Miscible displacement of non-Newtonian fluids in a vertical tube

The influence of rheology on the miscible displacement of a viscous fluid by a less viscous, Newtonian one in a vertical tube is studied experimentally as a function of the flow velocity. For Newtonian displaced fluids the transient residual film thickness is nearly of the tube radius at large viscosity ratios between the two fluids in agreement with experimental and numerical results from the literature. For shear-thinning fluids with a zero yield stress (mostly xanthan-water solutions), decreases down to of the radius for the most concentrated solutions. For fluids with a non-zero yield stess, further decreases down to 24-25% of the radius. The orders of magnitude of these values can be obtained through numerical simulations (commercial code) for the various types of fluids. Instabilities of the film at its boundary develop downstream and lead to a reduction of the final thickness of the film at longer times: this reduction is larger for lower viscosity ratios and larger velocities.Received: 15 February 2003, Published online: 8 July 2003PACS: 47.20.Gv Hydrodynamic stability: Viscous instability - 83.60.Wc Rheology: Flow instabilities     

Enhancement of the orientational order parameter of nematic liquid crystals in thin cells

We report measurements of birefringence of several nematic liquid crystals having transverse as well as longitudinal dipole moments in thin (1.4 to ) and thick (7 to cells. Rubbed polyimide-coated glass plates are used to get planar alignment of the nematic director in these cells. We find significant enhancement (6 to ) of ( , where S is the orientational order parameter) in thin cells in all compounds with aromatic cores even at temperatures far ( C) below the nematic-isotropic transition point. The enhancement is larger in compounds having several phenyl rings and lower if the number of phenyl rings is reduced. In a compound that does not have an aromatic core no significant enhancement is observed, implying that the strength of the surface potential depends on the aromaticity of the cores. Assuming a perfect orientational order at the surface, calculations based on the Landau-de Gennes theory show that the thickness averaged enhancement of S is sharply reduced as the temperature is lowered in the nematic phase. The measured order parameter S is further enhanced in thin cells because of the stiffening of the elastic constant which reduces the thermal fluctuations of the nematic director. The combined effect is however too small at low temperatures to account for the experimental data.Received: 22 February 2004, Published online: 24 May 2004PACS: 61.30.-v Liquid crystals - 61.30.Pq Microconfined liquid crystals: droplets, cylinders, randomly confined liquid crystals, polymer dispersed liquid crystals, and porous systems - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitionsSurajit Dhara: Present address: Department of Physics, Birla Institute of Technology and Science, Pilani 333 031, India.     

Blobs,channels and “cigars”: Morphologies of liquids at a step

We have studied the equilibria of liquid droplets wetting a step edge with an opening angle by a combination of analytical and numerical methods. Depending on the wetting properties of the substrate walls and on the liquid volume, different locally or globally stable liquid morphologies are found. Complete spreading of the liquid along the bottom edge of the step is observed at equilibrium contact angles satisfying . If the contact angle exceeds a threshold value the liquid exists in a blob-like configuration. Surprisingly, we find an intermediate regime at a sufficiently high liquid volume and in a range of contact angles , in which cigar-shaped configurations arise in addition to the blob. We close the paper by a detailed discussion of the stability of this novel liquid morphology.PACS: 47.55.Dz Drops and bubbles - 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 68.08.Bc Wetting     

Exact effective force between star-polymers in a $\Theta$-solvent

We re-examine here the computation of the effective force between two star-polymers of respective numbers of branches f₁ and f₂, immersed in a common -solvent. Such a force originates essentially from the repulsive three-body interactions. To achieve this, we take advantage of some established results using renormalization theory for three-dimensional star-polymers, or conformal invariance for two-dimensional ones. We first show that, in dimension d = 3, the force, , decreases with the center-to-center distance r as , with the exact universal amplitude . Second, in dimension d = 2, we find that the force decays more slowly as , with the exact universal amplitude . For high distances compared to the gyration radius, , of a single polymer chain at the -point, an exponential decay of the force is expected.Received: 3 February 2004, Published online: 24 May 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.20.-y Classical statistical mechanics     

Tails of the dynamical structure factor of 1D spinless fermions beyond the Tomonaga approximation

