Proximity effect on hydrodynamic interaction between a sphere and a plane measured by force feedback microscopy at different frequencies

Abstract

In this article, we measure the viscous damping G", and the associated stiffness G', of a liquid flow in sphere-plane geometry in a large frequency range. In this regime, the lubrication approximation is expected to dominate. We first measure the static force applied to the tip. This is made possible thanks to a force feedback method. Adding a sub-nanometer oscillation of the tip, we obtain the dynamic part of the interaction with solely the knowledge of the lever properties in the experimental context using a linear transformation of the amplitude and phase change. Using a Force Feedback Microscope (FFM)we are then able to measure simultaneously the static force, the stiffness and the dissipative part of the interaction in a broad frequency range using a single AFM probe. Similar measurements have been performed by the Surface Force Apparatuswith a probe radius hundred times bigger. In this context the FFM can be called nano-SFA.In this paper, we aim to measure the hydrodynamic interaction in water between a microsphere and a hard and plane surface at different distances and at different frequencies using a single probe. In this regime, the viscous behavior is expected to be dominating. Previous experiments have been run in air with conservative forces [1]. Using an electrical coupling between an AFM tip and a metallic surface as test interaction in air, we probed the static and dynamic part of the interaction where in this case the stiffness is expected to match the minus of the derivative of the static force and the damping to be null. In liquid, from the dynamic transition from a viscous-dominated behavior at large distance to an elastic-dominated behavior at short distance, we aim to extract mechanical properties of soft thin films as SFA does [2]. The hydrodynamic pressure will gently deform the soft sample without touching it and propose an alternative to the classical hard mechanical contact. The increase in the frequency range of this mechanical testing and the decrease of the tip radius, compare to the SFA[3], allows us to probe the viscoelastic properties of soft thin films and the possibility of the frequency dependence and compare it to bulk values. Properties can dramatically change with respect to the frequency as we have demonstrated in the case of capillary bridge [? ]. Here in this test experiment, we use non-deformable surface and spherical probe, and we explore the dissipation due to the flowing liquid. Other experiments with an AFM setup have been performed [4,5] in order to measure the hydrodymanic behavior either with respect to the sphere-plane separation or for different frequencies using one lever. The dissipation is expected to follow the lubrication approximation and to be frequency dependent, f=ω/2π, if reported in N/m. The lubrication approximation holds for low Reynolds number, thus R> >z, and the dissipation follow[2]:R is the tip radius, the dynamic viscous coefficient of the water, equal to 1 mPA.s at 20°C, from IAPWS standards, and z is the tip sample distance. The linear frequ...

A micro-nano-rheometer for the mechanics of soft matter at interfaces

“…Beyond seminal contributions on interactions, organization, and phase transitions in thin liquid films, the extension of the technique to dynamics forces has shown its ability to unravel interfacial hydrodynamics, and more recently, the non-contact mechanics of soft objects [2][3][4][5][6][7][8][9][10][11] . The wellcontrolled surface geometry and properties in SFA enables the proof-of-concept of methods further extended to the near-field probe techniques such as AFM 12 .…”

Frequency dependent visco-elastic properties of a water nanomeniscus : an AFM study in Force Feedback Mode

“…To apply this force in real time, a piezoelement changes the DC position of the clamped end part of the microlever. The displacement needed to maintain the tip position constant multiplied by the stiffness k gives access to the static capillary force acting on the tip, for details on experimental setup see Refs [7][8][9][10][11]. The tip oscillation is detected by an optical fiber positioned close to the cantilever backside, as depicted in Fig 1.…”

Influence of non-hydrodynamic forces on the elastic response of an ultra-thin soft coating under fluid-mediated dynamic loading

“…Thus, the solution for deflection in section 3 and the results in 4 continue to be valid so long as Γ 1 γ . In contrast, when Γ ∼ 1 γ , equations (35) to (38) are strongly coupled and not reducible to a de-coupled form. Such a coupled set of equations for the axisymmetric system considered here can be solved employing a Hankel-transformation approach [35,41,110,111], which is a scope for further generalization of current study.…”

“…Furthermore, there is rich literature on 'soft lubrication' too, where either the approaching object or the wall or both are deformable [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24], which finds applications in topics ranging from biotransport modelling [25][26][27][28] to tool design and analysis [29][30][31]. Such soft-lubrication setups are wide-spread in both natural and man-made world, examples being scanning probe microscope (SPM) and surface force apparatus (SFA) setups [32][33][34][35][36][37][38][39][40][41] and motion of biological entities like red blood corpuscles (RBCs) in fluidic environments [42][43][44]. With classical purely-hydrodynamic studies in hard-and soft-lubrication [45][46][47][48][49] serving as a solid foundation for further explorations, a number of later studies considered the...…”