Rheo-NMR studies of the behavior of a nematic liquid crystal in a low-shear-rate regime: the transition from director alignment to reorientation

Deuterium NMR spectroscopy has been used to study the director dynamics of the nematic liquid-crystal system cetyl trimethylammonium bromide/D2O under the action of applied viscous torques. Shear forces were applied using a custom-built Couette cell that was introduced into an NMR superconducting magnet, so that its rotational axis was parallel to the magnetic field direction, along which the liquid-crystal director originally aligned. Subsequently, the inner cylinder of the cell was rotated continuously at different rates using a stepper motor. The resulting time evolution and ultimate steady-state orientation of the director, governed by the competition between the applied viscous torque with elastic and magnetic terms, was measured via observed changes in the deuterium spectrum. Using a simple gearbox allowed unprecedented access to a low-shear-rate regime in which, above a threshold shear rate, the director of part of the sample was observed to reorient, while the remaining part still aligned with the magnetic field. Subsequent increases in the applied rotational rate were found to increase the relative proportion of the orienting fraction. Spatially resolved NMR spectra showed that the orienting and field-aligned fractions formed separated bands across the gap of the Couette cell, with director reorientation being initiated at the moving inner wall. The behavior was found to be consistent with the often ignored variation in velocity gradient manifest across the gap of a cylindrical cell, so that as the angular frequency of the inner cylinder was increased the radial location of the critical shear rate required for reorientation traversed the gap. Once the applied rotational rate was sufficient to reorient the director of the entire sample, the dependence of the exhibited steady-state orientation on the average applied shear rate was measured. These results could be fitted to an analytical solution of the force-balance equation, made tractable by the assumption that the elasticity term was of minor significance and could be ignored. Additionally, the use of a numerical solution of the full force-balance equation, which explicitly includes elasticity and secondary flow and additionally allows the time evolution of the director orientation to be calculated, was investigated.

Measurement of the self-diffusion coefficient of water as a function of position in wheat grain using nuclear magnetic resonance imaging

A pulsed field gradient spin echo sequence has been incorporated in a nuclear magnetic resonance (NMR) imaging experiment to provide an image contrast dependent on local molecular self-diffusion. The consequent image attenuation is shown to exhibit a dependence on applied magnetic field gradient consistent with the Stejskal-Tanner relationship. The method used represents a novel extension of microscopic imaging and demonstrates the possibility of measuring localized motion.Water self-diffusion rates normal to the transverse 1.3-mm section of a wheat grain have been measured in structural features at 150-mum resolution. The results are consistent with averaged measurements in the bulk grain obtained by other methods while local differences in water mobility correlate with differences in physiological function.

PGSE NMR measurement of the non-local dispersion tensor for flow in porous media

The non-local dispersion tensor provides a fundamental description of velocity correlations and displacement information in a pre-asymptotic dispersive system. Here we describe in detail how PGSE NMR may be used to measure this tensor, outlining the pulse sequences needed for signal superposition, as well as the data analysis procedures. The sequence is inherently two-dimensional, the first dimension giving the displacement resolution, the second giving correlation information. The technique is verified against simulated echo attenuation data from a lattice-Boltzmann simulation.

The dependence on magnetic field strength of correlated internal gradient relaxation time distributions in heterogeneous materials

Magnetic susceptibility differences in porous media produce local gradients within the pore space. At high magnetic fields, these inhomogeneities have the potential to greatly affect nuclear magnetic resonance measurements. We undertake a study using a new NMR technique to measure the internal gradients present in highly heterogeneous samples over a wide range of magnetic field strengths. Our results show that even at ultra-high fields there can exist signal at internal gradient strengths sufficiently small that techniques for suppressing unwanted side effects have the possibility to be used. Our findings encourage the use of these high and ultra-high field strengths for a broader range of samples. Our results also give experimental evidence to support the theory of internal gradient scaling as a function of field strength within pores.

Pore characterization through propagator-resolved transverse relaxation exchange

We use the propagator-resolved transverse relaxation exchange experiment to characterize the pore space and fluid behavior of water saturated, tight-packed quartz sand. The experiment uses T2 exchange plots to observe the number of molecules that shift their environment for a range of mixing times. The propagator dimension allows us to determine how far the molecules have moved. The peak intensities are integrated and then plotted as a function of displacement and mixing time. We also model our system using both a probabilistic pore-hopping simulation and a spreading Gaussian model. We use the results of these simulations to interpret the peak intensity plots. From this, we can estimate pore features such as characteristic time, pore radii, and interpore spacing. The tortuosity of the different pore sizes can then be calculated from these values.

