Adhesion force in fluids: Effects of fingering, wetting, and viscous normal stresses

Abstract

Probe-tack measurements evaluate the adhesion strength of viscous fluids confined between parallel plates. This is done by recording the adhesion force that is required to lift the upper plate, while the lower plate is kept at rest. During the lifting process, it is known that the interface separating the confined fluids is deformed, causing the emergence of intricate interfacial fingering structures. Existing meticulous experiments and intensive numerical simulations indicate that fingering formation affects the lifting force, causing a decrease in intensity. In this work, we propose an analytical model that computes the lifting adhesion force by taking into account not only the effect of interfacial fingering, but also the action of wetting and viscous normal stresses. The role played by the system's spatial confinement is also considered. We show that the incorporation of all these physical ingredients is necessary to provide a better agreement between theoretical predictions and experiments.

Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects

“…In many practical applications, the emergence of these hydrodynamic instabilities is undesirable and because of that much attention has been devoted to devising strategies for controlling the growth of such patterns. However, all existing studies that somehow try to control the emergence of these interfacial disturbances neglect the effects of the wetting film left behind by the displaced fluid during the flow, even though a considerable number of works [20,[39][40][41][42][43][44][45][46][47][48][49][50] have pointed to the fact that wetting has an important role in the nonlinear finger formation process.…”

“…A number of subsequent theoretical and experimental investigations in rectangular Hele-Shaw cells [40][41][42][43][44] have indicated that the inclusion of wetting effects helps to provide a better match between theory and experiments. This has also been the case for injection-driven flows in the radial Hele-Shaw cell setup [45][46][47][48][49] and for time-dependent gap flows in the lifting Hele-Shaw arrangement [20,50]. In particular, by employing a weakly nonlinear analysis, the authors of Ref.…”

“…Depending on how this process is conducted, rapidly evolving ramified fingers may bypass the oil in the reservoir and reach the point of extraction, and thus leading to poor oil recovery. It is also known that viscous fingering has a potentially harmful character in applications involving adhesives [10,15,20]. So, processes aimed towards minimizing the fingering instabilities, or controlling the growth of viscous fingers are of technological and scientific importance.…”

Attachment of bioinspired microfibrils in fluids: transition from a hydrodynamic to hydrostatic mechanism

“…The contribution of hydrodynamic forces to adhesion has mostly been investigated for standard configurations such as plate-plate or ball-plate in probe tack and colloid adhesion tests [20,23]. More complex geometries are of great interest for various applications and exist in natural wet adhesive systems, which are mainly composed of soft, deformable materials and non-regular geometries [12,[24][25][26][27][28][29][30][31].…”

Viscous normal stresses and fingertip tripling in radial Hele-Shaw flows

“…Nagel and Gallaire [13] used the Brinkman equation and took into account both normal and tangential viscous stresses to derive a quite complicated linear dispersion relation for the Saffman-Taylor instability, finding a good accordance with experiments. The consideration of interfacial fingering and normal viscous stresses effects has also been instrumental to provide a better agreement between theoretical predictions and experiments for fluid adhesion problems in Hele-Shaw geometry [14].…”