The hydrodynamic analysis of motion of small particles (e.g. proteins) within lipid bilayers appears to be naturally suitable for the framework of two-dimensional Stokes flow. Given the Stokes paradox, the problem in an unbounded domain is ill-posed. In his classical paper, Saffman (J. Fluid Mech., vol. 73, 1976, pp. 593–602) proposed several possible remedies, one of them based upon the finite extent of the membrane. Considering a circular boundary, that regularisation was briefly addressed by Saffman in the isotropic configuration, where the particle is concentrically positioned in the membrane. We investigate here the hydrodynamic problem in bounded membranes for the general case of eccentric particle position and a rectilinear motion in an arbitrary direction. Symmetry arguments provide a representation of the hydrodynamic drag in terms of ‘radial’ and ‘transverse’ coefficients, which depend upon two parameters: the ratio $\lambda$ of particle to membrane radii and the eccentricity $\beta$. Using matched asymptotic expansions we obtain closed-form approximations for these coefficients in the limit where $\lambda$ is small. In the isotropic case ($\beta = 0$) we find that the drag coefficient is $4\pi /(\ln ({1}/{\lambda })- {1})$, contradicting the value $4\pi /(\ln ({1}/{\lambda })- {1}/{2})$ obtained by Saffman. We explain the oversight in Saffman’s argument.

We revisit the model problem of Squires & Brady (Phys. Fluids, vol. 17, 2005, 073101), where a Brownian probe is dragged through a dilute dispersion of Brownian bath particles. In this problem, the microrheology due to excluded-volume interactions is represented by an effective viscosity, with the nonlinearity in the driving force entering via the dependence of the viscosity increment (relative to the viscosity of a pure solvent) upon the deformation of the dispersion microstructure. Our interest is in the limit of large Péclet numbers, $ P{\kern-1pt}e\gg 1$, where the microstructural deformation adopts the form of a boundary layer about the upstream hemisphere of the probe. We show that the boundary-layer solution breaks down at the equator of the probe and identify a transition region about the equator, connecting the layer to a downstream wake. The microstructural deformation in this region is governed by a universal boundary-value problem in a semi-bounded two-dimensional domain. The equatorial region continues downstream as a transition layer, which separates the wake of the probe from the undisturbed ambient; in that layer, the microstructure is governed by a one-dimensional heat-like equation. Accounting for the combined contributions from the respective asymptotic provinces we find the approximation $ ({1}/{2})[1+ (\ln P{\kern-1pt}e + 1.046)/ P{\kern-1pt}e]$ for the ratio of the large-$ P{\kern-1pt}e$ viscosity increment to the corresponding linear-response increment. Our asymptotic approximation is in excellent agreement with the increment predicted by a finite-difference numerical calculation of the microstructure deformation, tailored to the large-$ P{\kern-1pt}e$ topology.

We use a revealed preference approach to disentangle conformity, an intrinsic taste to follow others, from information-driven herding. We provide observations from a series of sequential decision-making experiments in which subjects choose the type of information they observe before making their decision. Namely, subjects choose between observing a private (statistically informative) signal or the history of play of predecessors who have not chosen a private signal (i.e., a statistically uninformative word-of-mouth signal). In our setup, subjects choose the statistically uninformative social signal $34\%$ of the time and, of those, $88\%$ follow their observed predecessors’ actions. When allowing for payoff externalities by paying subjects according to the collective action chosen by majority rule, the results are amplifed and the social signal is chosen in $51\%$ of all cases, and $59\%$ of those who pick the social signal follow the majority choice. The results from the majority treatment demonstrate that conformist behavior is not driven by inequality aversion, nor by strategic voting behavior in which voters balance others who are uninformed. Raising the stakes five-fold does not eliminate conformist behavior; in both treatments, the social signal is chosen nearly $50\%$ of the time. Individual level analysis yields the identification of rules of thumb subjects use in making their decisions.

