Traction force microscopy in physics and biology.

Adherent cells, crawling slugs, peeling paint, sessile liquid drops, bearings and many other living and non-living systems apply forces to solid substrates. Traction force microscopy (TFM) provides spatially-resolved measurements of interfacial forces through the quantification and analysis of the deformation of an elastic substrate. Although originally developed for adherent cells, TFM has no inherent size or force scale, and can be applied to a much broader range of mechanical systems across physics and biology. In this paper, we showcase the wide range of applicability of TFM, describe the theory, and provide experimental details and code so that experimentalists can rapidly adopt this powerful technique.

Patterning droplets with durotaxis.

Numerous cell types have shown a remarkable ability to detect and move along gradients in stiffness of an underlying substrate--a process known as durotaxis. The mechanisms underlying durotaxis are still unresolved, but generally believed to involve active sensing and locomotion. Here, we show that simple liquid droplets also undergo durotaxis. By modulating substrate stiffness, we obtain fine control of droplet position on soft, flat substrates. Unlike other control mechanisms, droplet durotaxis works without imposing chemical, thermal, electrical, or topographical gradients. We show that droplet durotaxis can be used to create large-scale droplet patterns and is potentially useful for many applications, such as microfluidics, thermal control, and microfabrication.

Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses.

Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Young's law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Young's law.

Deformation of an elastic substrate by a three-phase contact line.

Young's classic analysis of the equilibrium of a three-phase contact line ignores the out-of-plane component of the liquid-vapor surface tension. While it is expected that this unresolved force is balanced by the elastic response of the solid, a definitive analysis has remained elusive because of an apparent divergence of stress at the contact line. While a number of theories have been presented to cut off the divergence, none of them have provided reasonable agreement with experimental data. We measure surface and bulk deformation of a thin elastic film near a three-phase contact line using fluorescence confocal microscopy. The out-of-plane deformation is well fit by a linear elastic theory incorporating an out-of-plane restoring force due to the surface tension of the solid substrate. This theory predicts that the deformation profile near the contact line is scale-free and independent of the substrate elastic modulus.

Imaging in-plane and normal stresses near an interface crack using traction force microscopy.

Colloidal coatings, such as paint, are all around us. However, we know little about the mechanics of the film-forming process because the composition and properties of drying coatings vary dramatically in space and time. To surmount this challenge, we extend traction force microscopy to quantify the spatial distribution of all three components of the stress at the interface of two materials. We apply this approach to image stress near the tip of a propagating interface crack in a drying colloidal coating and extract the stress intensity factor.