Dynamics of spheroids in pressure driven flows of shear thinning fluids

Particles in inertialess flows of shear thinning fluids are a model representation for several systems in biology, ecology, and micro-fluidics.In this paper, we analyze the motion of a spheroid in a pressure driven flow of a shear thinning fluid.The shear thinning rheology is characterized by the Carreau model.We use a combination of perturbative techniques and the reciprocal theorem to delineate the kinematics of prolate and oblate spheroids.There are two perturbative strategies adopted, one near the zero shear Newtonian plateau and the other near the infinite shear Newtonian plateau.In both limits, we find that a reduction in effective viscosity decreases the spheroid's rotational time period in pressure driven flows.The extent to which shear thinning alters the kinematics is a function of the particle shape.For a prolate particle, the effect of shear thinning is most prominent when the spheroid projector is aligned in the direction of the velocity gradient, while for an oblate particle the effect is most prominent when the projector is aligned along the flow direction.Lastly, we compare the tumbling behavior of spheroids in pressure driven flow to those in simple shear flow.While the time period decreases monotonically with Carreau number for pressure driven flows, the trend is non monotonic for shear flows where time period first increases at low Carreau number and then decreases at high Carreau numbers.Shear thinning does not resolve the degeneracy of Jefferey's orbits

Image Analysis of a Vesicle to Calculate the Bending Modulus

The cell membrane is an essential component of living cells and the dynamics of the membrane will provide insight into how a biological cell reacts to mechanical strain. Membrane mechanics are important in a variety of cellular processes like secretion, trafficking, signaling, and storage. Giant unilamellar vesicles are a model system for cellular membranes since the major component of all membranes is a phospholipid bilayer. Giant unilamellar vesicles allow one to examine physicochemical processes that occur in all cellular membranes, such as fusion, budding, and fission in a more controlled fashion. Contour fluctuations of the vesicles are analyzed to calculate the bending modulus of the lipid bilayer, which will provide insight to the cell membrane’s rigidity. An image processing program was developed that traces the thermal fluctuations of the vesicle membrane through edge detection. Theory of spherical harmonics was then applied to calculate the elastic properties of the bilayer based on the measured fluctuations

Shape transitions of vesicles in linear, hyperbolic flows: asymmetric dumbbells, pearling, and buckling

When flexible vesicles are placed in an extensional flow (planar or uniaxial), they undergo a wide range of shape transitions. At intermediate aspect-ratios and high extension rates, a vesicle stretches into an asymmetric dumb-bell separated by a long, cylindrical thread. At high aspect-ratios, the vesicle extends indefinitely in a seemingly-symmetric fashion, in a manner similar to the breakup of liquid droplets. In this ``burst’’ phase, the vesicle may undergo “pearling” if the extension rate is above a critical value, i.e., the vesicle forms necklace-like structures in its central neck reminiscent of the Rayleigh-Plateau instability. In this discussion, we describe the mechanisms behind these shape transitions by solving the Stokes equations around a single, fluid-filled particle whose interfacial dynamics are governed by a Helfrich energy (i.e., the membrane is inextensible with bending resistance). We find that the shape transitions described above have their origins in a modified Rayleigh-Plateau analysis, even though the shapes look qualitatively different from each other. The stability criteria determined by our simulations and scaling analysis agree well with in-vitro, cross-slot microfluidic experiments (some of which we perform). In the last part of this discussion, we discuss the early time response of vesicles in uniaxial compressional flow. We find that vesicles undergo a variety of buckling/wrinkling instabilities, the physics of which we characterize using analytical theories. This study highlights the major differences between vesicle deformation and droplet breakup, the differences mostly being attributable to interface’s compressibility in the two systems

Peeling of linearly elastic sheets using complex fluids at low Reynolds numbers

We investigate the transient, fluid structure interaction (FSI) of a non-Newtonian fluid peeling two linearly elastic sheets at low Reynolds numbers. Two different non-Newtonian fluids are considered; a simplified sPTT model, and an inelastic fluid with shear thinning viscosity (generalized Newtonian fluid). In the limit of small gap between the sheets, we invoke a lubrication approximation and numerically solve for the gap height between the two sheets during the start-up of a pressure-controlled flow. What we observe is that for an impulse pressure applied to the sheet inlet, the peeling front moves diffusively toward the end of the sheet when the fluid is Newtonian. However, when one examines a complex fluid with shear thinning, the propagation front moves sub-diffusively in time , but ultimately reaches the end faster due to an order of magnitude larger pre-factor for the propagation speed. We provide scaling analyses and similarity solutions to delineate several regimes of peeling based on the sheet elasticity, Wi number (for sPTT fluid), and shear thinning exponent (for generalized Newtonian fluid). To conclude, this study aims to afford to the experimentalist a system of knowledge to delineate the peeling characteristics of a certain class of complex fluids