We consider one-dimensional (1D) interacting spinless fermions with a non-linear spectrum in a clean quantum wire (non-linear bosonization). We compute diagrammatically the 1D dynamical structure factor, S(ω,q), beyond the Tomonaga approximation focusing on it's tails, |ω| ≫vq, i.e. the 2-pair excitation continuum due to forward scattering. Our methodology reveals three classes of diagrams: two “chiral” classes which bring divergent contributions in the limits ω→±vq, i.e. near the single-pair excitation continuum, and a “mixed” class (so-called Aslamasov-Larkin or Altshuler-Shklovskii type diagrams) which is crucial for the f-sum rule to be satisfied. We relate our approach to the T=0 ones present in the literature. We also consider the case and show that the 2-pair excitation continuum dominates the single-pair one in the range: |q|T/k_F ≪ω±vq ≪T (substantial for q ≪k_F). As applications we first derive the small-momentum optical conductivity due to forward scattering: σ∼1/ω for T ≪ω and σ∼T/ω² for T ≫ω. Next, within the 2-pair excitation continuum, we show that the attenuation rate of a coherent mode of dispersion Ω_q crosses over from , e.g. γ_q ∼|q|³ for an acoustic mode, to , independent of Ω_q, as temperature increases. Finally, we show that the 2-pair excitation continuum yields subleading curvature corrections to the electron-electron scattering rate: , where V is the dimensionless strength of the interaction.     

Theoretical notes on dense polymers in two dimensions

Two models of dense two-dimensional (2d) polymers are considered: (1) when chain intersections in 2d are totally forbidden, and (2) when they are allowed to some extent. It is shown that both polymer chain statistics and dynamics are entirely different for the two models. In the first case studied by Duplantier in 1986 polymer chains are essentially segregated and are characterized by non-classical exponents. The contact line between segregated chains is fractal which leads to an unusual demixing behavior in 2d blends. In the second case (crossings are allowed) polymer coils are overlapping and show mean-field statistics with logarithmic corrections. The correlation function of concentration fluctuations in this system is predicted to exhibit a universal long range power tail (1/r ⁴) which is due to non-mean-field effects. The dynamical behavior of the two models is even more drastically different: The first model is characterized by a relatively fast dynamics with conformational relaxation time (i.e. t _N is slightly shorter than the Rouse time ). On the other hand an exponentially slow dynamics is predicted for model 2 (with 3d entanglements).Received: 3 September 2003PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 67.70. + n Films (including physical adsorption)     

Dynamics of propylene glycol and its oligomers confined in clay

The dynamics of propylene glycol (PG) and its oligomers 7-PG and PPG, with (about 70 monomers), confined in a Na-vermiculite clay have been investigated by quasi-elastic neutron scattering and dielectric spectroscopy. The liquids are confined to a single molecular layer between the clay platelets, thus giving a true 2D liquid. The results show that the average relaxation time , deduced from neutron scattering at a momentum transfer Q of about , is in perfect agreement with the dielectric -relaxation time, although neutron scattering does not only probe the main ( -) relaxation, but all motions of hydrogens on the experimental time scale. At room temperature is proportional to Q ², indicating that the relaxations are mainly due to ordinary translational diffusion. The most unexpected finding is that (or the dielectric -relaxation time) is almost unaffected by the 2D confinement, in contrast to the dielectrically active normal mode of PPG which is substantially slower in the confinement. Only the 7-mer has a significantly slower segmental translational diffusion in the clay. The results suggest that the interactions to the clay surfaces are weak and that the present 2D confinement has a very small influence on the time scale of all our observed relaxation processes, except the normal-mode relaxation.Received: 1 January 2003, Published online: 8 October 2003PACS: 61.25.Em Molecular liquids - 68.35.Ja Surface and interface dynamics and vibrations - 61.12.-q Neutron diffraction and scattering     

Surface and bulk interchange energy in binary mixtures of chain molecules

The interchange (interaction) parameter, controlling the phase behaviour of a binary mixture, is determined for the bulk and the surface of binary mixtures of different types of chain molecules, using surface tensiometry and a mean-field theory. For all mixtures and concentrations studied an identical behaviour is observed at the surface, depending only on the square of the reduced chain length mismatch , where and are the difference in and average of the number of carbons of the two components.Received: 21 December 2003, Published online: 25 March 2004PACS: 61.30.Hn Surface phenomena: alignment, anchoring, anchoring transitions, surface-induced layering, surface-induced ordering, wetting, prewetting transitions, and wetting transitions - 68.35.Md Surface thermodynamics, surface energies - 68.03.Cd Surface tension and related phenomena     

