Numerical study of the hydrodynamic drag force in atomic force microscopy measurements undertaken in fluids

Abstract

When atomic force microscopy (AFM) is employed for in vivo study of immersed biological samples, the fluid medium presents additional complexities, not least of which is the hydrodynamic drag force due to viscous friction of the cantilever with the liquid. This force should be considered when interpreting experimental results and any calculated material properties. In this paper, a numerical model is presented to study the influence of the drag force on experimental data obtained from AFM measurements using computational fluid dynamics (CFD) simulation. The model provides quantification of the drag force in AFM measurements of soft specimens in fluids.The numerical predictions were compared with experimental data obtained using AFM with a V-shaped cantilever fitted with a pyramidal tip. Tip velocities ranging from 1.05 to 105 µm/s were employed in water, polyethylene glycol and glycerol with the platform approaching from a distance of 6000 nm. The model was also compared with an existing analytical model. Good agreement was observed between numerical results, experiments and analytical predictions. Accurate predictions were obtained without the need for extrapolation of experimental data. In addition, the model can be employed over the range of tip geometries and velocities typically utilized in AFM measurements.

Application of the Johnson–Kendall–Roberts model in AFM-based mechanical measurements on cells and gel.

“…At the highest speed used (32 m/s), the hydrodynamic force acting on the cantilever was observed as increased separation between the non-contact parts of the approach and retraction curves [34,35]. It was taken into account by the independent determination of the zero force level for the approach and retraction curves using corresponding non-contact regions.…”

Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves

“…This effect manifested as the separation between precontact regions of approach and retraction curves, which increases with the piezo speed. We adapted the procedure from 80 to account for the hydrodynamic forces. As shown in previous work 80, 81 , the hydrodynamics forces are proportional to the probe velocity and the probe-sample separation.…”

“…We adapted the procedure from 80 to account for the hydrodynamic forces. As shown in previous work 80, 81 , the hydrodynamics forces are proportional to the probe velocity and the probe-sample separation. First, the baseline was determined as a median between precontact regions of approach and retraction curves, then these regions were independently fitted with the polynomial function (second order), normalized per the probe velocity, and then calculated hydrodynamic force were subtracted from both approach and retraction curves (Fig.…”

Numerical Study of Hydrodynamic Forces for AFM Operations in Liquid

“…Beside the increased sensitivity for detecting adhesive forces, the liquid environment also improves the investigation of very soft sample surfaces by applying very low forces. Therefore, in recent literature AFM measurements of biological samples were undertaken in liquid environment [ 9 – 11 ].…”

“…The density ρ water of ultrapure water is 999.615 kg/m 3 and the dynamic viscosity μ water is 1.009347 · 10 −3 Pa·s. The much higher density and viscosity of the liquid affect the force measurements by hydrodynamic drag forces [ 11 – 13 ]. Various researchers stated that the influence of this effect is more significant for cantilever tip velocities above a few μ m/s [ 11 – 15 ].…”