Jet penetration into soft gels is essential for optimising fluid delivery in medical therapies, biomedical engineering, and soft robotics. In this work, we visualise the jet flow of a Newtonian fluid into a soft viscoplastic gel using camera imaging and time-resolved tomographic particle image velocimetry (PIV) systems. The flow is primarily governed by the Reynolds number ($Re = 350-5000$) and the effective viscosity ratio ($m$ up to 22). We observe three flow regimes – mixing, jellyfish, and fingering – with transitions between them quantified in the $Re-m$ plane. An experimentally informed, systematic, practical, semi-analytical modelling framework is developed to estimate jet penetration depth over time, incorporating PIV results and an approximate functional decomposition approach to describe the velocity distribution and Reynolds stress contributions. The model provides reasonable estimations across all three regimes.

Porous membranes, like nets or filters, are thin structures that allow fluid to flow through their pores. Homogenisation can be used to rigorously link the flow velocity with the stresses on the membrane via several coefficients (e.g. permeability and slip) stemming from the solution of Stokes problems at the pore level. For a periodic microstructure, the geometry of a single pore determines these coefficients for the whole membrane. However, many biological membranes are not periodic, and the porous microstructure of industrial membranes can be modified to address specific needs, resulting in non-periodic patterns of solid inclusions and pores. In this case, multiple microscopic calculations are needed to retrieve the local non-periodic membrane properties, negatively affecting the efficiency of the homogenised model. In this paper, we introduce an adjoint-based procedure that drastically reduces the computational cost of these operations by computing the pore-scale solution’s first- and second-order sensitivities to geometric modifications. This adjoint-based technique only requires the solution of a few problems on a reference geometry and allows us to find the homogenised solution on any number of modified geometries. This new adjoint-based homogenisation procedure predicts the macroscopic flow around a thin aperiodic porous membrane at a fraction of the computational cost of classical approaches while maintaining comparable accuracy.

Cargo carrying by a spring connected chiral micro-swimmer in a square channel is numerical studied by the three-dimensional lattice Boltzmann method and a chiral squirmer model. The effects of the driving type (β), swimming Reynolds number (Rep), spin coefficient (ξ) and diameter ratio (S) on the changes of the cargo-carrying velocity, spring length and motion modes are investigated, respectively. Four kinds of interesting motion modes are observed. When the chirality is not considered, the optimal combination for maximising swimming velocity are the pusher–cargo and cargo–puller configurations when Rep = 0.1 ∼ 1. When Rep is enhanced, the swimming velocities of the pusher–cargo, puller–cargo and cargo–pusher are increased, while the velocity of the cargo–puller is gradually decreased. When considering the chirality, only the swimming velocity of cargo–pusher and cargo–puller keep an interesting increment, and the reverse motion mode for the pusher-cargo and puller-cargo is firstly found in the present work when ξ exceeds a certain value. The impact of S on the cargo-carrying behaviour is complex, three kinds of oscillatory trajectories will appear under different ξ and S. The swimming velocity is reduced and even zero velocity will be observed when S is large. This work reveals key factors on the movement of microorganisms, offering guidance for improving cargo-carrying capabilities.

Access to clean and reliable water is critically important for health, well-being, and economic development. The natural, built, and social systems – which interact with each other and comprise the water system-of-systems – are threatened by intensifying hazards and stressors like crumbling infrastructure, floods, droughts, storms, wildfires, sea level rise, population growth, cyber threats, and pollution. Marginalized communities, including disadvantaged and rural communities and Tribal nations with insufficient access to clean water or regenerative sources of water, are often the most impacted. Responses to these issues are hampered by fragmented and uncoordinated governance and management. A multi-stakeholder structured engagement process at the SWIM conference and workshop held in December 2023 identified the most critical current and future issues facing the water sector and what needs to change to find solutions. This paper synthesized these issues. Highlighted issues were the vulnerability and lack of resilience of water systems to hazards and stressors, inequities associated with water scarcity, and water quality problems – all affected by climate change, land-use change, and socio-economic changes. The Smart One Water (S1W) vision provided an important context for the conference. This paper expands the S1W vision with a synthesis of discussions about S1W-related fundamental concepts, practices, and implementation barriers.

The Kansas City, Missouri Smart Sewer Program has successfully implemented an adaptive management approach to cost-effectively reduce sewer overflows. This approach was implemented under the guidance of the third Consent Decree modification, which mandates the level of sewer overflow reduction. This approach includes iterative decision-making, continuous monitoring and flexible strategies to optimize environmental outcomes while managing costs. The adaptive management framework integrates system performance and past project data into an iterative planning, implementation, monitoring and analysis cycle. This process enables cost-effective decision-making aligned with Consent Decree compliance by managing the uncertainties in sewer system data and the interdependency of proposed project outcomes. The Smart Sewer Program adopted this approach in response to financial challenges and environmental requirements, resulting in key modifications to its original Overflow Control Plan projects. The adaptive management approach, enabled by the third Consent Decree modification, has proven pivotal in optimizing project performance, reducing costs and protecting vulnerable populations. By leveraging the adaptive management approach, Kansas City has reduced program expenses by hundreds of millions of dollars while aligning with Environmental Protection Agency (n.d.) environmental justice goals. Key project modification examples from the program presented in this article illustrate the effectiveness of adaptive management in achieving better outcomes. The first example showcases a project substitution. In this example, green infrastructure replaced a proposed relief sewer project, resulting in a more cost-effective solution with enhanced overflow reduction and environmental justice benefits. The second example involves project augmentation with creek separation, resolving double-counted sewer overflows, and significantly reducing annual overflow volume at minimal cost. A third example demonstrates project modification for a City project that was not a part of the Smart Sewer Program, where alternative gate configurations increased overflow capture without additional costs, potentially eliminating the need for a costly deep tunnel project. This article demonstrates the potential of an adaptive management approach for urban wastewater management programs, offering a replicable model for other municipalities. The Kansas City Smart Sewer Program example demonstrates how adaptive management can drive cost savings, enhance environmental outcomes and ensure regulatory compliance for a Consent Decree.

This paper is concerned with the boundary layer on the leading edge of an aerofoil with the aerofoil surface sliding parallel to itself in the upstream direction. The flow analysis is conducted in the framework of the classical Prandtl formulation with the pressure distribution given by the solution for the outer inviscid flow. Since a reverse flow region is always present near the wall, a numerical method, where the derivatives were approximated by the windward finite differences, was used to solve the boundary-layer equations. We were interested in the flow behaviour on the upper surface of the aerofoil, but to calculate the boundary-layer equations, we had to extend the computational domain from the upper surface of the aerofoil to the lower surface. The calculations were performed for a range of angles of attack, and it is found that there exists a critical value of the angle of attack for which the Moore–Rott–Sears singularity forms in the flow. This is accompanied by an abrupt thickening of the boundary layer at the singular point and the formation of a recirculation region with closed streamlines behind this point. We further found that the flow immediately behind the singular point and in the recirculation region could be treated as inviscid, which allowed us to use the Prandtl–Batchelor theorem for theoretical modelling of the flow. A similar formulation was used earlier by Bezrodnykh et al. (Comput. Maths Math. Phys. vol. 63, 2023, pp. 2359–2371). These authors considered the boundary-layer flow on a flat plate with the pressure gradient created by a dipole situated some distance from the plate. They also found that there exists a critical value of the dipole strength for which a singularity forms in the boundary layer. However, their interpretation of the flow behaviour differs significantly from what we observe in our study.