A dilute polymer solution is modelled as a suspension of dumbbells with finite extensibility. Time-dependent numerical calculations are performed of flow part cylindrical and spherical surfaces at low Reynolds number. A finite-difference scheme is employed in which the evolution in time of the dumbbells is followed from an initially unstretched equilibrium. Results are calculated with (i) a no-slip, and (ii) a zero-tangential-stress boundary condition at the body surface. At large Deborah number, D , the polymer is most highly stretched in thin regions of fluid close to and downstream of stagnation points of the flow. The most important region dynamically is found to be at the rear of the obstacle. Numerical refinements in space and time are included in order properly to resolve this fine-scale structure. Numerically stable results are obtained for values of D up to 16, and show that the flow field and drag force on the obstacle tend toward finite values at large D . Experimental measurements of the drag on a falling rigid sphere, and the velocity distribution around it, are compared with the numerical results for the no-slip boundary. Observations of bubble behaviour are discussed in the light of the results for the slip boundary.

Creeping flow of dilute polymer solutions past cylinders and spheres

Laser Doppler velocimetry (LDV) and video flow visualization are used to investigate the creeping motion of a highly elastic, constant-viscosity fluid flowing past a cylinder mounted centrally in a rectangular channel. A sequence of viscoelastic flow transitions are documented as the volumetric flow rate past the cylinder is increased and elastic effects in the fluid become increasingly important. Velocity profiles clearly show that elasticity has almost no effect on the kinematics upstream of the cylinder, but that the streamlines in the wake of the cylinder are gradually shifted further downstream . Finite element calculations with a nonlinear constitutive model closely reproduce the evolution of the steady two-dimensional velocity field. However, at a well defined set of flow conditions the steady planar stagnation ow in the downstream wake is experimentally observed to become unstable to a steady, three-dimensional cellular structure. The Reynolds number at the onset of the flow instability is less than 0.05 and inertia plays little role in the flow transition, LDV measurements in the wake close to the cylinder reveal large spatially periodic fluctuations of the streamwise velocity that extend along the length of the cylinder and more than five cylinder radii downstream of the cylinder. Fourier analysis shows that the characteristic spatial wavelength of these flow perturbations scales closely with the cylinder radius R . Flow visualization combined with LDV measurements also indicates that the perturbations in the velocity field are confined to the narrow region of strongly extensional flow near the downstream stagnation point. A second flow transition is observed at higher flow rates that leads to steady translation of the cellular structure along the length of the cylinder and time-dependent velocity oscillations in the wake. Measurements of the flow instability are presented for a range of cylinder sizes, and a stability diagram is constructed which shows that the onset point of the wake instability depends on both the extensional deformation of the fluid in the stagnation flow and the shearing flow between the cylinder and the channel.

The wake instability in viscoelastic flow past confined circular cylinders

The motion of a DNA molecule in a solvent flow reflects the deformation of a nano/microscale flexible mass–spring structure by the forces exerted by the fluid molecules. The dynamics of individual molecules can reveal both fundamental properties of the DNA and basic understanding of the complex rheological properties of long-chain molecules. In this study, we report the dynamics of isolated DNA molecules under homogeneous extensional flow. Hydrodynamic focusing generates homogeneous extensional flow with uniform velocity in the transverse direction. The deformation of individual DNA molecules in the flow was visualized with video fluorescence microscopy. A coil–stretch transition was observed when the Deborah number (De) is larger than 0.8. With a sudden stopping of the flow, the DNA molecule relaxes and recoils. The longest relaxation time of T2 DNA was determined to be 0.63 s when scaling viscosity to 0.9 cP.

