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Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and find that droplets exhibit a drift velocity and position dependent growth. As a consequence, the dissolution boundary moves through the system, thereby segregating droplets to one end. We show that for steep enough gradients, the ripening leads to a transient arrest of droplet growth that is induced by a narrowing of the droplet size distribution.

The gut microbiota features important genetic diversity, and the specific spatial features of the gut may shape evolution within this environment. We investigate the fixation probability of neutral bacterial mutants within a minimal model of the gut that includes hydrodynamic flow and resulting gradients of food and bacterial concentrations. We find that this fixation probability is substantially increased, compared with an equivalent well-mixed system, in the regime where the profiles of food and bacterial concentration are strongly spatially dependent. Fixation probability then becomes independent of total population size. We show that our results can be rationalized by introducing an active population, which consists of those bacteria that are actively consuming food and dividing. The active population size yields an effective population size for neutral mutant fixation probability in the gut.

Convective transport can significantly distort spatial concentration gradients. Interstitial flow is ubiquitous throughout living tissue, but our understanding of how interstitial flow affects concentration gradients in biological processes is limited. Interstitial flow is of particular interest for angiogenesis because pathological and physiological angiogenesis is associated with altered interstitial flow, and both interstitial flow and morphogen gradients (e.g., vascular endothelial growth factor, VEGF) can potentially stimulate and guide new blood vessel growth. We designed an in vitro microfluidic platform to simulate 3D angiogenesis in a tissue microenvironment that precisely controls interstitial flow and spatial morphogen gradients. The microvascular tissue was developed from endothelial colony forming cell-derived endothelial cells extracted from cord blood and stromal fibroblasts in a fibrin extracellular matrix. Pressure in the microfluidic lines was manipulated to control the interstitial flow. A mathematical model of mass and momentum transport, and experimental studies with fluorescently labeled dextran were performed to validate the platform. Our data demonstrate that at physiological interstitial flow (0.1–10 μm/s), morphogen gradients were eliminated within hours, and angiogenesis demonstrated a striking bias in the opposite direction of interstitial flow. The interstitial flow-directed angiogenesis was dependent on the presence of VEGF, and the effect was mediated by αvβ3 integrin. We conclude that under physiological conditions, growth factors such as VEGF and fluid forces work together to initiate and spatially guide angiogenesis.

Inspired by the paper platforms for 3-D cell culture, a paper-based microfluidic device containing drug concentration gradient was designed and constructed for investigating cell response to drugs based on high throughput analysis. This drug gradient generator was applied to generate concentration gradients of doxorubicin (DOX) as the model drug. HeLa cells encapsulated in collagen hydrogel were incubated in the device reservoirs to evaluate the cell viability based on the controlled release of DOX spatially. It was demonstrated that drug diffusion through the paper fibers created a gradient of drug concentration, which influenced cell viability. This drug screening platform has a great opportunity to be applied for drug discovery and diagnostic studies with simultaneous and parallel tests of drugs under various gradient concentrations.

Maximizing amendment potential is an emphasis in the HM-contaminated field of phytoremediation by hyperaccumulators due to the low bioavailability of HMs in soils and small biomass yields of plants. This study investigated the influence of different types and concentrations of plant growth regulators on Cd phytoremediation by Solanum nigrum in contaminated soil. Our conclusions showed that the shoot Cd extractions (μg plant −1 ) and the root and shoot biomasses at all the treatments remarkedly increased compared with that of the CK ( p  < 0.05), while the Cd concentrations at root and aboveground parts by S. nigrum , the extractable Cd concentrations, and pH value of soils did not change significantly compared with the CK ( p  < 0.05). Furthermore, correlation analysis showed that the shoot Cd phytoaccumulation and the root and aboveground biomasses of S. nigrum were particularly dependent upon the application of CTK and GA 3 concentration gradient ( p  < 0.05). Moreover, some related physicochemical indexes were determined for supervising the growth conditions of plants, and these results pointed out that after exogenous PGRs treatments, the chlorophyll content and antioxidative enzymes POD and SOD activities in vivo of plants clearly advanced, while the H 2 O 2 and MDA contents and CAT apparently declined. These consequence demonstrated that the exogenous PGR addition prominently reinforced the Cd phytoextraction capacity of S. nigrum in contaminated soil by stimulating plant growth and increasing shoot yields.

The entropy production in the polarization phenomena occurring in the underlimiting regime, when an electric current circulates through a single cation-exchange membrane system, has been investigated in the 3–40 °C temperature range. From the analysis of the current–voltage curves and considering the electro-membrane system as a unidimensional heterogeneous system, the total entropy generation in the system has been estimated from the contribution of each part of the system. Classical polarization theory and the irreversible thermodynamics approach have been used to determine the total electric potential drop and the entropy generation, respectively, associated with the different transport mechanisms in each part of the system. The results show that part of the electric power input is dissipated as heat due to both electric migration and diffusion ion transports, while another part is converted into chemical energy stored in the saline concentration gradient. Considering the electro-membrane process as an energy conversion process, an efficiency has been defined as the ratio between stored power and electric power input. This efficiency increases as both applied electric current and temperature increase.

