Author Description

Introduction In this preface, we delve into the realm of interfaces abundant in nature. These interfaces often find themselves enveloped or surrounded by disorder, as exemplified by the air-water interface of a droplet on a rough substrate, the domain wall of magnetization within a crystal riddled with defects, and a two-fluid interface nestled in a porous medium. The intricate interplay between interface elasticity and the disorder of the surrounding medium takes center stage, with elasticity striving to maintain a flat interface while disorder fosters roughness and deviations. This dynamic creates a complex energy landscape teeming with metastable states. While the static properties of these interfaces have garnered some understanding, the dynamics in the presence of disorder remain shrouded in mystery [1]. Frictional Forces and Threshold A defining characteristic of such systems lies in the frictional forces between the interface and the embedding medium, resulting in a finite critical or "threshold" force required to propel the interface through the medium. Pertinent questions regarding the dependence of this threshold force on disorder and the evolution of the interface under the influence of driving forces, both near and far from the threshold, are currently under active investigation [24, 2]. Multifaceted Approach Addressing these inquiries necessitates a multifaceted approach, combining bulk transport measurements, such as the flow velocity as a function of applied pressure, with mesoscopic length-scale imaging. While transport measurements offer insights into macroscopic behavior, mesoscopic imaging unveils the elementary processes that collectively or individually govern the overarching phenomenon. This conceptual and operational framework serves as the cornerstone for the research presented in this thesis. Research Scope Within the pages that follow, this thesis embarks on a journey of exploration, employing im