Although many Fertility Centers have adopted day 5 or 6 embryo transfer policy, yet, 30% of embryo transfers in the US are performed on day 3. This is mainly due to concerns related to longer embryo culture effect and higher rates of embryo transfer cancellation on day 5, with no effect on cumulative pregnancy rate. We conducted a retrospective cohort study comparing individual embryo transfer order rank, best embryo for fresh transfer and intention to freeze, of day-3 and day-5 embryos based on their morphology score. Day-3 embryos of each patient were ranked by embryologists for the order of transfer and intention to freeze, based on morphological score, blinded to actual blastulation outcome. The corresponding blastocysts were similarly ranked for the order of transfer and vitrification intention. Ranking was compared to test the predictive value of day-3 morphological assessment. Sixty patients with 784 day-3 embryos were included. There was only a moderate positive significant correlation between ranks on day-3 and ranks on day-5 [r = 0.662 95% CI (0.611–0.706, p < 0.001)]. Only 25% of the best embryos for transfer on day 3 (rank = 1) were chosen for fresh transfer on day 5. A total of 441 embryos were intended to be frozen on day 3. Of those, 201 were not transferred nor vitrified on day 5–6 (45%), 3.35 embryos per patient. No significant difference was found between average day-3 rank of embryos ranked 1, 2 (3.12 vs 4.12, p = 0.074) and 3 (3.12 vs 4.08, p = 0.082) on day-5–6. To conclude, this study brings a different perspective to the comparison of day 3 and day 5 by following each embryo’s putative and actual designation. Day-3 ranking of embryo morphology did not provide a reliable prediction for blastocyst formation, transfer order and vitrification intention, and may support transfer or cryopreservation of blastocysts over cleavage stage embryos.

Sorption of aniline and its derivatives by montmorillonite substituted by cations of widely different acidity depends upon the polarizing power of the interlayer cations. Infra-red spectra indicate that the anilines are mostly bound to the interlayer cations through water molecules, except in Cs montmorillonite, where bonding to the oxygen surfaces of the alumino-silicate sheets seems to predominate. Anilines are weak bases, which compete with the oxygen surfaces for protons of acidic interlayer water. Consequently, the tendency of anilines to act as proton donors in the clay interlayers increases with the polarizing power of the exchangeable cation. The concept of ‘basic’ water is introduced to account for some of the features of the spectra of Cs montmorillonite treated with the organic ligands.

The presence of Al-bearing goethites has been unequivocally established in Venezuelan laterite sediments by means of infrared spectroscopy (IR), chemical dissolution, and X-ray powder diffraction (XRD) methods. The composition of these samples ranges from [Fe0.89Al0.11]O(OH) to [Fe0.76Al0.24]O(OH). The data of dissolution experiments using a modified dithionite (CDB) treatment suggest a parallel behavior between Fe and Al; the gradual dissolution of Al is associated with the destruction of the Al-containing goethite. The interpretation of the CDB dissolution results for SiO2/Fe2O3 is different; silica was only slightly extracted from phases other than goethite. Substitution of Fe3+ by Al3+ in these goethites was represented on the XRD patterns by a lowering of the (110) and (111) reflections corresponding to a reduction in size of the unit cell of goethite. IR spectroscopy showed the formation of such solid solutions by a shift of the 405 cm−1 absorption band, assigned to v (Fe-O) in synthetic goethite, to >460 cm−1 in the spectrum of Al-bearing natural goethite. Moreover, this spectrum shows a shift of the 3140 cm−1 absorption, due to v (OH), to higher frequencies, indicating a H-bond weakening in [FexAl(1−x)]O(OH) compared to FeO(OH).

The adsorption mechanism of iso-propylammonium (PAH+), the cationic component of Roundup, by various homoionic montmorillonites and the structures of the associations obtained in the interlayer space were investigated, using infrared, X-ray, and carbon analysis methods. Adsorption from aqueous and ethanol solutions of Roundup was studied. The infrared spectra were compared with those obtained by the treatment of montmorillonites with ethanol and CCl4 solutions of the free iso-propylamine (PA). The adsorption of PA from ethanol gives rise to protonation of the amine. PA sorbed from CCl4 solution forms an ammonium-amine association. Adsorption of PAH+ from alcohol solution of Roundup occurs by the mechanism of cation exchange. With transition metal exchangeable cations, PAH+ is sorbed in excess, forming hydrogen bonds between NH3+ groups and hydroxyls resulting from dissociation of water molecules. The process of adsorption of PAH+ from aqueous solutions of Roundup depends on the concentration of the solution. If montmorillonite is reacted with 0.5% solution of Roundup, PAH+ is adsorbed by exchanging metal cations and the adsorption capacity of the clay does not exceed the c.e.c. If the montmorillonite is reacted with 5.0% solution of Roundup, the PAH+ exchanges protons originating from the hydrolysis of the interlayer water. Protons which are transferred from the interlayer space to the water solution are accepted by the anion component of Roundup. The amounts of PAH+ adsorbed from concentrated Roundup solutions are much higher than the cation exchange capacity of montmorillonite. Hydrogen bonds are formed between the ammonium and water or hydroxyl groups on the interlayer space. With the trivalent exchange ions Al and Fe, which tend to polymerize in the interlayer space, excess sorption gives rise to hydrogen bonding of NH3+ to oxygen of the polymer.

