Culturing living cells in three-dimensional environments increases the biological relevance of laboratory experiments, but requires solutes to overcome a diffusion barrier to reach the centre of cellular constructs. We present a theoretical and numerical investigation that brings a mechanistic understanding of how microfluidic culture conditions, including chamber size, inlet fluid velocity and spatial confinement, affect solute distribution within three-dimensional cellular constructs. Contact with the chamber substrate reduces the maximally achievable construct radius by 15%. In practice, finite diffusion and convection kinetics in the microfluidic chamber further lower that limit. The benefits of external convection are greater if transport rates across diffusion-dominated areas are high. Those are omnipresent and include the diffusive boundary layer growing from the fluid-construct interface and regions near corners where fluid is recirculating. Such regions multiply the required convection to achieve a given solute penetration by up to 100, so chip designs ought to minimize them. Our results define conditions where complete solute transport into an avascular three-dimensional cell construct is achievable and applies to real chambers without needing to simulate their exact geometries.

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, accurate methods for drag prediction rely on experiments or numerical simulations which are costly and time consuming. Data-driven regression methods have the potential to provide a prediction that is accurate and fast. We assess the performance and limitations of linear regression, kernel methods and neural networks for drag prediction using a database of 1000 homogeneous rough surfaces. Model performance is evaluated using the roughness function obtained at a friction Reynolds number $Re_\tau$ of 500. With two trainable parameters, the kernel method can fully account for nonlinear relations between the roughness function $\Delta U<^>+$ and surface statistics (roughness height, effective slope, skewness, etc.). In contrast, linear regression cannot account for nonlinear correlations and displays large errors and high uncertainty. Multilayer perceptron and convolutional neural networks demonstrate performance on par with the kernel method but have orders of magnitude more trainable parameters. For the current database size, the networks' capacity cannot be fully exploited, resulting in reduced generalizability and reliability. Our study provides insight into the appropriateness of different regression models for drag prediction. We also discuss the remaining steps before data-driven methods emerge as useful tools in applications.

Cycle injection schemes are often encountered in underground hydrogen storage (UHS), and the involved hysteresis directly impacts storage and extraction efficiency. The geological formation generally has hierarchical features containing multiple-level pore sizes. Nevertheless, we still lack a comprehensive understanding of this phenomenon and the pore-scale mechanism behind the geometry affects saturation hysteresis and its cyclic responses. In this work, by 3D printing technology, we fabricated a hierarchically structured porous media with dual permeability and uniform one for comparison. Gas-liquid injection cycles were performed to investigate the impact of hierarchical structure on invasion behavior. The phase morphology shows the preferential invasion in 1st-order structure and the capillary trapping in 2nd-order structure, which are supported by the phase saturation at each level of the hierarchical structure. Furthermore, ganglion motion is suppressed in the hierarchical structure. Through analyzing local invasion behaviors, the connect-jump invasion mode is identified as the primary reason for this suppression. Then, the hysteresis effect was quantified based on the Land model, revealing a weaker hysteresis effect in the hierarchical structure compared with the uniform structure, indicating that the hierarchical structure has a lower storage and extraction efficiency in UHS. Finally, the upward trend of relative permeability with saturation was fitted by the van Genuchten model. The model parameter in the hierarchical structure is higher than that in the uniform structure, which is caused by extra pore space in 2nd-order structure. The findings improve the understanding of hysteresis effect and can promote optimizing strategies for storage and extraction in UHS.

We report an anomalous capillary phenomenon that reverses typical capillary trapping via nanoparticle suspension and leads to a counterintuitive self-removal of non-aqueous fluid from dead-end structures under weakly hydrophilic conditions. Fluid interfacial energy drives the trapped liquid out by multiscale surfaces: the nanoscopic structure formed by nanoparticle adsorption transfers the molecular-level adsorption film to hydrodynamic film by capillary condensation, and maintains its robust connectivity, then the capillary pressure gradient in the dead-end structures drives trapped fluid motion out of the pore continuously. The developed mathematical models agree well with the measured evolution dynamics of the released fluid. This reversing capillary trapping phenomenon via nanoparticle suspension can be a general event in a random porous medium and could dramatically increase displacement efficiency. Our findings have implications for manipulating capillary pressure gradient direction via nanoparticle suspensions to trap or release the trapped fluid from complex geometries, especially for site-specific delivery, self-cleaning, or self-recover systems.

Biofilms constitute one of the most common forms of living matter, playing an increasingly important role in technology, health, and ecology. While it is well established that biofilm growth and morphology are highly dependent on the external flow environment, the precise role of fluid friction has remained elusive. We grew Bacillus subtilis biofilms on flat surfaces of a channel in a laminar flow at wall shear stresses spanning one order of magnitude (τw = 0.068 Pa to τw = 0.67 Pa). By monitoring the three-dimensional distribution of biofilm over seven days, we found that the biofilms consist of smaller microcolonies, shaped like leaning pillars, many of which feature a streamer in the form of a thin filament that originates near the tip of the pillar. While the shape, size, and distribution of these microcolonies depend on the imposed shear stress, the same structural features appear consistently for all shear stress values. The formation of streamers occurs after the development of a base structure, suggesting that the latter induces a secondary flow that triggers streamer formation. Moreover, we observed that the biofilm volume grows approximately linearly over seven days for all shear stress values, with a growth rate inversely proportional to the wall shear stress. We develop a scaling model, providing insight into the mechanisms by which friction limits biofilm growth.

