Journey through Interface Realms

<p><strong><em>Introduction</em></strong></p><p>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].</p><p><strong><em>Frictional Forces and Threshold</em></strong></p><p>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].</p><p><strong><em>Multifaceted Approach</em></strong></p><p>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.</p><p><strong><em>Research Scope</em></strong></p><p>Within the pages that follow this thesis embarks on a journey of exploration employing imaging and transport measurements to unravel the dynamics of interfaces in two distinct phenomena: (1) the adhesion of a sphere to a plate and (2) the invasion of fluids in porous media. Both areas hold intrinsic fascination and are regarded as distinct domains of research. Therefore this thesis employs terminologies specific to these fields. In the subsequent sections we provide a foundation of background ideas for each of these two intriguing problems.</p><p><strong><em>Surface Interactions</em></strong></p><p>Consider for a moment the interaction that occurs when two solid bodies make contact giving rise to contact forces of action and reaction. Such interactions can be thought of as surface interactions. Let us envision a hypothetical experiment wherein a compact object like a stone or a book rests upon a horizontally extended surface such as a tabletop or the ground for a brief duration before being lifted away. At first glance this experiment may appear to have left the surface interaction largely unchanged. Throughout the interaction the object remained at rest on the surface and a total reaction force was transmitted across the interface.</p>