60th Annual Report on Research 2015

Microbial enhanced oil recovery is an emerging strategy employing bacteria and their metabolic by-products to increase petroleum yields from porous reservoirs.  In these applications, the bacteria assemble at the oil-water interface to form films.  These films of bacteria at interfaces (FBI) strongly affect the interfacial properties.  The changes thought to aid extraction include reduction of interfacial tension and selective plugging of permeable zones that otherwise shunt applied pressure.  Despite their importance, limited previous research has sought to characterize systematically the dynamical and mechanical properties of FBI.  The film microstructure, which typically includes living and dead bacteria and macromolecular surfactants secreted by the bacteria, resembles a suspension of active and inert colloids in an adsorbed polymer film.  Hence, ideas from soft-matter physics could provide insight.  In this project, we have undertaken a comprehensive study of the dynamical and (micro)mechanical evolution of FBI. We studied FBI formation at initially bacteria-free interfaces using the model organism Pseudomonas sp. with a combination of particle tracking and pendant drop elastometry.  Our experiments reveal three stages of behavior: active films, viscoelastic films, and elastic films.  In our 2014 annual report, we described properties of the viscoelastic transition in FBI, which we infer is driven by accumulation of polysaccharides and surfactants in the interface and which possesses hallmarks of a soft glass transition.  In this report, we focus on the active stage.

We monitored the dynamical behaviour of FBI by tracking colloids (0.5 micrometer spheres) pinned to the interface between hexadecane and the bacteria solution.  The bacteria adhere to the interface and quickly populate it. The colloidal motion was strongly affected by hydrodynamic interactions with the swimming bacteria, which typically comprised 10% area fraction of the interface.  The significance of such colloidal dynamics in suspensions of swimming microbes is their utility as models for the non-equilibrium statistical mechanics of active complex fluids. Further, the colloid motion provides insight into biomixing, the enhanced transport of nutrients and other material by active suspensions. Since FBI formation involves transport of polysaccharides and other constituents to and within the interface, biomixing could be an important feature of the film development. Hence, we characterized the colloidal motion during the active stage of FBI formation in detail.

Figure 1 shows the mean-squared displacement <r²(t)> of the colloids during the active stage of FBI formation.  For reference, <r²(t)> of colloids at the oil interface of water containing no bacteria is also shown.  In the absence of bacteria, <r²(t)> varies linearly with lag time t indicating simple diffusion, with a diffusion coefficient, D₀ = 0.12 μm²/s, consistent with the water and hexadecane viscosities.  The mean-squared displacement of the colloids at the active interface similarly varies linearly with t at large lag times, but with an enhanced effective diffusion coefficient.  At smaller lag times, <r²(t)>  grows more rapidly than linearly, indicating superdiffusive motion.  Such superdiffusive motion signals temporal correlations in the forcing of the colloids due to hydrodynamic interactions with the swimmers.  A simple model for these correlations ascribes the particle velocities an exponentially decaying memory with correlation time t_v, which leads to a mean-squared displacement of the form <r²(t)> = 4D[t + t_v*(exp(-t/t_v) - 1)].  At short lag times, t << t_v, this form predicts ballistic motion, <r²(t)> ~ t², and at large lag times it reduces to diffusion, <r²(t)> = 4Dt, with diffusion coefficient D.   The solid line in Fig. 1 is the result of a fit using this form, giving D =1.8 μm²/s.   The value of D compared to that without bacteria indicates pronounced biomixing at the interface via the hydrodynamic flows created by the swimming bacteria, which likely has strong influence on FBI formation.

To quantify more directly the tracer velocity correlations, we identified the instantaneous direction of motion for each particle examined its time autocorrelation function F_n(t).  As shown in Fig. 2, F_n(t) has a peak near t = 0.03 s, which we attribute to a tendency for colloids to follow u-shaped trajectories on short times due to bacteria swimming past in close proximity, and hence to make negative contributions to F_n(t). At longer times, F_n(t) decays exponentially, as shown by the line in Fig. 2, with a correlation time that agrees with the characteristic time t_v.  Thus, through F_n(t) we observe directly the nature of the correlated tracer dynamics in an active suspension inferred by analysis of <r²(t)>. 

While the colloid dynamics at large lag times with diffusivity D suggest that the suspension of swimming bacteria acts like a thermal bath, as seen previously the statistical properties of the colloidal displacements differ from a system in thermal equilibrium. For instance, Fig. 3(a) shows the probability distribution function (PDF) for displacements at fixed lag time P_t(x), where x is the displacement along one direction, at three lag times spanning the superdiffusive and diffusive behaviors. While the PDFs of particles in thermal equilibrium are Gaussian, the PDFs in the active FBI show large non-Gaussian tails at large |x| signalling enhanced probability of large displacements. Qualitatively similar PDFs have been observed among tracers in other microbial suspensions. To compare the PDFs at different lag times, we plot in Fig. 3(b) the normalized PDFs with displacement normalized by the root mean-squared displacement. Remarkably, the PDFs collapse onto a single lineshape, indicating the distribution maintains a self-similar form with increasing lag time.

Another feature of the colloidal motion was their spatial correlations. As an illustration, the inset of Fig. 4 depicts direction of motion of colloids at one instant. Alignment between the direction of nearby colloids is apparent. This coordinated motion is quantified in Fig. 4, which shows the normalized pair direction–direction correlation function, C_n(r). The spatial correlations decay exponentially with separation, as depicted by the line in Fig. 4. Together, F_n(t) and C_n(r) give a quantitative picture of the spatiotemporal correlations in tracer motion that characterize the dynamical behaviour of the active FBI.

Daniel Allan, a Physics PhD student at Johns Hopkins who led the work, is currently a postdoctoral fellow at Brookhaven National Laboratory.