Transport processes are an integral part of many engineered and natural systems. I will discuss how ideas from viscous flow modeling lend themselves to two such systems at vastly different scales. The first pertains to suspension transport near flexible structures; we show using asymptotic theory and experiments that thin membranes induce an elasto-hydrodynamic repulsion of suspended particles in flow. We use the Lorentz reciprocal theorem to calculate particle motion near soft surfaces without the need to compute the detailed flow field that results from elasto-hydrodynamic interactions.  In the second half of my talk, I will discuss a transport process of climatic relevance – the stoppage (or bridging) of sea ice as it flows through narrow Arctic straits. Using long-wave asymptotics, we show that the formation of ice bridges is governed by balance between the driving wind stress and frictionally generated shear stresses. The result is a reduced-order model reminiscent of viscous lubrication theory, whose predictions we validate against simulations and field measurements. The framework can inform climate models in which straits are often under-resolved, and suggests broader connections to jamming in particulate systems.