Calculation of the persistence length of a flexible polymer chain with short-range self-repulsion

For a self-repelling polymer chain consisting of n segments we calculate the persistence length , defined as the projection of the end-to-end vector on the direction of the j-th segment. This quantity shows some pronounced variation along the chain. Using the renormalization group and -expansion we establish the scaling form and calculate the scaling function to order . Asymptotically, the simple result emerges for dimension d = 3. Also away from the excluded-volume limit is found to behave very similar to the swelling factor of a chain of length . We carry through simulations which are found to be in good accord with our analytical results. For d = 2 both our and previous simulations as well as theoretical arguments suggest the existence of logarithmic anomalies.Received: 17 November 2003, Published online: 30 March 2004PACS: 61.25.Hq Macromolecular and polymer solutions; polymer melts; swelling - 05.10.Cc Renormalization group methods     

ZZ production in e+ e- int eractions at $\sqrt{s} =$ 183-209 G eV

Measurements of on-shell ZZ production are described, using data from the DELPHI experiment at LEP in e ⁺ e ^- collisions at centre-of-mass energies between 183 and 209 GeV, corresponding to an integrated luminosity of about 665 pb^-1. Results obtained in each of the final states , , , , , l ⁺ l ^- l ⁺ l ^-, and (with ) are presented. The measured production cross-sections are consistent with the Standard Model expectations. These results update and supersede those already published at 183 and 189 GeV.Received: 3 March 2002, Revised: 28 May 2003, Published online: 19 September 2003     

Mechanical properties of mono-domain side chain nematic elastomers

We investigate the behavior of the shear rigidity modulus G = G + iG of three mono-domain side chain liquid-crystalline elastomers composed of side chain polysiloxanes cross-linked by either flexible or rigid cross-linkers. The measurements were taken in a frequency domain ranging form Hz to Hz applying the shear in a plane perpendicular to or containing the director. The measurements as a function of temperature show an anisotropy of G which appears around , when decreasing the temperature, and which is due to the expected lowering of coming from the coupling between the shear and the director. The measurements as a function of frequency show that G has two components for both geometries, in both the isotropic phase and in the nematic phase around the phase transition. One reflects the network behavior in its hydrodynamic regime (G is constant and , where f is the frequency), the other which appears at higher frequencies is characterized by a scaling law behavior ( ) of the Rouse type. We discuss the results in the framework of available theories and show that the three elastomers present a non-soft behavior, even for the elastomer for which the contrary was claimed, and that there is no separation of time scales between the director and the network. We also present data on a poly-domain sample and a non-mesomorphic one which complement these results.Received: 19 February 2004, Published online: 24 August 2004PACS: 83.80.Va Elastomeric polymers - 61.30.-v Liquid crystals - 83.60.Bc Linear viscoelasticityPresented at the First World Congress on Biomimetics and Artificial Muscles, 9-11 December 2002, Albuquerque, New Mexico, USA. Some aspects of this work have been published as an abridged version in the Proceedings of the Conference.     

Multi-quasiparticle states in 184 W via multi-nucleon transfer

A multi-nucleon transfer reaction using an 850 MeV ¹³⁶Xe beam incident on a ¹⁹⁸Pt target was used to populate high-spin states in ¹⁸⁴W, 14 nucleons from the target. A 4-quasiparticle isomer with ns has been observed for the first time and its de-excitation through collective and intrinsic structures studied. The results are compared with predictions of blocked BCS Nilsson calculations. Observation of this metastable state completes the tungsten 4-quasiparticle isomer systematics from A = 176 to 186. Mapping out the most yrast 4-quasiparticle isomers in these even-even tungsten isotopes suggests the existence of a highly favoured state in ¹⁸⁸W, within reach of current experimental set-ups.Received: 14 October 2003, Revised: 14 November 2003, Published online: 18 May 2004PACS: 21.10.Tg Lifetimes - 23.20.Lv transitions and level energies - 27.70. + q      