Aging, yielding, and shear banding in soft colloidal glasses

Soft colloidal interactions in colloidal glasses are modeled using suspensions of multiarm star polymers. Using a preshearing protocol that ensures a reproducible initial state ("rejuvenation" of the system), we report here the evolution of the flow curve from monotonically increasing to one dominated by a stress plateau, demonstrating a corresponding shear-banded state. Phenomenological understanding is provided through a scalar model that describes the free-energy landscape.

NMR measurement of nonlocal dispersion in complex flows

The flow and diffusion driven separation of initially adjacent liquid molecules is known as dispersion. The primary physical quantity describing this process, the nonlocal dispersion tensor, provides insight regarding both the spatial and temporal correlations of molecular velocity fluctuations in complex flows. We here propose and demonstrate a nuclear magnetic resonance method for the measurement of this tensor, validating its implementation for the case of cylindrical Couette flow, and demonstrating its application to the study of fluid dispersion in a random bead pack.

Effect of shear on an onion texture

Lamellar systems are self-assemblies of surfactant molecules forming planar bilayers separated by layers of solvent. At sufficiently high shear rates, they are known to form spherical objects often referred to as onions. In this paper, we are concerned with the effect of shear on those multi-lamellar vesicles. We measure solvent diffusion by nuclear magnetic resonance (NMR) using a method which is sensitive to the time dependence of mean-squared displacements. This method, combined with NMR velocimetry, allows us to infer onion structure as a function of shear rate, identifying different regimes in which local viscosity is related to the onion size. The role of slip is examined and the stress dependence of wall slip velocities is determined.

Propagator resolved transverse relaxation exchange spectroscopy

We present in this communication a novel propagator-resolved transverse relaxation exchange experiment. This experiment enhances the previous technique of transverse relaxation exchange by enabling spatial resolution. Hence, we are able to obtain separate, and remarkably different, T2-T2 exchange plots, corresponding to different spatial displacement of the spin bearing water molecules in a porous sand matrix. This experiment is the first to combine two inverse Laplace dimensions with a Fourier dimension, opening the door to a host of new experiments combining Fourier and inverse Laplace spectroscopy.

Shear deformation of polymer melt observed via proton NMR: theory and experiment

We here develop a theory for the effect of shearing flow on residual proton dipole-dipole interactions for polymer melts. The model is based on the use of correlation functions which derive from the return to origin probability for polymers reptating in the tube of surrounding constraints. Using Doi-Edwards theory we calculate the spin-echo response under equilibrium conditions and then consider the effect of a shearing flow which deforms the tube, finding that there exists a strong dependence of transverse relaxation on Weissenberg number. The results are compared with NMR measurements of shear-perturbed proton T2 relaxation in 494kDa poly (dimethylsiloxane).

A mobile one-sided NMR sensor with a homogeneous magnetic field: the NMR-MOLE

A new portable NMR sensor with a novel one-sided access magnet design, termed NMR-MOLE (MObile Lateral Explorer), has been characterised in terms of sensitivity and depth penetration. The magnet has been designed to be portable and create a volume with a relatively homogeneous magnetic field, 15,000 ppm over a region from 4 to 16 mm away from the probe, with maximum sensitivity at a depth of 10 mm. The proton NMR frequency is 3.3 MHz. We have demonstrated that with this approach a highly sensitive, portable, unilateral NMR sensor can be built. Such a design is especially suited for the characterisation of liquids in situations where unilateral or portable access is required.

Tracking pore to pore exchange using relaxation exchange spectroscopy

We observe the movement of water over time between pores of differing sizes in Castlegate sandstone. To achieve this, we perform an NMR transverse relaxation exchange experiment for several mixing times. The resulting data are converted to 2D T2 distributions using a 2D inverse Laplace transform (ILT). We show for the first time that quantitative analysis of ILT distributions enables one to extract characteristic times for different pores sizes. This information is potentially useful for permeability determination as well as better understanding of exchange between specific pore subpopulations.

