Rayleigh-Taylor-instability experiments with elastic-plastic materials

A rotating wheel experimental facility was developed to investigate incompressible Rayleigh-Taylor instability in elastic-plastic materials. A soft solid (mayonnaise) was chosen as the elastic-plastic material for experiments; material properties that include shear modulus and yield strength were fully characterized using a vane spindle type rheometer. Initial perturbations of varying amplitudes and wavelengths were generated on the interface of the soft solid using sinusoidal cutting guides. A backlit imaging technique was used in conjunction with a high-speed camera to track the motion of the interface at various phases of the instability. Results for both two- and three-dimensional perturbations were compared to study the acceleration required for instability and the growth after the interface yielded. Exponential growth rates were observed after instability was reached with trends of increasing growth rates for lower initial amplitudes. It was found that the acceleration required for instability increased when initial amplitude and wavelength decreased. Three-dimensional interfaces were found to be more stable. For both cases, a decrease in initial amplitude produced a more stable interface that increased the threshold acceleration required for the instability. Critical amplitude conditions for instability were calculated and compared with various analytical models and other experimental results.

Figure 1

Schematic of RT-strength rotating wheel experiment [component labels: (a) rotating disk, (b) test section, (c) mirror assembly, (d) light source, (e) high-speed camera, (f) counterweights].

Figure 2

(a) Backlit image of test section at the start of the experiment; (b) initial perturbation 3D interface, $\lambda =60\mathrm{mm}, {\xi }_i=4\mathrm{mm}$. (c) Initial perturbation 2D interface, $\lambda =60\mathrm{mm}, {\xi }_i=4\mathrm{mm}$. (d) Schematics of 3D interface, $\lambda =60\mathrm{mm}, {\xi }_i=4\mathrm{mm}$; (e) front view of perturbation generated indicating the initial wavelength $\left(\lambda \right)$ and amplitude $\left({\xi }_i\right)$.

Figure 3

matlab image processing of experimental images: (a) original image $\lambda =60\mathrm{mm}, {\xi }_i=4\mathrm{mm}$, 3D interface; (b) edge detection and Hough lines used for rotation; (c) before the perturbation growth where the peak is at the center, and (d) near maximum growth where the peak deviates from the normal axis.

Figure 4

(a) Shear stress and apparent viscosity (inset plot) as a function of shear rate for $\dot{\gamma }=25{\mathrm{s}}^{-1}$ and $\mathrm{\Delta }t=60\mathrm{s}$; (b) storage and viscous moduli vs strain (amplitude sweep test) for 1 and 5 Hz; (c) storage and viscous moduli vs amplitude (frequency sweep test) at strain = 0.1.

Figure 5

Scaled dimensionless amplitude vs time plot for the interface with ${\xi }_i\approx 4\mathrm{mm}$ and $\lambda =60\mathrm{mm}$. Regimes of elastic-plastic (EP: slow) growth and instability (IN: fast) growth is observed as the test section is accelerated. The onset of the instability growth is demonstrated in the inset plot defined as $t^{\prime }=0$ where $t=43.54\mathrm{s}$ with the corresponding instability amplitude denoted as ${\xi }_o$.

Figure 6

Experimental images for 3D initial perturbation with wavelength $\left(\lambda \right)=60\mathrm{mm}$ and varying initial amplitudes of (a) ${\xi }_i=6\mathrm{mm}$, (b) ${\xi }_i=4\mathrm{mm}$, (c) ${\xi }_i=2\mathrm{mm}$, and (d) ${\xi }_i=1\mathrm{mm}$, where $t^{\prime }$ is in seconds.

Figure 7

Experimental images for 2D initial perturbation with wavelength $\left(\lambda \right)=60\mathrm{mm}$ and varying initial amplitudes of (a) ${\xi }_i=6\mathrm{mm}$, (b) ${\xi }_i=4\mathrm{mm}$, (c) ${\xi }_i=2\mathrm{mm}$, and (d) ${\xi }_i=1\mathrm{mm}$, where $t^{\prime }$ is in seconds.

Figure 8

Peak amplitude growth at instability for 3D interface, $\lambda =60\mathrm{mm}$.

Figure 9

Estimating ${\xi }_{\mathrm{crit}}$ based on the threshold amplitudes $\left({\xi }_o\right)$ determined from instability tests with varying perturbation amplitude and constant wavelength.

Figure 10

Experimental images for 3D initial perturbation with initial amplitude $\left({\xi }_i\right)=4\mathrm{mm}$ and wavelengths: (a) $\lambda =30\mathrm{mm}$, (b) $\lambda =15\mathrm{mm}$. The time $t^{\prime }$ is in seconds and is defined at the onset of the instability.

Figure 11

Experimental images for 2D initial perturbation with initial amplitude $\left({\xi }_i\right)=4\mathrm{mm}$ and wavelengths: (a) $\lambda =30\mathrm{mm}$, (b) $\lambda =15\mathrm{mm}$. The time $t^{\prime }$ is in seconds and is defined at the onset of the instability.

Figure 12

Peak amplitude growth at instability for 3D initial perturbation with ${\xi }_i=4\mathrm{mm}$ and varying wavelengths.