Figure 1

Behavior of a viscoelastic fluid in response to applied stress. Consider a block of material, at rest prior to $t=0$, to which a constant shear stress is applied over the time interval $t\in [0,T]$ after which time the applied stress is removed. Resulting response curves for idealized elastic solid, viscous fluid, and viscoelastic fluid are labeled. An (ideally) elastic solid responds at $t=0$ with an instantaneous strain. The strain is reversed instantaneously at $t=T$; the deformation is temporary. An (ideally) viscous fluid responds with a linear in time shear flow until $t=T$ when the shear is removed. No recoil occurs; the deformation is permanent. An (ideally) viscoelastic fluid responds with a combination of the two behaviors, a reversible elastic strain and an irreversible viscous creep.Reuse & Permissions

Figure 2

Representative examples of creep test data. Compliance $J$ (measured strain/applied stress) is plotted versus time. Here “applied stress” refers to the constant stress applied during the initial creep period of the experiments. Top: photograph of a cyanobacterial biofilm collected from Nymph Creek, Yellowstone National Park, together with creep curve. Applied stress was 1 Pa for 6 min followed by 6 min of recovery. Middle: photograph of an algal biofilm collected from Chico Hot Springs, Montana, together with creep curve. Applied stress was 3000 Pa for 5 min followed by 5 min of recovery. Bottom: Confocal micrograph of a S. mutans biofilm grown on a 20 mm hydroxyapatite coated rheometer plate (plan view is $1\times 1{\mathrm{m}\mathrm{m}}^2$, cross sections through vertical and horizontal planes are 1 mm long and 0.2 mm in height) together with creep curve. Applied stress was 0.5 Pa for 10 min followed by 10 min of recovery. All show characteristic viscoelastic fluid response with similar elastic relaxation times. Viscosities $\eta$ were calculated from the inverse asymptotic slope normalized by stress during the applied stress period. Shear moduli $G$ were calculated from the strain displacement (minus the flow displacement) normalized by stress during the applied stress period.Reuse & Permissions

Figure 3

Plot of effective shear modulus vs effective viscosity for 44 tested biofilms. The straight line is $\log \eta =1.03\log G+\log \overline{\lambda }$, the least squares best fit. $\overline{\lambda }\approx 1100\mathrm{s}$ is the best fit for the elastic relaxation time.Reuse & Permissions