Rheo-NMR phenomena of wormlike micelles

Using a combination of rheology and nuclear magnetic resonance (NMR) spectroscopy/velocimetry we demonstrate the existence of shear banding fluctuations under Couette flow of the micellar system 10% w/v cetylpyridinium chloride and sodium salicylate (CPyCl-NaSal) molar ratio 2 : 1 in 0.5 M NaCl in either HO or HO, using both time-averaged and real-time measurements. These shear banding fluctuations are consistent not only with the shear stress fluctuations observed in rheological measurements but also with fluctuations in the change of the constrained fraction of the amphiphile chain (Δ) observed in H-NMR spectroscopy experiments. Using H-NMR spectroscopy on a deuterated probe molecule (-decane) located in the wormlike micellar interior, direct measurement of the shear-induced nematic phase transition is reported.

Diffusion-diffusion correlation and exchange as a signature for local order and dynamics

We demonstrate the use of new two-dimensional nuclear magnetic resonance experiments in the examination of local diffusional anisotropy under conditions of global isotropy. The methods, known as diffusion-diffusion correlation spectroscopy and diffusion exchange spectroscopy, employ successive pairs of magnetic field gradient pulses, with signal analysis using two-dimensional inverse Laplace transformation. Diffusional anisotropy is measured for water molecules in a polydomain lamellar phase lyotropic liquid crystal, 40 wt % nonionic surfactant C10E3 (C10H21O(CH2CH2O)6H) in H2O.

Measurement of diffusion in the presence of shear flow

We demonstrate here a method whereby molecular diffusion coefficients may be measured in the presence of the deformational flow field of a rheo-NMR cell. The method, which uses a repetitive CPMG train of rf pulses interspersed with magnetic field gradient pulses, allows the anisotropic diffusion spectrum to be directly probed. We focus on the cylindrical Couette cell, for which the radial, tangential, and axial directions correspond to the hydrodynamic velocity gradient, velocity, and vorticity directions. While ideal Couette flow does not perturb the vorticity direction, it does perturb diffusion measurements for the velocity gradient direction, and to a lesser extent, the velocity direction. We show that with closely spaced gradient pulses operating in a flow-compensating mode, there exists a diffusion limit below which one cannot measure, that scales as T(2)gamma(4), where gamma is the shear rate and T the gradient pulse repetition period. For a typical rheo-NMR cell, and for the more challenging velocity gradient direction, diffusion rates above 10(-12) m(2) s(-1) can be accurately measured (to 1% error) at shear rates up to 3s(-1). We demonstrate the use of the method in measuring the diffusion spectrum of a lyotropic lamellar phase under shear.

Undulations and fluctuations in a lamellar phase lyotropic liquid crystal and their suppression by weak shear flow

Using multi-echo pulsed gradient nuclear magnetic resonance (NMR) we measure the anisotropic diffusion of water molecules in the lamellar phase of lyotropic system composed of cetylpyridinium chloride/hexanol diluted in brine. The technique reveals the Fourier spectrum of the molecular velocity autocorrelation function, and its repetitive compensating nature permits effective measurement in the presence of shear flow. We show that under zero shear the phase is highly oriented and that both the amplitude and fluctuation correlation time of lamellar undulations can be measured. The suppression of undulations by weak shear is apparent. We further measure transverse lamellae permeability arising from defects.

Diffusion correlation NMR spectroscopic study of anisotropic diffusion of water in plant tissues

The anisotropic diffusion of water in chive (Allium schoenoprasum) tissues has been investigated using two-dimensional nuclear magnetic resonance methods: diffusion-diffusion correlation spectroscopy and diffusion-relaxation correlation spectroscopy. Corresponding one-dimensional T2 and diffusion measurements confirm independently the results of the two-dimensional investigations. In particular the diffusion-diffusion correlation spectroscopy method proves to be very powerful in resolving the different components of the diffusion tensor at different sites in the sample.

