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Previously conducted studies have established that the soil–rock mixture in the Chongqing area has the characteristics of loose structure, poor stability, strong permeability, and so on. When building a tunnel in a soil–rock mixture stratum, it is necessary to reinforce the surface rock mass and surrounding rock by grouting to improve the safety of tunnel excavation. To study the diffusion mechanism of cement slurry (Bingham fluid) in soil–rock mixtures, based on the Bingham fluid flow equation and slurry diffusion model, the Bingham fluid fracture diffusion formula was derived, and field grouting tests and indoor model tests were carried out with soil–rock mixtures in the Chongqing area as the research object. The fracture grouting diffusion formula was verified and analyzed using the test data. The research results show that the theoretical calculation results of various working conditions are close to the actual test results (the error of indoor model test results is less than 3%, and the error of field test results is less than 5%). A Bingham fluid fracture diffusion formula has been developed that applies to various working conditions of fracture grouting of soil–rock mixtures and has a good prediction effect on the value of the fracture diffusion radius.

The aim of this research was to conduct randomized trials assessing the extent of cement diffusion following robot-assisted percutaneous vertebroplasty (R-PVP) for osteoporotic vertebral compression fractures (OVCF). A total of 96 OVCF patients meeting the inclusion criteria and admitted between January 2023 and November 2023 were included in the study. Among them, 48 patients were assigned to the robotic-assisted PVP group (R-PVP group) and 48 patients were assigned to the traditional PVP group (PVP group). The study examined the differences in age, sex, BMD T-value, fracture segment, preoperative, postoperative, and 3-month postoperative visual analogue scale (VAS) and Oswestry disability index (ODI) pain scores, fluoroscopic dose, frequency of fluoroscopy, volume of bone cement injected, angle of puncture abduction, degree of cement diffusion, and bone cement spillage among the two patient groups. A logistic regression model was employed to analyze the factors influencing the extent of postoperative bone cement diffusion. The findings indicated that the R-PVP group exhibited a significantly larger puncture abduction angle, improved postoperative cement dispersion, increased cement injection volume, and decreased incidence of cement spillage compared to the PVP group. Furthermore, the R-PVP group demonstrated superior outcomes in these aspects, as well as lower intraoperative fluoroscopic frequency and radiation exposure. Additionally, bone density, puncture abduction angle, cement injection volume, and surgical approach were identified as independent factors associated with the extent of postoperative cement dispersion.

Background Bone cement leakage causes severe complication following percutaneous vertebroplasty. This study probed the diffusion and leakage status of bone cement injected within diverged time duration, so as to find the optimal injection time for bone cement. Methods A total of 70 patients with osteoporotic vertebral compression fractures with a symptom of low back pain, who underwent treatment at hospital were enrolled in this study. Patients were randomized into three groups: < 180 s, 180–300, and > 300 s of injection time duration from the beginning to the completion of the injection. The scenarios of vertebral bone cement leakage and diffusion were inspected using postoperative CT. Results The diffusion coefficient was higher in group A than in group B whereas it was higher in group B than in group C, but without statistical significance among the three groups. The leakage rate was without statistical significance among the three groups. The injection time of bone cement was negatively correlated with the diffusion coefficient, at the correlation coefficient of − 0.253. Conclusions The diffusion coefficient of high-viscosity bone cement is negatively correlated with the injection time, and the leakage rate of high-viscosity bone cement does not reduce with the prolongation of injection time.

The optimal cement diffusion pattern in unilateral percutaneous kyphoplasty (PKP) for osteoporotic vertebral compression fractures (OVCFs) remains debated. This multicenter retrospective study investigated whether crossing the vertebral midline with bone cement is necessary under the DGOU classification. A total of 440 patients with single-level OVCFs treated by unilateral PKP (2020–2023) were categorized into OF1, OF2, or OF3 types based on the DGOU classification and further divided into crossing and non-crossing groups according to postoperative CT. Outcomes included VAS, ODI, and radiographic parameters. In OF1 fractures, no significant differences were observed between the two groups. However, for OF2 and OF3 fractures, the crossing group demonstrated significantly better ODI scores at 6 and 12 months ( P  < 0.001) and improved vertebral height maintenance ( P  < 0.001), without increasing complications. These findings suggest that achieving cross-midline cement diffusion may not be necessary for stable OF1 fractures, but it is associated with significantly better mid- to long-term functional and radiographic outcomes in unstable OF2/OF3 fracture types.