Lubricated textured surfaces immersed in liquid flows offer tremendous potential for reducing fluid drag, enhancing heat and mass transfer, and preventing fouling. According to current design rules, the lubricant must chemically match the surface to remain robustly trapped within the texture. However, achieving such chemical compatibility poses a significant challenge for large-scale flow systems, as it demands advanced surface treatments or severely limits the range of viable lubricants. In addition, chemically tuned surfaces often degrade over time in harsh environments. Here, we demonstrate that a lubricant-infused surface (LIS) can resist drainage in the presence of external shear flow without requiring chemical compatibility. Surfaces featuring longitudinal grooves can retain up to 50% of partially wetting lubricants in fully developed turbulent flows. The retention relies on contact-angle hysteresis, where triple-phase contact lines are pinned to substrate heterogeneities, creating capillary resistance that prevents lubricant depletion. We develop an analytical model to predict the maximum length of pinned lubricant droplets in microgrooves. This model, validated through a combination of experiments and numerical simulations, can be used to design chemistry-free LISs for applications where the external environment is continuously flowing. Our findings open up new possibilities for using functional surfaces to control transport processes in large systems.

Understanding the influence of surface roughness on drag forces remains a significant challenge in fluid dynamics. This paper presents a convolutional neural network (CNN) that predicts drag solely by the topography of rough surfaces and is capable of discovering spatial patterns linked to drag-inducing structures. A CNN model was developed to analyze spatial information from the topography of a rough surface and predict the roughness function, Δ U + , obtained from direct numerical simulation. This model enables the prediction of drag from rough surface data alone, which was not possible with previous methods owing to the large number of surface-derived parameters. Additionally, the retention of spatial information by the model enables the creation of a feature map that accentuates critical areas for drag prediction on rough surfaces. By interpreting the feature maps, we show that the developed CNN model is able to discover spatial patterns associated with drag distributions across rough surfaces, even without a direct training on drag distribution data. The analysis of the feature map indicates that, even without flow field information, the CNN model extracts the importance of the flow-directional slope and height of roughness elements as key factors in inducing pressure drag. This study demonstrates that CNN-based drag prediction is grounded in physical principles of fluid dynamics, underscoring the utility of CNNs in both predicting and understanding drag on rough surfaces.

In this study, we investigate the stability of a film that is attached to a corner between a cylinder and a substrate, using a combination of theoretical and numerical approaches. Notably, we place our focus on flat and thin films where the contact line is almost perpendicular to the cylinder wall whereas a small angle forms between the contact line and the substrate, and the film size is smaller than the cylinder radius. The film stability, which depends on the film size and the wall wettability, is first predicted by a standard linear stability analysis (LSA) within the long-wave theoretical framework. We find that the film size plays the most important role in controlling the film stability. Specifically, the thicker the film is, the less sensitive it becomes to the large-wavenumber perturbation. The wall wettability mainly impacts the growth rates of perturbations and slightly influences the marginal stability and postinstability patterns of wrapping films. We compare the LSA predictions with numerical results obtained from a disjoining pressure model (DPM) and volume-of-fluid (VOF) simulations, which provide more insights into the film breakup process. At the early stage there is a strong agreement between the LSA predictions and the DPM results. Notably, as the perturbation grows, thin film regions connecting two neighbouring satellite droplets form which may eventually lead to a stable or temporary secondary droplet, an aspect which the LSA is incapable of capturing. In addition, the VOF simulations suggest that beyond a critical film size, merging between two neighbouring drops becomes involved during the breakup stage. Therefore, the LSA predictions are able to provide only an upper limit on the final number of satellite droplets.

Turbulent flows over porous lattices consisting of rectangular cuboid pores are investigated using scale-resolving direct numerical simulations. Beyond a certain threshold which is primarily determined by the wall-normal Darcy permeability, K_y, near-wall turbulence transitions from its canonical regime, marked by the presence of streak-like structures, to another marked by the presence of Kelvin-Helmholtz-like (K-H-like) spanwise-coherent structures. The threshold agrees well with that previously established in studies where permeable-wall boundary conditions had been used as surrogates for a porous substrate. In the smooth-wall-like regime, none of the investigated substrates demonstrate any reduction in drag relative to a smooth-wall flow. At the permeable surface, a notable component of the flow is that which adheres to the pore geometry and undergoes modulation by the turbulent scales of motions due to the interaction mechanism described by Abderrahaman-Elena et al. (2019). Its resulting effect can be quantified in terms of an amplitude modulation (AM) using the approach of Mathis et al. (2009). This pore-coherent flow component persists throughout the porous substrate, highlighting the importance of a given substrate's microstructure in the presence of an overlying turbulent flow. This geometry-related aspect of the flow is not accounted for when continuum-based models for a porous medium or effective representations of them such as wall boundary conditions are used. The intensity of the AM effect is enhanced in the K-H-like regime and becomes strengthened with larger permeability. As a result, structured porous materials may be designed to exploit or mitigate these flow features depending upon the intended application.