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Universal Similitude Across Scales

What is the compelling question or challenge?

Can we develop universal similitude principles that describe fundamental processes in systems or humans across scales from femto to Giga to enhance scientific knowledge and technological innovation?

What do we know now about this Big Idea and what are the key research questions we need to address?

Similitude is a concept used in engineering to describe the geometric, kinematic or dynamic similarity between a model and the real application. Most often used in hydraulic and aerospace engineering to test flow conditions using scaled models, similitude drives the science and engineering of fluid mechanics.

Similitude principles, if articulated, would be transformational for addressing numerous challenges faced by our society from the femto-scale to the Giga scale. Flow in porous media, for example, is fundamentally similar to flow through a membrane albeit at a different scale of observation. While flow through a membrane can be tested at the laboratory scale, understanding flow in porous media requires significant investments in experimental and simulation models due to the scale involved. Additionally, understanding micro- and nano-filtration, and microfluidics is challenged by our ability to understand fluid flow behavior at very small scales. When combined with the presence of particles of different sizes and/or chemical and biological constituents within the fluid in the porous medium or across a membrane, the complexity is magnified, as is the number of variables that are involved. Similitude, in this case, would describe the mechanistic and functional similarities between the membrane and the porous medium at scale and would enable the translation of this knowledge into better technologies at any scale for enhanced oil recovery, membrane filtration and ground water remediation, to name a few.

Other examples of similitude abound, for instance, downscaling of global climate scenarios to interpret and understand the implications of climate change at localized scales. Fundamentally, similitude can be leveraged to more rigorously address this challenge by understanding the variables or groups of variables that drive global climate phenomena at any scale. Another example is corrosion and scale formation which are both phenomena associated with physical materials and biological human tissue.

In addition to phenomena, similitude principles can be developed for system behavior (systems of systems or systems within systems) and for network analysis (power grids, water distribution networks, transportation arterial traffic flow, blood flow in the human body).

Little is known about similitude in other domains and for other phenomena besides non-dimensional analysis in engineering that connects laboratory scale models to the real application. The key research questions involve identifying similitude across scales in various domains and for different phenomena, determining the variables that are involved, and developing the non-dimensional quantities that express relationships among the variables in order to determine their functional relationships. Some phenomena, being more complex, will dictate the need to identify groups of variables that might be involved and designing and undertaking the collection of experimental data that would be needed to develop analytical relationships between the groups. Additionally, and while engineering examines dimensional, kinetic and dynamic similitude, other types of similitude can be defined and explored. Other key research questions have to do with enabling technologies that support this novel approach to scientific inquiry. Analytical quantitation, for example, drives regulatory standards in drinking water, thus, it can be argued that enabling technologies would be needed that enhance our ability to leverage similitude. Imaging, for instance, is such an enabling technology that can be used for flow in porous media, membrane filtration as well as interstitial fluid flow in the brain and across membranes in the brain. Thus, advanced imaging technologies that leverage similitude principles would be needed.

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