Molecular diffusion is a critical mechanism of enhance oil recovery (EOR) in developing shale oil reservoir by huff “n” puff. The ultra‐low permeability lead to the accumulation of injected gas within the complex fracture networks (CFNs), thereby, enhancing concentration gradient and mass transfer by molecular diffusion between the CFNs and matrix. A proper understanding of CFNs influence on molecular diffusive mass transfer becomes critical for predicting oil recovery and remaining oil distribution in shale oil reservoirs. Therefore, a multiphase and multicomponent mathematical model with molecular diffusion was developed for describing mass transfer of molecular diffusion. Molecular diffusion coefficients were predicted by the extend Sigmund method. The finite volume method (FVM) and two‐point flux approximation (TPFA) were applied to discretize and approximate mass transfer equations. The embedded discrete fracture model (EDFM) was utilized to explicitly simulate CFNs and extended to couple mass transfer by molecular diffusion in the fracture to that in the matrix. Model validation clearly demonstrates that the proposed numerical model is capable of effectively and accurately simulating diffusion mass transfer in shale oil reservoirs with CFNs. By applying the proposed numerical compositional model, a series of synthetical models with molecular diffusion were developed by CO 2 huff “n” puff. The simulation results indicated that molecular diffusion is crucial to EOR in developing shale oil reservoirs with CFNs by huff “n” puff, particularly in the injection and soaking stage. However, molecular diffusion contributes to an increased gas production during the production phase. In addition, larger fracture density benefits diffusive mass transfer to EOR by increasing contact areas. And higher diffusion coefficients improve diffusive mobility, which boosts diffusive mass transfer. Meanwhile, greater injection rate additionally makes concentration difference of injected component between fractures and matrix system to rise, resulting in more injected component transferring into matrix. This paper provides a better understanding of molecular diffusion mechanism for EOR in development shale oil reservoirs with CFNs by huff “n” puff.

Pollutant transport in discrete fracture networks (DFNs) exhibits complex dynamics that challenge reliable model predictions, even with detailed fracture data. To address this issue, this study derives an upscaled integral‐differential equation to predict transient anomalous diffusion in two‐dimensional (2D) DFNs. The model includes both transmissive and dead‐end fractures (DEFs), where stagnant water zones in DEFs cause non‐uniform flow and transient sub‐diffusive transport, as shown by both literature and DFN flow and transport simulations using COMSOL. The upscaled model's main parameters are quantitatively linked to fracture properties, especially the probability density function of DEF lengths. Numerical experiments show the model's accuracy in predicting the full‐term evolution of conservative tracers in 2D DFNs with power‐law distributed fracture lengths and two orientation sets. Field applications indicate that while model parameters for transient sub‐diffusion can be predicted from observed DFN distributions, predicting parameters controlling solute displacement in transmissive fractures requires additional field work, such as tracer tests. Parameter sensitivity analysis further correlates late‐time solute transport dynamics with fracture properties, such as fracture density and average length. Potential extensions of the upscaled model are also discussed. This study, therefore, proves that transient anomalous transport in 2D DFNs with DEFs can be at least partially predicted, offering an initial step toward improving model predictions for pollutant transport in real‐world fractured aquifer systems. Plain Language Summary This study develops a physical model to predict how pollutants move through fractured aquifers, particularly focusing on the behavior of solutes in fractures that trap water, known as dead‐end fractures (DEFs). These fractures complicate the movement of pollutants, causing them to spread more slowly than expected. We combine detailed simulations and simplified models to predict pollutant behavior in fractured rock systems. This approach accounts for both transmissive fractures, which allow easy flow, and DEFs, where water stagnates. The model is validated using real‐world data and demonstrates that it can accurately predict how pollutants move through fractured media. It also reduces computational costs by requiring less detailed fracture data, making it practical for large‐scale applications. This study shows that we can at least partly predict the slow, irregular movement of pollutants in fractured rock systems with DEFs. This is a first step toward improving how we predict pollutant transport in real‐world fractured aquifer systems. Key Points Transport in 2D fracture networks with dead‐end fractures (DEFs) can be partially predicted by an upscaled integral‐differential equation Transient sub‐diffusion parameters are linked to DEFs' distribution properties, while solute displacement parameters require field‐fitting The upscaled model can be readily enhanced with additional terms/parameters to capture subtle real‐world transport processes and factors