Translocation dynamics of knotted polymers under a constant or periodic external field

We perform Brownian dynamics simulations to examine how knots alter the dynamics of polymers moving through nanopores under an external field. In the first part of this paper, we study the situation when the field is constant. Here, knots halt translocation above a critical force with jamming occurring at smaller forces for twist topologies compared to non-twist topologies. Slightly below the jamming transition, the polymer's transit times exhibit large fluctuations. This phenomenon is an example of the knot's molecular individualism since the conformation of the knot plays a large role in the chain's subsequent dynamics. In the second part of the paper, we study the motion of the chain when one cycles the field on and off. If the off time is comparable to the knot's relaxation time, one can adjust the swelling of the knot at the pore and hence design strategies to ratchet the polymer in a controllable fashion. We examine how the off time affects the ratcheting dynamics. We also examine how this strategy alters the fluctuations in the polymer's transit time. We find that cycling the force field can reduce fluctuations near the knot's jamming transition, but can enhance the fluctuations at very high forces since knots get trapped in metastable states during the relaxation process. The latter effect appears to be more prominent for non-torus topologies than torus ones. We conclude by discussing the feasibility of this approach to control polymer motion in biotechnology applications such as sequencing.Singapore-MIT Alliance for Research and Technology (SMART)National Science Foundation (U.S.) (Grant CBET-1335938

Knots modify the coil–stretch transition in linear DNA polymers

We perform single-molecule DNA experiments to investigate the relaxation dynamics of knotted polymers and examine the steady-state behavior of knotted polymers in elongational fields. The occurrence of a knot reduces the relaxation time of a molecule and leads to a shift in the molecule's coil-stretch transition to larger strain rates. We measure chain extension and extension fluctuations as a function of strain rate for unknotted and knotted molecules. The curves for knotted molecules can be collapsed onto the unknotted curves by defining an effective Weissenberg number based on the measured knotted relaxation time in the low extension regime, or a relaxation time based on Rouse/Zimm scaling theories in the high extension regime. Because a knot reduces a molecule's relaxation time, we observe that knot untying near the coil-stretch transition can result in dramatic changes in the molecule's conformation. For example, a knotted molecule at a given strain rate can experience a stretch-coil transition, followed by a coil-stretch transition, after the knot partially or fully unties.National Science Foundation (U.S.) (Grant CBET-1602406

Dynamics and deformation of complex interfaces â study of vesicles and droplet-like systems

There is a lot of interest in characterizing the mechanics of complex interfaces that compose biological systems such as cells. In this talk, we discuss some of our recent work on the micromechanics of vesicles, i.e., sacs of fluid of ~20 microns containing a phospholipid bilayer. Here, we focus on how these systems behave in extensional flows, probing the conditions under which they become mechanically unstable and break up. We find that vesicles exhibit qualitatively different shape transitions than droplets under flow due to the bending and dilatational resistance of the phospholipid bilayer. We discuss the microfluidic experiments and boundary element simulations to quantify the different shape transitions, and describe how flow type and flow history alters these dynamics. In the second half of the talk, we discuss more general problems on how shear and dilatational resistance of a membrane alter the dynamics of droplet-like systems found in biology. We develop analytical theories to quantify how linear shear and dilatational surface moduli alter droplet translation, shape, breakup, and particle lift. We find that one can use simple symmetry/scaling arguments to illuminate how interfacial shear viscosity alters the translational speed of a droplet.Non UBCUnreviewedAuthor affiliation: Purdue UniversityResearche

Effect of Droplet Viscosity Ratio and Surfactant Adsorption on the Coalescence of Droplets with Interfacial Viscosity

Surface rheology becomes important for droplets with adsorbed proteins, solid particulates, lipids, or polymers, and understanding how surface rheology alters basic droplet processes like coalescence provides insight into the processing of dispersions in industrial and biological systems. In this work, we model the approach of two equal-size deformable droplets under an axisymmetric, biaxial extensional flow in the Stokes flow limit. We explore how the viscosity contrast between the drop and suspending fluid alters the film drainage behaviour when interfacial viscosity is present. For a clean droplet at a fixed capillary number, the drainage time is observed to be independent of the viscosity ratio (λ) for λ≤O(1), while the drainage increases linearly with the viscosity ratio for λ≥O(1). Surface viscosity increases the drainage time by causing the thin film between the droplets to flatten and widen, and shifts the viscosity ratio at which the aforementioned scaling behaviour changes to larger values. The drainage time is increased more significantly at lower viscosity ratio values than higher values. In the second half of the paper, we examine how surface viscosity alters film drainage when the surfactant can be soluble. We examine the kinetically controlled adsorption/desorption limit. We find that surfactant solubility abolishes surface tension gradients and increases the prominence of surface viscosity effects, the effects of which are quantified for Boussinesq numbers Bq∼O(0.1)