# Boundary condition and geometry engineering in electronic hydrodynamics

## TL;DR

This paper explores how boundary geometry influences viscous electronic flows and proposes methods to engineer boundary conditions, such as slip length, to control flow behavior in electronic hydrodynamics.

## Contribution

It introduces a micropatterned boundary design that achieves effective no-slip conditions and analyzes the impact of boundary curvature on slip length and flow properties.

## Key findings

- Finned barriers can produce effectively no-slip boundary conditions.
- Boundary curvature affects the slip length and flow regimes.
- Circular junction flow can help measure slip parameters experimentally.

## Abstract

We analyze the role of boundary geometry in viscous electronic hydrodynamics. We address the twin questions of how boundary geometry impacts flow profiles, and how one can engineer boundary conditions -- in particular the effective slip parameter -- to manipulate the flow in a controlled way. We first propose a micropatterned geometry involving finned barriers, for which we show by an explicit solution that one can obtain effectively no-slip boundary conditions regardless of the detailed microscopic nature of the channel surface. Next we analyse the role of mesoscopic boundary curvature on the effective slip length, in particular its impact on the Gurzhi effect. Finally we investigate a hydrodynamic flow through a circular junction, providing a solution, which suggests an experimental set-up for determining the slip parameter. We find that its transport properties differ qualitatively from the case of ballistic conduction, and thus presents a promising setting for distinguishing the two.