Buckling Instability of Self-Assembled Colloidal Columns

Suspended, slender self-assembled domains of magnetically responsive colloids are observed to buckle in microgravity. Upon cessation of the magnetic field that drives their assembly, these columns expand axially and buckle laterally. This phenomenon resembles the buckling of long beams due to thermal expansion; however, linear stability analysis predicts that the colloidal columns are inherently susceptible to buckling because they are freely suspended in a Newtonian fluid. The dominant buckling wavelength increases linearly with column thickness and is quantitatively described using an elastohydrodynamic model and the suspension thermodynamic equation of state.

Figure 1

(a) The position of the columns in the field is illustrated in the experimental apparatus as installed in the microgravity sciences glovebox onboard the ISS. (b) The RT camera with field of view transverse to the magnetic field images columnar structures that form after toggling the field. The dark regions are the condensed colloidal columns. (c) The field is toggled with a 50% duty cycle for more than one hour at frequencies between 0.66 and 20 Hz.

Figure 2

A column in its (a) unbuckled, field-on state. (b) Subsequent growth of the buckling instability when the field is toggled off. (c) The maximum deflection. (d) The column returning to the unbuckled state as the field toggles on. The magnetic field is oriented left to right. The field strength is $2\mathrm{kA}/\mathrm{m}$ and the toggle frequency is 0.66 Hz. The scale bar is $100\mu \mathrm{m}$.

Figure 3

The buckling wavelength versus domain width measured in 12 separate experiments with domains assembled with different magnetic field strengths and pulse frequencies.

Figure 4

Buckling occurs for field strengths and frequencies indicated by closed symbols, but is not observed at high frequencies when the suspension structure is sample spanning (open triangles) or at low field strengths for free, suspended columns (open squares).