Halloysite was mechanically ground in the presence of NaCl, KCl, RbCl, RbCl and CsCl, and i.r. spectra were recorded after various periods of grinding, up to 10 min. Changes in the wave-numbers and sharpness of absorption bands were interpreted using assignments accepted for kaolinite. Diminution of absorption bands of OH groups and the appearance of new bands indicate formation of complexes of halloysite with KCl, KBr, RbCl, and CsCl. Water was essential in the complex formation, which may be formulated:

The amount of the complex formed depended on the salt and the time of grinding. Complex formation requires that the cation be large enough to serve as a “structure breaker” of the interlayer water sheet. Complex formation also requires that the cation be a weak electron acceptor. Grinding also led to changes in the fine structure of the tactoid.

The possibility of using the i.r. spectrum of halloysite as a finger print for identification of the mineral is discussed. It was concluded that NaCl is the most reliable dispersing agent to determine whether or not a mineral sample belongs to the kaolinite group. Disks in RbCl may be used to differentiate between kaolinite and hydrated halloysite.

The reaction between the herbicide “Roundup,” (PAH)3G, which is the commercial name of the iso-propylammonium salt of glyphosate (H3G, N-phosphonomethyl glycine), and montmorillonite was studied. The adsorption of the anionic component of Roundup glyphosate anion, G−3, from an ethanol solution is achieved by repeated immersion of the clay film in the alcohol solution followed by drying for 6–12 hr after each immersion. During the adsorption process the surface acidity of the interlayer space must be sufficiently high to protonate the anion. A zwitterion glyphosate is thereby formed in the interlayer space. Association forms are obtained in the interlayer space in which the COOH and the PO3H groups are linked to the exchangeable cations through water bridges. Adsorption of the glyphosate anion from aqueous solution of Roundup occurs when this anion forms a neutrally or positively charged complex with the exchangeable cation. This may occur with Al- and Fe-montmorillonite, when the molar ratio glyphosate:metal is such that a complex with a 1:1 ratio can be formed in the interlayer space. To clarify the reaction mechanism, adsorption of glycine by montmorillonite from ethanol solution was also studied. The associations obtained between glyphosate and exchangeable cations are less variable than those obtained between glycine and exchangeable cations in the interlayer space of montmorillonite. The following species of adsorbed glycine were identified: glycinium cation, zwitterion glycine, glycine complexed with metal cations either as a monodentate or as a bidentate ligand. In the latter case a chelate is formed.

The sorption of commercial K-Cu chlorophyllin by a sample of montmorillonite saturated with different exchange ions was studied. The organic anions are sorbed on external surfaces while K displaces most of the exchangeable cations. The samples sorb the constituents of chlorophyllin selectively and in different amounts, depending on the exchangeable cations of the clay. These also affect the amount of material peptized and the relative orientation and aggregation of the particles.

Possible assignments are suggested for some of the absorption bands in the 1150–400 cm−1 region of the i.r. spectra of serpentines. Polarized light was used to identify the out-of-plane vibrations in antigorites and platy lizardites and the vibrations parallel to the fibre axis in chrysotiles and fibrous lizardites. An attempt is made to correlate some known structural characteristics and the chemical composition of the serpentines with some features of the i.r. spectra.

While the problem governing Stokes flow about a single particle that is subject to an external force is ill posed in two dimensions (the ‘Stokes paradox’), the related problem of two mutually repellent particles is well posed. Motivated by self-assembly phenomena in thin viscous membranes, we consider this problem in the limit of remote particles. Such limits are typically handled in the literature using reflection techniques, which provide successive approximations to the mutual hydrodynamic interactions. Since their starting point is a single particle in an unbounded fluid domain, these techniques are futile in the present two-dimensional problem. We show how this apparent contradiction is resolved via use of singular perturbations. We obtain a two-term approximation for the velocity acquired by circular disks, considering both rigid and free particle surfaces. We also illustrate our perturbation scheme for elliptic disks, deriving a renormalised single-particle velocity. The utility of our asymptotic scheme is illustrated in the general problem of hydrodynamic interaction between a cluster of remote disks.