Bulk doping of aluminum ions (Al 3+ ) is promising to solve the problems of poor safety and short cycling life of nickel-rich cathodes. A crucial chelating agent of sodium lactate is found here to realize the best co-precipitation of Al 3+ with other transition-metal ions at an atomic level for the first time. The discharge capacity of this cathode is increased by 13.17% at 1 C, while its cycle retention is promoted by 12.76% compared to a commercial counterpart. Additionally, the amount of chelating agent complexed with Al 3+ is optimized, and the gradient directions of Al-doping for the full concentration gradient materials are also investigated. It is found that the gradually increased Al 3+ concentration from core to shell can integrate the surface coating and bulk doping, improving the electrochemical performance. Its discharge capacity is 149.3 mAh/g at a high rate of 5 C. An approach for bulk Al-doping and synthesis of commercial NCA cathode materials is provided.

Hair follicles play an important role in hair development. This study aimed to develop a microgel-spotting device to fabricate a multilayered gel bead culture model and to mimic the early development of skin appendages to regenerate hair follicles in vitro. The model consists of an alginate gel layer containing cytokines as the core layer, a collagen gel layer containing mouse embryonic stem cells as the middle layer, and a collagen gel layer containing fetus-derived epidermal cells as the outer layer. A concentration gradient of cytokines is formed, which promotes interactions between epidermal and stem cells. Histological and immunnohistological analyses confirmed the reconstruction of hair follicle structures. As a result, the cell number and gel bead size could be precisely controlled by the developed microgel-spotting device. In the multilayered gel bead, the embryonic and epidermal cells cultured with the cytokine gradient formed cell aggregates with keratinized tissue in the center similar to “native” hair follicle structure. Sweat gland-like luminal tissue and erector pilorum-like structures were also observed around aggregates with concentric structures. In conclusion, the multilayered gel bead culture model demonstrated potential for in vitro hair follicle regeneration. The findings of this study provide insight into the early development of skin appendages.

This paper presents a new paradigm of deep neural network (DNN) for the inverse design of microfluidic concentration gradient generators (µCGGs) with complex network topology. In this method, a concentration gradient (CG) and design parameters yielding the CG are, respectively, used as inputs and outputs of DNN, and the relationship between them is mapped. Several new elements are also proposed, including utilization of fast-running physics-based component model in the closed form to generate a large amount of data for DNN learning which otherwise is not available through computationally demanding computational fluid dynamics (CFD) simulation; and a divide-and-conquer strategy and DNN formulation combining classification and regression to mitigate many-to-one design complications for enhanced accuracy. Several DNN structures are investigated and developed, including single fully connected neural network (FCNN), convolutional neural network, and a new cascade FCNN for a divide-and-conquer implementation. Case studies are performed on a triple-Y µCGG to evaluate design performance of the proposed method in a six-dimensional space that only includes sample concentrations at inlet reservoirs as design parameters, and in a nine-dimensional design space, to which inlet flow pressures are also added. It is verified in high-fidelity CFD simulation that widely used CGs can be produced using DNN-predicted design parameters accurately with average error < 4% and < 8.5% relative to the prescribed CGs, respectively, in the six- and nine-dimensional design space. The learned design rules are packaged into the DNN model that allows to generate accurate µCGGs designs instantaneously (~ 3 ms) and eliminates requirements of simulation and optimization knowledge, facilitating distribution of the design capabilities to microfluidic end users.

Concentration gradient generation plays a pivotal role in advancing applications across drug screening, chemical synthesis, and biomolecular studies, yet conventional methods remain constrained by labor-intensive workflows, limited throughput, and inflexible gradient control. This study presents a novel multilayer microfluidic chip leveraging shear flow-driven partitioning–recombination mechanisms to enable the flexible and high-throughput generation of concentration gradient droplets. The chip integrates interactive upper and lower polydimethylsiloxane (PDMS) layers, where sequential fluid distribution and recombination are achieved through circular and radial channels while shear forces from the oil phase induce droplet formation. Numerical simulations validated the dynamic pressure-driven concentration gradient formation, demonstrating linear gradient profiles across multiple outlets under varied flow conditions. The experimental results revealed that the shear flow mode significantly enhances mixing uniformity and droplet generation efficiency compared to continuous flow operations, attributed to intensified interfacial interactions within contraction–expansion serpentine channels. By modulating hydrodynamic parameters such as aqueous- and oil-phase flow rates, this system achieved tunable gradient slopes and droplet sizes, underscoring the intrinsic relationship between flow dynamics and gradient formation. The proposed device eliminates reliance on complex channel networks, offering a compact and scalable platform for parallelized gradient generation. This work provides a robust framework for optimizing microfluidic-based concentration gradient systems, with broad implications for high-throughput screening, combinatorial chemistry, and precision biomolecular assays.