Vorticity Elongation in Polymeric Emulsions

Abstract

Video microscopy is used to measure the shear-induced deformation of dilute emulsions composed of viscoelastic polymer melts. In the limit of strong shear, a transition in which the droplets elongate perpendicular to the flow field is observed. A force-balance argument relates this behavior to the change in first normal stress difference across the droplet interface. [S0031-9007(99)09504-6] PACS numbers: 83.50. Ax, 47.55.Dz, 61.25.Hq, 83.70.Hq When a fluid dispersed in a second fluid is subjected to shear, the droplets deform and burst, and the use of shear flow to emulsify immiscible liquids is ubiquitous in the processing of soft materials. Although the pioneering work of Taylor [1-4] on isolated Newtonian emulsions remains at the foundation of our understanding, with the underlying intuition that the droplets elongate along the direction of flow at sufficiently high shear rates, the shear response of fluids that exhibit rheological complexity, such as semidilute entangled polymer solutions [5][6][7][8], wormlike micelles [9], and thixotropic clay gels [10], suggests that the shear can induce domains with extended correlation along the direction of vorticity, perpendicular to the flow field. In this Letter, stroboscopic video microscopy is used to measure the shear response of dilute emulsions composed of viscoelastic polymer melts. At low shear rates, the behavior is in agreement with the Taylor picture. In the limit of strong shear, however, the droplets become extended along the vorticity axis, and a simple forcebalance argument is presented that relates this unusual transition to the change in first normal stress difference across the droplet interface.The pressure-driven optical flow cell [11] is shown schematically in Fig. 1. The instrument easily achieves shear rates at which elastic stresses in the melt become much larger than the shear stress, which typically cannot be achieved in a rotating-geometry device. The shear rate ͑ ᠨ g͒ is a function of the distance from one of the walls, and the measurements presented here were taken at the surface of the bottom window [12]. The materials are polystyrene (PS) and polyethylene (PE) at T 195 ± C, with molecular weights [13] M w 195 3 10 3 ͑M n 83 3 10 3 ͒ for PS 1 , M w 342 3 10 3 ͑M n 141 3 10 3 ͒ for PS 2 , M w 85.2 3 10 3 ͑M n 15.4 3 10 3 ͒ for PE 1 , and M w 83.1 3 10 3 ͑M n 25.6 3 10 3 ͒ for PE 2 , where PE 1 is low-density with long-chain branching and PE 2 is linear high-density. The melt rheology at 195 ± C was measured independently in a rotating-plate rheometer, and the shear viscosity is shown in Fig. 2. Under small-amplitude oscillatory shear, the storage modulus, G 0 ͑v͒, exceeds the loss modulus, G 00 ͑v͒, at v c 8, 30, 700, and 800 rad͞s for PS 1 , PS 2 , PE 1 , and PE 2 , respectively. The extruded blends are 0.01 mass fraction PS 1 in PE 1 , PS 1 in PE 2 , and PS 2 in PE 1 .We observe a variety of droplet shapes as a function of ᠨ g and the viscosity ratio l ͑h 0 ͒ PS ͑͞h 0 ͒ PE , where h 0 is the low-ᠨ g viscosity. For PS 2 ͞PE 1 (l 240), ...

Experimental investigation of viscoelastic drop deformation in Newtonian matrix at high capillary number under simple shear flow

“…The increase in R 3 /R 0 at high capillary number is very dramatic that it can be as high as 3. The drop elongation in vorticity direction was also observed by other researchers [14,17,43,51], however, they did not perform quantitative study of the deformation with accuracy in three dimensions. Mode II resembles the rod-climbing phenomenon and is attributed to the viscoelastic nature of the fluid [14,52].…”

“…At such high capillary numbers, the drop deformation and breakup can be very different since elasticity is expected to dominate the deformation process at high shear rate. Hobbie and Migler [14], Migler [43] and Mighri and Huneault [17] found that at high capillary numbers with strong elastic effect, viscoelastic drops under shear elongated and broke up in the vorticity direction, which is the direction perpendicular to the flow direction and the velocity gradient direction. However, there is a lack of quantitative studies on drop deformation in viscoelastic systems sheared at high capillary numbers.…”

“…The critical capillary number for viscoelastic drop breakup is higher than that of its Newtonian counterpart [12,13,40]. The effects of elastic properties on drop deformation and breakup are often attributed to the first normal stress difference in viscoelastic fluids [14,17,36,38]. Aggarwal and Sarkar [25] developed a simple qualitative ordinary differential equation model on the force balance among shear stress, interfacial stress and the first normal stress difference to depict the essential physics underlying the experimental observations and numerical results.…”

“…The deformation of a Newtonian drop in a Newtonian matrix has been extensively investigated by both experimental and numerical approaches providing a reasonably clear understanding on the essential physical mechanism [2][3][4][5][6][7][8][9][10][11]. However, drop deformation in viscoelastic fluid systems is much more complicated than that in pure Newtonian systems because of the complexity of the rheological properties and the modification of stresses and flow due to viscoelasticity [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].…”

Single Droplet Break-up in Controlled Mixed Flows

“…This is however, not a general break-up mechanism and can mostly be attributed to the presence of impurities or a nonuniform surfactant distribution along the drop surface (14,15). Other break-up mechanisms have been described in literature, for instance when dealing with viscoelastic components (16,17) or when using microfluidic devices in which confinement effects become important (18,19). Here, however, we focus on bulk behavior of systems with Newtonian components.…”