Power law polydispersity and fractal structure of hyperbranched polymers

Using the complementary approaches of Flory theory and the overlap function, we study the molecular weight distribution and conformation of hyperbranched polymers formed by the melt polycondensation of A-R_N0-B_{f - 1} monomers in their reaction bath close to the mean field gel point p_A = 1, where p_A is the fraction of reacted A groups. Here , N₀ is the degree of polymerisation of the linear spacer linking the A group and the f-1 B groups and condensation occurs exclusively between the A and B groups. For , we assume that the number density of hyperbranched polymers with degree of polymerisation N generally obeys the scaling form and we explicitly show that this scaling assumption is correct in the mean field regime (here N_l is the largest characteristic degree of polymerisation and the function cuts off the power law sharply for ). We find the upper critical dimension for this system is d_c = 4, so that for the mean field values for the polydispersity exponent and fractal dimension apply: , d_f = 4. For d = 3, mean field theory is still correct for where is the Ginzburg point; for , mean field theory applies on small mass scales N<N_c but breaks down on larger mass scales N>N_c where is a cross-over mass. Within the Ginzburg zone (i.e., d<d_c, ), we show that the hyperbranched chains on mass scales N>N_c are non-Gaussian with fractal dimension given by d_f = d (for d = 2,3,4). Our results are qualitatively different from those of the percolation model and indicate that the polycondensation of AB_f-1, unlike polymer gelation, is not described by percolation theory. Instead many of our results are similar to those for a monodisperse melt of randomly branched polymers, a consequence of the fact that so that polydispersity is irrelevant for excluded volume screening in hyperbranched polymer melts.Received: 15 December 2003, Published online: 2 March 2004PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.70.Jk Critical point phenomena     

Monte Carlo simulation of particle aggregation and gelation: II. Pair correlation function and structure factor

Diffusion-limited cluster aggregation and gelation are studied using lattice and off-lattice Monte Carlo simulations. The pair correlation function g(r) and the structure factor S(q) of the particle gels were investigated as a function of the volume fraction ( ) and time. At volume fractions below , the gel structure is fractal on small length scales with . g(r) shows a weak minimum at the correlation length ( ), before reaching the average concentration at large length scales. The cut-off function of g(r) varies during the aggregation process, but at a given , where is the gel time, it is a universal function of . At high volume fractions, the structure is dominated by excluded-volume interactions, while at low volume fractions, it is determined by the connectivity.Received: 27 April 2004, Published online: 26 October 2004PACS: 64.60.Ak Renormalization-group, fractal, and percolation studies of phase transitions - 02.70.Uu Applications of Monte Carlo methods     

Budding and fission of a multiphase vesicle

We present a model of bi-phasic vesicles in the limit of large surface tension. In this regime, the vesicle is completely stretched and well described by two spherical caps with a fold, which concentrates the membrane stress. The conservation laws and geometric constraints restrict the space of possible shapes to a pair of solutions labeled by a parameter given by line tension/pressure. For a given value of , the two solutions differ by the length of the interface between domains. For a critical value, , the two vesicle shapes become identical and no connected solution exists above this critical value. This model sheds new light on two proposed mechanisms (osmotic shocks and molecule absorption) to explain the budding and the fission in recent experiments.     

Irreversible adsorption from dilute polymer solutions

We study irreversible polymer adsorption from dilute solutions theoretically. Universal features of the resultant non-equilibrium layers are predicted. Two broad cases are considered, distinguished by the magnitude of the local monomer-surface sticking rate Q: chemisorption (very small Q) and physisorption (large Q). Early stages of layer formation entail single-chain adsorption. While single-chain physisorption times are typically micro- to milli-seconds, for chemisorbing chains of N units we find experimentally accessible times , ranging from seconds to hours. We establish 3 chemisorption universality classes, determined by a critical contact exponent: zipping, accelerated zipping and homogeneous collapse. For dilute solutions, the mechanism is accelerated zipping: zipping propagates outwards from the first attachment, accelerated by occasional formation of large loops which nucleate further zipping. This leads to a transient distribution of loop lengths s up to a maximum size after time t. By times of order the entire chain is adsorbed. The outcome of the single-chain adsorption episode is a monolayer of fully collapsed chains. Having only a few vacant sites to adsorb onto, late-arriving chains form a diffuse outer layer. In a simple picture we find for both chemisorption and physisorption a final loop distribution and density profile whose forms are the same as for equilibrium layers. In contrast to equilibrium layers, however, the statistical properties of a given chain depend on its adsorption time; the outer layer contains many classes of chain, each characterized by a different fraction of adsorbed monomers f. Consistent with strong physisorption experiments, we find the f values follow a distribution .Received: 13 January 2003, Published online: 8 July 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 68.08.-p Liquid-solid interfaces     

