Research Highlights of Polymers Division

Micro-Confined Blends

Fluid strings, which can be observed during typical polymer processing operations, develop prominence in confined systems (Figure 1). The formation and stability of strings is being understood through unique observations of micro-confined polymer blends.

Figure 1. Strings in a flowing emulsion: a larger confinement stabilized string is shown at left, and a smaller string that is stabilized by shear alone is shown at right. The scale bars represent the gap spacing between the flow cell boundaries, 36 µm and 100 µm, respectively. After stopping shear, the string at right breaks on timescales on the order of 10 s, whereas breakup of the confinement stabilized string requires timescales on the order of 1000 s.

Their stability arises from the effects of shear and confinement. We are exploring the stability of bulk, unconfined strings, as we directly test a recent theory that predicts a new regime of processing conditions wherein strings are stable. Confinement greatly promotes the stability of strings, because the relaxation and breakup rate is suppressed several fold due to hydrodynamic interactions between the string and the wall (Figure 2).

In addition, we are also making direct observations of the mechanism of breakup of bulk strings (classical Rayleigh-Tomotika instability and end pinching) in simple shear flow. Direct comparisons will be made between our experimental data and predictions of hydrodynamic theories on quantities such as the time taken to break up by a string and the size of the final droplets produced. Direct observation of this phenomenon in simple shear flow has not been reported thus far.

Figure 2. Lattice Boltzmann simulation of the breakup of a stationary string confined between parallel plates. Simulation results agree in detail with experimental observations of the string shape and breakup rate. Notice the ellipsoidal cross section of the string.

Figure 3. Morphology diagram describing microstructure in confined PDMS/PIB (polydimethylsiloxane / polyisobutylene) emulsions in the parameter space of mass fraction and shear rate, for a uniform gap-width (36 µm) and a fixed viscosity ratio (l = 1). Points denote shear rates where experimental data were obtained, and smooth curves are guides to the eye drawn by the authors to demarcate regions of different microstructure. Shaded points denote experimental observation of ordered pearl-necklace chains of droplets.

Figure 4. Pearl necklace arrangement of PDMS drops in a confined 5 % mass fraction PDMS/PIB emulsion flowing in the horizontal direction at a shear rate of 4.25 s-1, viewed normal to the confining planes, which are spaced 36 µm apart.

In confined blends, the formation of strings is facilitated by migration of drops away from the walls, which leads to enhanced concentration and coalescence of drops in the center of the flow channel. When coalescence is inhibited either by increasing the flow rate or by decreasing the total concentration of drops, interesting new arrangements of drops are discovered (Figure 3). At low drop concentration, pearl necklace structures form (Figure 4). At higher shear rates, the drops arrange into two layers that slide by one another. Although the drop migration effect pushes drops toward the center plane between the confining boundaries, collisions between drops push them apart so that separate layers are maintained.

As the drops become smaller at still higher rates due to breakup, collisions become more numerous and random, inducing random diffusive motion of the droplets transverse to the flow. The spatial distribution of drops under such conditions results from the interplay of this diffusive motion and migration away from the walls (Figure 5). By integrating the non-linear convective-diffusion drop-transport equation, an analytical expression is obtained for the steady state droplet concentration. The degree to which the drops are concentrated to the center depends on the dimensionless parameter Pe. At steady state, we derive the following volume fraction profile:

Pe = Ca (a/h) (4a/(fgy fØo) , where Ca is the capillary number, a is the average drop radius, h is the spacing between plates, a is a function of viscosity ratio, fgy is the dimensionless diffusivity, y is a dimensionless position, and fØo is the nominal volume fraction of dispersed phase (Figure 5).

Figure 5. Dispersed phase concentration as a function of dimensionless position across the gap in which the emulsion flows, shown here for Pe = 2.4. Results of theory (curve) and experiment (symbols) are in good agreement. Near the walls, the emulsion is denuded of drops, having important implications for materials properties, including the surface finish of extruded polymer materials. A recently published linearized theory (gray curve) is not nearly as accurate.

As implied above, interfacial properties and coalescence phenomena have a large influence over the morphology that develops in microscale processing. Coalescence rates are measured through observation of the evolution of the drop size distribution following a step down in shear rate. Governing dimensionless parameters and the effect of associated material parameters are determined. In experiments involving weakly adsorbed surfactant, we find that, at small capillary number, the coalescence rate is limited by diffusion-limited sorption, and at high capillary number, when collision causes slight drop deformation, coalescence is arrested by drop interface immobilization.

These measurements and observations demonstrate that a remarkable variety of phenomena occur in micro-confined blends. We plan to develop new tools, based in part on these phenomena, to investigate interfacial properties. These phenomena are also relevant for micro- and nano-fabrication and for microreactors, because multiphase flow can also be used for separation and encapsulation of desired products. The development of such reactors requires the aid of polymer materials science, which will yield optimal fluids, substrates, surface treatment, and active devices.

For more information on this topic:

Please contact S. D. Hudson, K.B. Migler, J. Pathak

J. F. Douglas, J.G. Hagedorn (ITL), or N. Martys (BFRL).