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Deformation of DNA molecules by hydrodynamic focusing

Wormlike micellar surfactant solutions are encountered in a wide variety of important applications, including enhanced oil recovery and ink-jet printing, in which the fluids are subjected to high extensional strain rates. In this contribution we present an experimental investigation of the flow of a model wormlike micellar solution (cetyl pyridinium chloride and sodium salicylate in deionised water) in a well-defined stagnation point extensional flow field generated within a microfluidic cross-slot device. We use micro-particle image velocimetry (μ-PIV) and full-field birefringence microscopy coupled with macroscopic measurements of the bulk pressure drop to make a quantitative characterization of the fluid's rheological response over a wide range of deformation rates. The flow field in the micromachined cross-slot is first characterized for viscous flow of a Newtonian fluid, and μ-PIV measurements show the flow field remains symmetric and stable up to moderately high Reynolds number, Re ≈ 20, and nominal strain rate, nom ≈ 635 s−1. By contrast, in the viscoelastic micellar solution the flow field remains symmetric only for low values of the strain rate such that nom ≤ λM−1, where λM = 2.5 s is the Maxwell relaxation time of the fluid. In this stable flow regime the fluid displays a localized and elongated birefringent strand extending along the outflow streamline from the stagnation point, and estimates of the apparent extensional viscosity can be obtained using the stress-optical rule and from the total pressure drop measured across the cross-slot channel. For moderate deformation rates (nom ≥ λM−1) the flow remains steady, but becomes increasingly asymmetric with increasing flow rate, eventually achieving a steady state of complete anti-symmetry characterized by a dividing streamline and birefringent strand connecting diagonally opposite corners of the cross-slot. Eventually, as the nominal imposed deformation rate is increased further, the asymmetric divided flow becomes time dependent. These purely elastic instabilities are reminiscent of those observed in cross-slot flows of polymer solutions, but seem to be strongly influenced by the effects of shear localization of the micellar fluid within the microchannels and around the re-entrant corners of the cross-slot.

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Extensional rheology and elastic instabilities of a wormlike micellar solution in a microfluidic cross-slot device

Conformational relaxation time in polymer solutions by elongational flow experiments: 2. Preliminaries of further developments: chain retraction; identification of molecular weight fractions in a mixture

Related to the problem of the drag-reduction mechanism due to the elastic properties of macromolecular additives, we study theoretically and experimentally the dynamically behaviour of the molecules and the corresponding flow field. Optical properties, orientation, configuration or change of shape are studied by flow birefringence in classical or original, elongational flow devices. The dependence of the birefringence threshold on the molecular weight, nature, ionic character, concentration and level of degradation of the polymer is studied. The flow field is determined experimentally and by computation using a simple rheological model. A correlation with drag-reduction measurement in capillaries is tried.

Dynamical behaviour of drag-reducing polymer solutions☆

Dans certaines conditions, l'action d'un gradient elongationnel permet d'obtenir une deformation tres importante des macromolecules souples se traduisant par l'apparition de birefringence d'ecoulement tres localisee. On montre que des ecoulements, a l'arriere d'obstacles, peuvent produire de tels effets. Dans le cas d'un diedre a angle droit, on a trace les courbes de birefringence d'ecoulement en fonction du debit en differents points du champ et pour differentes concentrations, mettant ainsi en evidence la necessite d'un gradient elongationnel minimum pour obtenir le deploiement des macromolecules dissoutes. On note egalement la difference de comportement entre particules rigides et deformables.

Biréfringence D'écoulement Localisée Induite à L'arrière D'obstacles

On etudie experimentalement la birefringence d'ecoulement apparaissant aux differents regimes de vitesses de rotation de deux cylindres d'axes paralleles places dans des solutions de macromolecules. Cette birefringence localisee se manifeste comme une ligne brillante extremement fine apparaissant quel que soit le sens de rotation des cylindres lorsque certaines conditions (de vitesse angulaire, de masse moleculaire, de viscosite, de geometrie, de deformabilite…) sont reunies. Cet effet pourrait s'expliquer par la presence d'un gradient elongationnel qui, outre une tendance a l'orientation, se traduirait par une deformation importante des macromolecules.

R. Hocquart

Papers

Dynamical behaviour of drag-reducing polymer solutions☆

Biréfringence D'écoulement Localisée Induite à L'arrière D'obstacles

Biréfringence D'écoulement Localisée Dans un Dispositif à Deux Rouleaux