Multiphasic reaction of bicarbonate hydrogenation to form formate using homogeneous Ru PNP pincer catalyst in a continuous flow tubular reactor is reported. The reaction system consists of three phases. Catalyst is dissolved in toluene while potassium bicarbonate is dissolved in water. The significance of efficient mixing among the organic phase, aqueous phase and gaseous hydrogen to improve hydrogenation reaction by using different inert packing materials is studied by operando visualization and also quantitatively discussed. The bicarbonate conversion of up to 67% is achieved after optimization of important reaction and reactor parameters. The designed reactor setup comprised of effective recycling system that recycles the catalyst with >99% activity.

Herein, we present a practical strategy to enhance the performance of a multiphase system for bicarbonate hydrogenation based on a molecular Ru-PNP pincer catalyst. This study demonstrates that the use of organic antioxidants not only mitigates catalyst degradation but also significantly boosts its intrinsic activity. This enables efficient catalyst recycling at ultra-low concentrations. Systematic screening and optimization of a range of organic antioxidants has identified TDTBP (tris(2,4-di-tert-butylphenyl) phosphite) as being exceptionally efficient in stabilizing and enhancing the performance of the Ru-PNP catalyst. With the optimized system an unprecedented integral turnover frequency (TOF) of 115,000 h⁻¹ and a total turnover number (TTON) of 9.43×10⁶ across four recycling tests were demonstrated, conducted at a reaction temperature of 90 ºC and H₂ pressure of 50 bar. These findings represent a substantial advancement in sustainable formate/formic acid production, offering a scalable and highly efficient method suitable for industrial-scale application.

Sags and tunnels are major bottlenecks, where the road capacity is reduced, and the “capacity drop” phenomenon occurs; however, there is no simple model or theory that can explain the formation and other characteristics of capacity drop. This paper presents a car-following model, which is equivalent to a continuum model in the Lagrangian coordinates. The model is built on two main assumptions: (i) inhomogeneous fundamental diagrams with location-dependent time gaps, and (ii) bounded acceleration. We first demonstrate that the stationary speed profiles, the low acceleration rates, the dropped capacity, and the approximate time duration of the capacity drop formation in the model are consistent with empirical observations. Then the impacts on the stationary states and dropped capacity of the numerical viscosity caused by the discretization method are investigated, and it is shown that the dropped capacity converges to the theoretical value. Further, a one-dimensional iterated function system is proposed to model the formation mechanism of the capacity drop, which is derived by investigating the spatial pattern of equilibrium and bounded acceleration traffic states that arises in a lead-vehicle problem. Utilizing this model, we uncover a set of properties of the capacity drop such as existence, uniqueness, global convergence, and convergence speed. Finally, the model is applied to analyze the impacts of heterogeneous drivers. The model and insights in this study will help to develop control and management schemes to alleviate capacity drop effects with connected and autonomous vehicles in the future.