Morphology of Anisotropic Banded Structures in an Emulsion under Simple Shear

The formation of flow-induced, oriented structures in two-phase systems, as in this study, is a phenomenon of considerable interest to the scientific and industrial sectors. The main difficulty in understanding the formation of bands of droplets is the simultaneous interplay of physicochemical, hydrodynamic, and mechanical effects. Additionally, banded structure materials frequently show multiple length scales covering several decades as a result of complex time-dependent stress fields. Here, to facilitate understanding a subset of these structures, we studied water in oil emulsions and focused on the effects of three variables specifically: the confinement factor<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mtext> </mtext><mo>(</mo><mi>C</mi><mi>o</mi><mo>=</mo><mn>2</mn><mi>R</mi><mo>/</mo><mi>H</mi><mo>)</mo></mrow></semantics></math></inline-formula>, the viscosity ratio <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>)</mo><mo>,</mo></mrow></semantics></math></inline-formula> and the applied shear rate <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mover accent="true"><mrow><mi>γ</mi></mrow><mo>˙</mo></mover><mo>)</mo></mrow></semantics></math></inline-formula>. The confinement <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>C</mi><mi>o</mi><mo>)</mo></mrow></semantics></math></inline-formula> is the ratio between the drop’s diameter (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>R</mi></mrow></semantics></math></inline-formula>) and the separation of (the gap between) the circular rotating disks (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>H</mi></mrow></semantics></math></inline-formula>) containing the emulsion. We carried out (a) observations of the induced structure under different simple shear rates, as well as (b) statistical and morphological analysis of these bands. At low shear rates, the system self-assembles into bands along the direction of the flow and stacked normal to the velocity gradient direction. At higher shear rates is possible to observe bands normal to the vorticity direction. Here, we show that a detailed analysis of the dynamics of the band structures is amenable, as well as measurements of flow field anomalies simultaneously observed. The local emulsion viscosity varies in time, increasing in regions of higher droplet concentration and subsequently inducing velocity components perpendicular to the main flow direction. Thus, the emulsion morphology evolves and changes macroscopically. A relatively plausible explanation is attributed to the competitive effects of coalescence and the rupture of drops, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi></mrow></semantics></math></inline-formula> values less than one predominate coalescence.