predictable decision-making process where the heterogeneity of cell proliferation and death decisions at any given timepoint largely derives from nongenetic heterogeneity in the founder cells. This means that contrary to previous models, only a minority of genetically identical founder cells contribute the majority to the population response. We computationally predict and experimentally confirm nongenetic molecular determinants that are predictive of founder cells' proliferative capacity. While founder cell heterogeneity may arise from different exposure histories, we show that it may also be due to the gradual accumulation of small amounts of intrinsic noise during the lineage differentiation process of hematopoietic stem cells to mature B cells. Our finding of the largely deterministic nature of B lymphocyte responses may provide opportunities for diagnostic and therapeutic development.