We consider heat or mass transport from a circular cylinder under a uniform crossflow at small Reynolds numbers, $\mathrm{Re}\ll 1$. This problem has been thwarted in the past by limitations inherent in the classical analyses of the singular flow problem, which have used asymptotic expansions in inverse powers of $\log \mathrm{Re}$. We here make use of the hybrid approximation of Kropinski, Ward & Keller [(1995) SIAM J. Appl. Math. 55, 1484], based upon a robust asymptotic expansion in powers of $\mathrm{Re}$. In that approximation, the “inner” streamfunction is provided by the product of a pre-factor $S$, a slowly varying function of $\mathrm{Re}$, with a $\mathrm{Re}$-independent “canonical” solution of a simple mathematical form. The pre-factor, in turn, is determined as an implicit function of $\log \mathrm{Re}$ via asymptotic matching with a numerical solution of the nonlinear single-scaled “outer” problem, where the cylinder appears as a point singularity. We exploit the hybrid approximation to analyse the transport problem in the limit of large Péclet number, $\mathrm{Pe}\gg 1$. In that limit, transport is restricted to a narrow boundary layer about the cylinder surface – a province contained within the inner region of the flow problem. With $S$ appearing as a parameter, a similarity solution is readily constructed for the boundary-layer problem. It provides the Nusselt number as $0.5799(S\,\mathrm{Pe})^{1/3}$. This asymptotic prediction is in remarkably close agreement with that of the numerical solution of the exact problem [Dennis, Hudson & Smith (1968) Phys. Fluids 11, 933] even for moderate $\mathrm{Re}$-values.

KCl-, KBr-, and KI-kaolinite intercalation complexes were synthesized by gradually heating potassium-halide discs of the dimethylsulfoxide (DMSO)-kaolinite intermediate at temperatures to 330°C. Two types of complexes were identified by infrared spectroscopy: almost non-hydrous, obtained during thermal treatment of the DMSO complex; and hydrated, produced by regrinding the disc in air. The former showed basal spacings with integral series of 00l reflections indicating ordered stacking of parallel 1:1 layers. Grinding resulted in delamination and formation of a disordered “card-house” type structure. The frequencies of the kaolinite OH bands show that the strength of the hydrogen bond between the intercalated halide and the inner-surface hydroxyl group decreases as Cl > Br > I. The positions of the H2O bands imply that halide-H2O interaction decreases in the same order. Consequently, the strength of the hydrogen bond between H2O and the oxygen atom plane increases in the opposite sequence.

In the non-hydrous KCl-kaolinite complex the inner hydroxyl band of kaolinite at 3620 cm-1 is replaced by a new feature at 3562 cm-1, indicating that these OH groups are perturbed. It is suggested that Cl ions penetrate through the ditrigonal hole and form hydrogen bonds with the inner OH groups. In contrast, Br and I ions are too large to pass into the ditrigonal holes and do not form hydrogen bonds with the inner hydroxyls.

The OH-stretching region in curve-fitted micro-Raman, photoacoustic and transmission IR spectra of St. Claire dickite was investigated. Polarized Raman spectra recorded from th. (001) an. (010) faces of the dickite crystal displayed six prominent OH bands. The relative intensities depend strongly on both the orientation of the crystallographic axes and the direction of the electric vector of the laser beam. Four out-of-plane vibrations, AA, Az, CA and Cz, at ~3710, 3706, 3654 and 3643 cm-1 respectively, predominate when the electric vector is perpendicular to the dickite plates. Two in-plane vibrations, Dz and DA at 3627 and 3623 cm-1, intensify when the electric vector is parallel to the plane. The relationship between band intensity and crystal orientation was interpreted in terms of longitudinal optic (LO) and transverse optic (TO) crystal vibration modes. These LO and TO crystal modes were also observed in curve-fitted photoacoustic and transmission IR spectra of coarse, non-oriented crystals of the dickite.

Polarized micro-Raman spectra of a single large crystal of Keokuk kaolinite were recorded in the OH-stretching region with the laser beam directed along the different crystal axes. The Raman spectra are characterized by five OH-stretching bands at 3694, 3683, 3668, 3650 and 3620 cm−1 labeled A, Z, B, C and D, respectively. The relative intensities of these five bands depend on the orientation of the crystal and the scattering geometry. The spectra agree with the assertion that bands A and Z arise from out-of-plane vibrations, whereas band D corresponds to an in-plane vibration. The area ratios of the various bands were calculated from fitted curves of spectra recorded with the electric vector of the laser beam parallel to different crystallographic planes. The increments in the relative areas of bands B and C were parallel to those of bands A and Z and it appears that out-of-plane vibrations made considerable contributions to these bands also. From the change of area ratios with the change in the direction of the electric vector of the laser beam, bands A and Z were attributed to LO and TO frequencies of one inner-surface hydroxyl vibration. Bands A + Z, B, C and D were attributed to the vibrations of the hydroxyls assigned by Bish (1993) as OH(3), OH(4), OH(2) and OH(1), respectively. These observations were supported by photoacoustic and transmission IR spectra.