Dynamics of living polymers

We study theoretically the dynamics of living polymers which can add and subtract monomer units at their live chain ends. The classic example is ionic living polymerization. In equilibrium, a delicate balance is maintained in which each initiated chain has a very small negative average growth rate (velocity) just sufficient to negate the effect of growth rate fluctuations. This leads to an exponential molecular weight distribution (MWD) with mean . After a small perturbation of relative amplitude , e.g. a small temperature jump, this balance is destroyed: the velocity acquires a boost greatly exceeding its tiny equilibrium value. For the response has 3 stages: (1) Coherent chain growth or shrinkage, leaving a highly non-linear hole or peak in the MWD at small chain lengths. During this episode, lasting time , the MWDs first moment and monomer concentration m relax very close to equilibrium. (2) Hole-filling (or peak decay) after . The absence or surfeit of small chains is erased. (3) Global MWD shape relaxation after . By this time second and higher MWD moments have relaxed. During episodes (2) and (3) the fast variables ( ) are enslaved to the slowly varying number of free initiators (chains of zero length). Thus fast variables are quasi-statically fine-tuned to equilibrium. The outstanding feature of these dynamics is their ultrasensitivity: despite the perturbations linearity, the response is non-linear until the late episode (3). For very small perturbations, , response remains non-linear but with a less dramatic peak or hole during episode (1). Our predictions are in agreement with viscosity measurements on the most widely studied system, -methylstyrene.Received: 23 September 2003PACS: 82.35.-x Polymers: properties; reactions; polymerization - 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian Motion - 87.15.Rn Biomolecules: structure and physical properties; Reactions and kinetics; polymerization     

Variational theory for a single polyelectrolyte chain revisited

We reconsider the electrostatic contribution to the persistence length, , of a single, infinitely long-charged polymer in the presence of screening. A Gaussian variational method is employed, taking as the only variational parameter. For weakly charged and flexible chains, crumpling occurs at small length scales because conformational fluctuations overcome electrostatic repulsion. The electrostatic persistence length depends on the square of the screening length, , as first argued by Khokhlov and Khachaturian by applying the Odijk-Skolnick-Fixman (OSF) theory to a string of crumpled blobs. We compare our approach to previous theoretical works (including variational formulations) and show that the result found by several authors comes from the improper use of a cutoff at small length scales. For highly charged and stiff chains, crumpling does not occur; here we recover the OSF result and validate the perturbative calculation for slightly bent rods.PACS: 36.20.-r Macromolecules and polymer molecules - 82.70.-y Disperse systems; complex fluids - 87.15.-v Biomolecules: structure and physical properties     

Motions induced by asymmetric vibrations

We discuss theoretically the motions of a coin on a horizontally vibrating plate, with dry friction between the coin and the plate. As first noticed by Daniel and Chaudhury in a different situation (droplets on a plate), when the periodic acceleration γ(t) imposed by the plate is unsymmetrical, the coin can move macroscopically with a certain drift velocity . We analyse here: (a) the vibration threshold below which , and the generic behavior expected just above threshold; (b) the limiting behavior at very high amplitudes, where should become independent of the amplitude; (c) the complications due to small, macroscopic inhomogeneities on the supporting plate.     

Di-electrons from η -meson Dalitz decay in proton-proton collisions

The reaction is discussed within a covariant effective meson-nucleon theory. The model is adjusted to data of the subreaction . Our focus is on di-electrons from Dalitz decays of η -mesons, , and the role of the corresponding transition form factor . Numerical results are presented for the intermediate-energy kinematics of HADES experiments.