NMR velocimetry studies of the steady-shear rheology of a concentrated hard-sphere colloidal system

NMR velocimetry has been used to observe the steady-shear rheological behaviour of a concentrated suspension of hard-sphere like 370 nm diameter PMMA core-shell latex particles at the volume fraction phi = 0.46, the liquid core of the spheres rendering possible NMR observation of the particles themselves. Rheological measurements in a cone-and-plate geometry indicate that when aged (i.e. left at rest for two weeks), the material exhibits yield stress behaviour at very low shear rates. For shear rates greater than 1 s(-1) a transition to liquid-like behaviour was observed, leading to a rejuvenated fluid state which exhibits shear-thinning behaviour over a wide range of shear rates. A similar yield stress behaviour was reflected in NMR velocimetry measurements in a Couette geometry, where the solid-to liquid transition could be clearly observed. Under steady-state flow, the fluid state inside the radius at which yield stress was observed, exhibited shear-thinning behaviour with a power law exponent n slowly approaching unity with increasing shear rate. This behaviour has some similarities with a model of Derec et al. in which aging and rejuvenation effects compete. Substantial wall slip was observed both at the inner and at the outer wall, an effect which disappeared as the shear rate was increased. No radial particle migration from the high-shear region at the inner wall was observed.

Diffusion exchange NMR spectroscopic study of dextran exchange through polyelectrolyte multilayer capsules

Diffusion exchange of dextran with molecular weights 4.4 and 77 kDa through polyelectrolyte multilayer (PEM) hollow capsules consisting of four bilayers of polystyrene sulfonate/polydiallyldimethylammonium chloride has been investigated using two-dimensional nuclear-magnetic-resonance methods: diffusion-diffusion exchange spectroscopy (DEXSY) and diffusion-relaxation correlation spectroscopy (DRCOSY). Results obtained in DRCOSY experiments show that the diffusion process of dextran 77 kDa exhibits an observation time dependence suggesting a diffusion behavior restricted by confinement. We find evidence for both single capsule and capsule aggregate states, with a partitioning of the 77-kDa dextran between the free and capsule states much larger than that suggested by volume fraction alone. Results from DEXSY experiments show that dextran 77 kDa is in diffusive exchange through the capsules with an exchange time of around 1 s. In contrast, the capsules have no detectable influence on the diffusion process of the dextran 4.4 kDa. This quantitative information may be used in designing PEM capsules as drug carriers.

Time-dependence of nuclear magnetic resonance quadrupole interactions for polymers under shear

We consider the problem of performing NMR spectroscopy under conditions of flow, a central issue in Rheo-NMR. By way of example, the effects of rotational motion on the deuterium NMR spectrum are considered for Couette cell experiments involving deformation of polymers under shearing conditions. The polymer was modelled as a power law fluid and for each streamline, the spin Hamiltonian evolved to allow for flow reorientation. The gap-integral spectra are compared with the 'ideal' spectra for a polymer under shear, but without reorientation. It is found that flow does affect the shape of the deuterium spectra, as well as slightly perturbing the splittings.

Shear banding fluctuations and nematic order in wormlike micelles

Using rapid NMR velocimetry we demonstrate the existence of shear band fluctuations in the Couette flow of the wormlike micelle system, 10% w/v cetylpyridinium chloride and sodium salicylate (molar ratio 2:1) in 0.5 M 2H2O NaCl brine. We show that the fluctuations may be either quasirandom or periodic, the fluctuation spectrum being similar to that observed in the stress. Despite the equilibrium fluid being far from an isotropic-nematic transition, deuterium NMR shows that the onset of shear banding is associated with a nematic micellar state whose order parameter depends on shear rate.

Imaging the velocity profiles in tubeless siphon flow by NMR microscopy

We report on the use of NMR micro-imaging to observe flow within a tubeless siphon. The flow is maintained in a visco-elastic liquid of high extensional viscosity, namely 0.5% w/v 8 million Dalton polyethylene oxide in water. The velocity profiles reveal a significant velocity gradient in the vertical direction as well as a transition from near-Poiseuille flow at the pipe entrance to plug flow far from the pipe entrance towards the base of the tubeless siphon.

Diffusion-relaxation correlation in simple pore structures

The effects of independent encoding for relaxation and for diffusion using separate time and gradient dimensions are calculated for spins diffusing in plane parallel and spherical pores with relaxing walls. Two-dimensional inverse Laplace transformation is used to obtain computed (D,T(2)) maps for both geometries, in the regime in which the dimensionless diffusion coefficient is less than unity and the dimensionless relaxation parameter of order unity or greater. It is shown that there exist two distinct branches on the (D,T(2)) maps, one with diffusion and relaxation strongly correlated and one in which the diffusion coefficients vary widely independently of relaxation.