In view of the problems of goaf water and harmful gas discharge in a coal mine, a new method of prevention and control is proposed in this paper, namely, mining fracture repair via slurry grouting. Research on the diffusion law of grout in rock strata to improve grouting theory and improve the grouting sealing effect is of great theoretical significance and engineering application value. The diffusion rules of grouting slurries under different working conditions are systematically explored and analyzed. The research results indicate that the slurry diffuses uniformly along the radial direction in the smooth crack in the smooth single crack grouting experiment. In addition, the faster the grouting speed is and the closer the distance from the grouting hole is, the greater the grout pressure and the greater the grout diffusion speed. Therefore, increasing the grouting speed moderately in grouting engineering practice can effectively accelerate the grouting process. The pressure of the grouting slurry at the measuring point at the same distance as the grouting hole is basically the same, which is also the main reason for the uniform diffusion of the slurry along the radial direction. The pressure decreases to the same level value when the slurry diffuses to a certain distance under different grouting speeds, which indicates that reducing the spacing of grouting holes can accelerate the grouting process more effectively than increasing the grouting speed. Highlights Grouting slurry diffuses uniformly in smooth fractures, enhancing sealing effectiveness. Faster grouting speeds increase pressure and diffusion rate, speeding up the process. Reducing the spacing of grouting holes is more effective than increasing grouting speed.

Objective To evaluate the influence of insufficient bone cement distribution on outcomes following percutaneous vertebroplasty (PVP). Methods This retrospective matched-cohort study included patients 50–90 years of age who had undergone PVP for single level vertebral compression fractures (VCFs) from February 2015 to December 2018. Insufficient (Group A)/sufficient (Group B) distribution of bone cement in the fracture area was assessed from pre- and post-operative computed tomography (CT) images. Assessments were before, 3-days post-procedure, and at the last follow-up visit (≥12 months). Result Of the 270 eligible patients, there were 54 matched pairs. On post-operative day 3 and at the last follow-up visit, significantly greater visual analogue scale (VAS) pain scores and Oswestry Disability Index (ODI) scores were obtained in Group B over Group A, while kyphotic angles (KAs) and vertebral height (VH) loss were significantly larger in Group A compared with Group B. Incidence of asymptomatic cement leakage and re-collapse of cemented vertebrae were also greater in Group A compared with Group B. Conclusions Insufficient cement distribution may relate to less pain relief and result in progressive vertebral collapse and kyphotic deformity post-PVP.

Background Bone healing process includes four phases: inflammatory response, soft callus formation, hard callus development, and remodeling. Mechanobiological models have been used to investigate the role of various mechanical and biological factors on bone healing. However, the effects of initial healing phase, which includes the inflammatory stage, the granulation tissue formation, and the initial callus formation during the first few days post-fracture, are generally neglected in such studies. Methods In this study, we developed a finite-element-based model to simulate different levels of diffusion coefficient for mesenchymal stem cell (MSC) migration, Young’s modulus of granulation tissue, callus thickness and interfragmentary gap size to understand the modulatory effects of these initial phase parameters on bone healing. Results The results quantified how faster MSC migration, stiffer granulation tissue, thicker callus, and smaller interfragmentary gap enhanced healing to some extent. However, after a certain threshold, a state of saturation was reached for MSC migration rate, granulation tissue stiffness, and callus thickness. Therefore, a parametric study was performed to verify that the callus formed at the initial phase, in agreement with experimental observations, has an ideal range of geometry and material properties to have the most efficient healing time. Conclusions Findings from this paper quantified the effects of the initial healing phase on healing outcome to better understand the biological and mechanobiological mechanisms and their utilization in the design and optimization of treatment strategies. It is also demonstrated through a simulation that for fractures, where bone segments are in close proximity, callus development is not required. This finding is consistent with the concepts of primary and secondary bone healing.

The very long molecules found in synthetic polymers, and their tendency to entangle and partially crystallize, impart many of the polymers' useful properties. However, these same characteristics also mean that chain dynamics are slow, which impedes potential self-healing. Yanagisawa et al. developed a family of ether-thiourea linear polymers that form hydrogen-bonded networks and still manage to stay amorphous. The polymers are stiff, showing the strength of the hydrogen bonding; however, because these bonds can easily reform, the polymer is also able to self-heal when compressed. Science , this issue p. 72 A stiff amorphous polymer can be repaired without heating, solely by compression. Expanding the range of healable materials is an important challenge for sustainable societies. Noncrystalline, high-molecular-weight polymers generally form mechanically robust materials, which, however, are difficult to repair once they are fractured. This is because their polymer chains are heavily entangled and diffuse too sluggishly to unite fractured surfaces within reasonable time scales. Here we report that low-molecular-weight polymers, when cross-linked by dense hydrogen bonds, yield mechanically robust yet readily repairable materials, despite their extremely slow diffusion dynamics. A key was to use thiourea, which anomalously forms a zigzag hydrogen-bonded array that does not induce unfavorable crystallization. Another key was to incorporate a structural element for activating the exchange of hydrogen-bonded pairs, which enables the fractured portions to rejoin readily upon compression.