We present an efficient and robust numerical model for the simulation of electrokinetic phenomena in porous media and microstructure networks considering a wide range of applications including energy conversion, deionization, and microfluidic-based lab-on-a-chip systems. Coupling between fluid flow and ion transport in these networks is governed by the Poisson-Nernst-Planck-Stokes equations. These equations describe a wide range of phenomena that can interact in a complex fashion when coupled in networks involving multiple pores with variable properties. Capturing these phenomena by direct simulation of the governing equations in multidimensions is prohibitively expensive. We present here a reduced-order model that treats a network of many pores via solutions to 1D equations. Assuming that each pore in the network is long and thin, we derive a 1D model describing the transport in the pore's longitudinal direction. We take into account the cross-sectional nonuniformity of potential and ion concentration fields in the form of area-averaged coefficients in different flux terms representing fluid flow, electric current, and ion fluxes. These coefficients are obtained from the solutions to the Poisson-Boltzmann equation and are tabulated against dimensionless surface charge and dimensionless thickness of the electric double layer (EDL). Although similar models have been attempted in the past, distinct advantages of the present framework include a fully conservative discretization with zero numerical leakage, fully bounded area-averaged coefficients without any singularity in the limit of infinitely thick EDLs, a flux discretization that exactly preserves equilibrium conditions, and extension to a general network of pores with multiple intersections. In part II of this two-article series, we present a numerical implementation of this model and demonstrate its applications in predicting a wide range of electrokinetic phenomena in microstructures.

No abstract

Aim We aim to evaluate the reproductive outcome of fertility-sparing surgery and chemotherapy among young women diagnosed with MOGCT of any stage. Methods In the current retrospective study we evaluated 79 patients with malignant ovarian germ cell tumors (MOGCT) who visited at Imam Center, Vali-e-asr Hospital, Gynecologic Oncology department during 2001–2016. Reproductive outcomes (menstruation status and childbearing) followed fertility-preserving surgery and adjuvant chemotherapy by filling questionnaires. Statistical analysis was done with SPSS software, Chi-Square Tests were done, and significance was determined at P ≤ 0.05. Results among 79 young women who underwent fertility-sparing treatment, 72 patients followed up for reproductive outcome, and 7 patients excluded because of death (3 cases), XY genotyping (3 cases), and bilateral ovarian involvement (1 case). The mean age at presentation was 23 years. (Range: 19–33 years). The 5 and 10-year disease-free survival rate was 87% and 94.4%, respectively. The overall survival rate (OSR) was 94.4% at 5 and 10 years. Regular menstruation recovered in 60 of 72 patients after treatment (83%). All patients without adjuvant chemotherapy experienced regular menstruation, while normal menstruation was retrieved in 78% in the adjuvant chemotherapy group at the end of treatment. This retrieval of regular menstruation was not dependent on the age or number of chemotherapy cycles. 19 of 26 patients who attempted pregnancy were led to delivery (73%). No one required infertility treatments. The mean of chemotherapy cycles is related to a successful pregnancy. Conclusion We showed patients with MOGCT could become pregnant and give birth if they desire. The advanced tumor stage wasn't the convincing factor for avoiding fertility preservation. Fertility sparing surgery with adjuvant chemotherapy is a safe treatment and results in a high fertility rate.

The first part of this two-article series presented a robust mathematical model for the fast and accurate prediction of electrokinetic phenomena in porous networks with complex topologies. In the second part of this series, we first present a numerical algorithm that can efficiently solve the model equations. We then demonstrate that the resulting framework is capable of capturing a wide range of transport phenomena in microstructures by considering a hierarchy of canonical problems with increasing complexity. The developed framework is validated against direct numerical simulations of deionization shocks in micropore-membrane junctions and concentration polarization in micro- and nanochannel systems. We demonstrate that for thin pores subject to concentration gradients our model consistently captures correct induced osmotic pressure, which is a macroscopic phenomena originally derived from thermodynamic principles but here is naturally predicted through microscopic electrostatic interactions. Moreover, we show that the developed model captures current rectification phenomena in a conical nanopore subject to an axial external electric field. Finally, we provide discussions on examples involving stationary and moving deionization shocks in micropore nanopore T-junctions as well as induced-flow loops when pores of varying sizes are connected in parallel.