Spatial dependence of dispersion

The use of Pulsed Gradient Spin Echo (PGSE) NMR to investigate flow in porous media is well established. Using two pairs of position-encoding pulses in the PGSE experiment gives the possibility of examining velocity fluctuations, by comparing displacements, during the two encoding intervals. This method may be used to measure the asymptotic dispersion coefficient as well as the Velocity Auto-Correlation Function (VACF) in porous media flow. Some examples of two-dimensional maps of density and velocity distributions are accompanied by the first attempt to perform localized measurements of flow dispersion in porous media.

Use of the second dimension in PGSE NMR studies of porous media

2-dimensional methods based on PGSE NMR may be used to correlate or separate molecular dynamical properties, or to elucidate fluctuations. These may utilize either the gradient (q-vector) domain, in which molecular displacements are measured, or the time domain, in which relaxation is measured, and may be analyzed by combinations of inverse Fourier or Laplace transforms. Existing methodologies are reviewed and new experiments proposed. In particular the use of diffusion-diffusion exchange and correlation analysis is demonstrated using the case of water diffusion in a lamellar phase liquid crystal.

2D relaxation/diffusion correlations in porous media

2D correlations between NMR relaxation and/or diffusion have been used to investigate water and oil dynamics in food and micro-emulsion systems. In the case of Mozzarella and Gouda cheese samples, a significant change in D/T2 correlation is appearing with cheese aging. In the case of a water/toluene micro-emulsion, some evidence for coalescence effects is suggested by D/D exchange spectra.

NMR visualization of displacement correlations for flow in porous media

The temporal correlations of velocities for both water and a water-glycerol mixture flowing through a random packings of monodisperse spherical particles have been investigated using two-dimensional nuclear magnetic resonance methods. By combining various flow rates, fluid viscosities, and bead sizes, a wide range of flow parameters has been covered, the dimensionless Peclet number ranging from 100 to 100 000. The velocity exchange spectroscopy (VEXSY) technique has been employed to measure the correlation between velocities during two intervals separated from each other by a mixing time tau(m). This time is made both large and small compared with the time constant tau(c), required for a fluid element possessing the average flow velocity to cover a distance equal to the characteristic size in the system, the bead diameter. The two-dimensional conditional probability of displacement resulting from the VEXSY method reveals the existence of different "subensembles" of molecules, including a slow moving pool whose displacement is dominated by Brownian motion, an intermediate ensemble whose velocities change little over the mixing time, and a fast flowing ensemble which loses correlation due to mechanical dispersion. We find that that the approach to asymptotic dispersion, as tau(c)/tau(m) increases, depends strongly on the Peclet number, the deviation of the velocity autocorrelation function from a monoexponential Ornstein-Uhlenbeck process becoming more pronounced with increasing Peclet number.

Biaxial deformation of a polymer under shear: NMR test of the Doi-Edwards model with convected constraint release

2H NMR quadrupole interaction spectroscopy has been used to measure the deformation of a 670 kD poly(dimethylsiloxane) melt under shear in a Couette cell. The signals were acquired from a per deuterated benzene probe molecule which provides a motionally averaged sampling of the entire segmental ensemble. We have measured the dependence on shear rate of the S(XX) (velocity), S(YY) (velocity gradient), S(ZZ) (vorticity), and S(XY) (shear) elements of the segmental alignment tensor, as well as the angular dependence of the deuterium quadrupole splitting at fixed shear rate. We show that the data agree quite well with the Doi-Edwards theory but significantly better when convected constraint release effects are included. These fits return a value for the tube disengagement time of 100 ms.

Two-dimensional NMR of velocity exchange: VEXSY and SERPENT

Two different multidimensional pulsed field gradient sequences are compared which have the purpose of correlating spin displacements in different time intervals with each other. The simplest possible sequence, three-pulse SERPENT, measures displacements in two interleaved time intervals, while in VEXSY, consisting of two independent pairs of gradient pulses separated by a mixing time, displacements during the two encoding intervals are compared to each other. The formalism for both sequences is discussed in q space and in displacement space and common features as well as differences between the two types of experiments are highlighted, employing the particular case of the concurrent VEXSY scheme which allows treatment according to both formalisms.

