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.

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.

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.

Carbon dioxide and hydrogen storage in geological formations at Gt scale are two promising strategies toward net-zero carbon emissions. To date, investigations into underground hydrogen storage (UHS) remain relatively limited in comparison to the more established knowledge body of underground carbon dioxide storage (UCS). Despite their analogous physical processes can be used for accelerating the advancements in UHS technology, the existing distinctions possibly may hinder direct applicability. This review therefore contributes to advancing our fundamental understanding on the key differences between UCS and UHS through multi-scale comparisons. These comparisons encompass key factors influencing underground gas storage, including storage media, trapping mechanisms, respective fluid properties, petrophysical properties, and injection scenarios. They provide guidance for the conversion of our existing knowledge from UCS to UHS, emphasizing the necessity of incorporating these factors relevant to their trapping and loss mechanisms. The article also outlines future directions to address the crucial knowledge gaps identified, aiming to enhance the utilisation of geological formations for hydrogen and carbon dioxide storage.

Unfavorable fluid-fluid displacement, where a low-viscosity fluid displaces a higher-viscosity fluid in permeable media, is commonly encountered in various subsurface processes. Understanding the formation and evolution of the resulting interfacial instability can have practical benefits for engineering applications. Using gradient capillary tubes as surrogate models of permeable media, we numerically investigate interfacial dynamics during gas-driven drainage. Our focus is on understanding the impact of tube geometry on interface stability. In a gradient tube, since the interface shape changes during the drainage process, we measure interfacial stability using the difference between the contact-line velocity Ucl and the meniscus tip velocity Utip. We define instability as a rapid reduction in the contact line velocity Ucl compared to the tip velocity Utip. Beyond the onset of this instability, gas penetrates into the liquid, forming a finger, and entraining a liquid film on the tube wall. The observed stability transition can be rationalized to a large extent by adaptation of an existing theory for cylindrical tubes in terms of a critical capillary number Cacrit. For an expanding tube, simulations suggest that a stability transition from an initially unstable meniscus to a final stable one, with Ucl catching up with Utip, can occur if the local capillary number is initially slightly larger than Cacrit and then drops below Cacrit. The insights gained from this study can be beneficial in estimating the mode and efficiency of subsurface fluid displacement. We numerically investigate the dynamics of a gas-liquid interface during drainage in a gradient capillary tube The observations from our numerical simulations can be rationalized by an adapted theoretical model We find a unique stabilization in drainage along expanding tubes, suppressing film entrainment even when the system is initially unstable

We present an unexplored regime, where the binary random close packing fraction ϕRCPb is smaller than that of the mono-sized one ϕRCPm. This is against previous observations and common perceptions that binary packing tends to be denser than mono-sized packing. We numerically confirm the critical condition for reaching this exceptional regime in the size ratio (Rr) and mole fraction (Xs) space, where Rr is close to 1, and the mole fraction of the smaller sphere Xs close to 0. Under the same loading condition, the stiffness of the packing at this exceptional regime is found to be significantly higher than that of the mono-sized packing. The formation and transition of this regime for varying Rr and Xs are theoretically modelled based on the hard-sphere fluid theory. This exceptional regime remains unreported in existing literature, yet significant for our fundamental understanding of binary packing systems.

Spontaneous imbibition flows within confined geometries are commonly encountered in both natural phenomena and industrial applications. A profound knowledge of the underlying flow dynamics benefits a broad spectrum of engineering practices. Nonetheless, within this area, especially concerning complex geometries, there exists a substantial research gap. This work centers on the cylinder-plane geometry, employing a combined theoretical and numerical approach to investigate the process of a wetting film wrapping a cylinder corner. It is found that the advance of the liquid front generally follows the Lucas-Washburn kinetics, i.e., t1/2 scaling, but it also depends on the dynamics of the liquid source. Furthermore, a theoretical estimation of the timescale associated with the imbibition process is also provided, especially the merging time as an important time length characterizing the duration of the wetting process. The timescale is highly dependent on the wettability conditions and the properties of the involved liquid. The conclusion of this work lays a theoretical foundation for comprehensively understanding the capillary phenomena in complex media and shedding light on various microfluidic applications.

Droplet mobility is essential in a wide range of engineering applications, e.g., fog collection and self-cleaning surfaces. For structured surfaces to achieve superhydrophobicity, the removal of stains adhered within the microscale surface features strongly determines the functional performance and durability. In this study, we numerically investigate the mobility of the droplet trapped within porous surfaces. Through simulations covering a wide range of flow conditions and porous geometries, three droplet mobility modes are identified, i.e., the stick-slip, crossover, and slugging modes. To quantitatively char-acterise the droplet dynamics, we propose a droplet-scale capillary number that considers the driving force and capillary resistance. By comparing against the simulation results, the proposed dimensionless number presents a strong correlation with the leftover volume. The dominating mechanisms revealed in this study provide a basis for further research on enhancing surface cleaning and optimising design of anti-fouling 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 for wettability, θ₁ ∈ [75°, 95°] and θ₂ ∈ [15°, 45°]; for film size, r_w/r₁ ∈ [0.12, 0.30]. The film stability, which depends on the film size and the wall wettability, is firstly 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 post\nobreakdash-instability 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 neighboring 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 neighboring 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.