Shear banding and the isotropic-to-nematic transition in wormlike micelles

Using deuterium NMR spectroscopy in a Couette cell, we observe shear-induced nematic ordering in the concentrated wormlike-micelle system CTAB/D(2)O, and our results are qualitatively consistent with birefringence studies, and in exact quantitative agreement with the degree of order measured in neutron-diffraction measurements. The width of the nematic region depends on shear rate, as well as on the temperature proximity to the equilibrium isotropic-nematic transition. Comparison of the nematic order profiles with velocity profiles obtained under identical conditions shows quite clearly that the nematic state is not identifiable with a highly sheared, low viscosity layer, and we conclude that the process of shearing induces a nematic state of high viscosity, possibly associated with mesoscale ordering. We present a simple model in which transition from the high shear branch to the viscous nematic branch is counterbalanced by subsequent relaxation of nematic order.

Selective storage of magnetization in strongly relaxing spin systems

We have investigated the use of a "split-sinc" RF pulse to selectively store magnetization from a selected region of a sample, for later recall in imaging or spectroscopy experiments. The pulse sequence is based on an original suggestion by Post et al. (West German Patent No. P3209263.6, 13 March 1982), later implemented by Aue et al. (J. Magn. Reson. 56, 350 (1984)). We have carried out detailed numerical calculations using the Bloch equations and show that this particular sequence is robust in the face of strong transverse relaxation, and we demonstrate its application to imaging of polymer samples in shearing and extensional flow cells.

Low-frequency velocity correlation spectrum of fluid in a porous media by modulated gradient spin echo

In addition to the fast correlation for local stochastic motion, the molecular velocity correlation function in a fluid enclosed within the pore boundaries features a slow long time-tail decay. Here we present its study by the NMR modulated gradient spin-echo method (MGSE) [1] on a system of water trapped in the space between the closely packed polystyrene beads. With MGSE pulse sequence, a repetitive train of RF pulses with interspersed gradient pulses periodically modulates the spin phase. It gives the spin echo attenuation proportional to a value of the molecular velocity correlation spectrum at the modulation frequency. Covering the frequency range between Hz and MHz, it is a complement to the quasi-elastic neutron scattering, and so a suitable technique for the investigation of low frequency molecular dynamics in fluids. In our experiment, it enables to extract the low frequency correlation spectrum of water molecules confined in porous media. The function exhibits a negative long time-tail characteristic (a low frequency decay of the spectrum), which can be interpreted as a molecular back scattering on boundaries. The results can be well fitted with the spectrum calculated from the solution of the Langevin equation for restricted diffusion (which exhibits an exponential decay) [2] as well as with the spectrum obtained when simulating the hydrodynamics of molecular motion constrained by capillary walls (which gives an algebraic decay) [3]. Despite much work on theories and simulation, which predict slow negative long time tail of molecular velocity correlation dynamics in confined fluids, the obtained velocity correlation spectrum is the first experimental evidence to confirm these effects. The obtained dependence of spin echo attenuation on time, gradient strength and modulation frequency is also the first experimental verification of the recently developed approach to the spin echo in porous media, that uses the spin phase average with the cumulant expansion to get the attenuation as a discord of spin spatial coherence [4].

Time-dependent velocities in porous media dispersive flow

Pulsed Gradient Spin Echo (PGSE) NMR methods may be used to measure the asymptotic dispersion coefficient as well as the velocity autocorrelation function (VACF) in porous media flow. The VACF can be measured in the frequency domain using repetitive gradient pulse trains, and in the time domain using double PGSE encoding. The one dimensional double PGSE method, and the two dimensional velocity exchange experiment (VEXSY) are briefly outlined and their application to flow in monodisperse 0.5 mm diameter beads packs described, both axial and transverse VACFs being examined. The measured correlation times are shown to agree well with calculated values. The asymptotic dispersion coefficients agree with literature values in the case of transverse flow while in axial flow it is shown that asymptotic conditions are not achieved, even for observation times longer than the correlation time for flow around a bead.

One-shot velocimetry using echo planar imaging microscopy

A rapid version of PEPI (pi-echo planar imaging) velocimetry has been implemented, enabling a velocity image, at microscopic resolution, to be acquired in less than 1 s. The velocity map was reconstructed using the phase information from the ratio of two PEPI images, one obtained with a velocity-encoding filter applied prior to the imaging sequence and the other image without. The acquisition time for each image was about 80 ms and the two complete image acquisitions were acquired in one shot in 500 ms. This rapid velocimetry sequence gave a good representation of laminar pipe flow. It has also been used to examine extensional flow in a biaxial extension in which the transient extension takes about 3 s.