David S. Cannell

Physical optics treatment of the shadowgraph

We present an analysis of the shadowgraph method of visualizing convective flows based on physical optics, treating the refractive-index perturbation caused by the flow as a transmission grating. Various patterns in thermal convection of an isotropic fluid as well as normal rolls in electroconvection of a nematic liquid crystal are considered. The results differ significantly from those of geometrical optics, showing that use of the shadowgraph as a quantitative tool for amplitude measurements should not, in general, be based on geometrical optics.

Apparatus for the study of Rayleigh–Bénard convection in gases under pressure

We review the history of experimental work on Rayleigh–Benard convection in gases, and then describe a modern apparatus that has been used in our experiments on gas convection. This system allows for the study of patterns in a cell with an aspect ratio (cell radius/fluid layer depth) as large as 100, with the cell thickness uniform to a fraction of a μm, and with the pressure controlled at the level of one part in 105. This level of control can yield a stability of the critical temperature difference for the convective onset of better than one part in 104. The convection patterns are visualized and the temperature field can be inferred using the shadowgraph technique. We describe the flow visualization and image processing necessary for this. Some interesting results obtained with the system are briefly summarized.

Multiple-scattering suppression by cross correlation

We describe a new method for characterizing particles in turbid media by cross correlating the scattered intensity fluctuations at two nearby points in the far field. The cross-correlation function selectively emphasizes single scattering over multiple scattering. The usual dynamic light-scattering capability of inferring particle size from decay rate is thus extended to samples that are so turbid as to be visually opaque. The method relies on single-scattering speckle being physically larger than multiple-scattering speckle. With a suitable optical geometry to select nearby points in the far field or equivalently slightly different scattering wave vectors (of the same magnitude), the multiple-scattering contribution to the cross-correlation function may be reduced and in some cases rendered insignificant. Experimental results demonstrating the feasibility of this approach are presented.

Photometer for quasielastic and classical light scattering

An accurate light scattering photometer capable of measuring both the angular distribution of intensity and the intensity fluctuation spectrum of laser light scattered from a wide variety of samples including solutions of polymers and other macromolecules is described. The photometer employs 18 fixed scattering angles ranging from 2.6° to 163° and is sufficiently accurate to measure a molecular radius of gyration as small as 60 A reliably. Stray elastically scattered light normally comprises less than 1% of the light scattered from pure toluene at the smallest scattering angle and is unmeasurable at other angles. The apparatus employs optical fibers to transmit the scattered light to a single photomultiplier tube and functions automatically under microprocessor control, with sample temperature controlled to ±0.1 mK.

Osmotic susceptibility and diffusion coefficient of charged bovine serum albumin

We report measurements of the osmotic susceptibility and mutual diffusion coefficient of solutions of charged bovine serum albumin molecules made using laser light scattering. The measurements were made as a function of solution ionic strength for various macromolecular charge states ranging from −4e to −13e. We find that the osmotic susceptibility data may be interpreted quantitatively in terms of the simple Verwey–Overbeek interaction potential, provided that adequate care is taken in computing the radial distribution function. Current theoretical treatments of the dynamics, with hydrodynamic interactions included to first order in the concentration, are found to deviate significantly (≲50%) from the diffusion coefficient data. The deviations occur under all conditions of charge and ionic strength for which the susceptibility has been reduced to less than half the ideal gas value.

Fractal fronts of diffusion in microgravity

Spatial scale invariance represents a remarkable feature of natural phenomena. A ubiquitous example is represented by miscible liquid phases undergoing diffusion. Theory and simulations predict that in the absence of gravity diffusion is characterized by long-ranged algebraic correlations. Experimental evidence of scale invariance generated by diffusion has been limited, because on Earth the development of long-range correlations is suppressed by gravity. Here we report experimental results obtained in microgravity during the flight of the FOTON M3 satellite. We find that during a diffusion process a dilute polymer solution exhibits scale-invariant concentration fluctuations with sizes ranging up to millimetres, and relaxation times as large as 1,000 s. The scale invariance is limited only by the finite size of the sample, in agreement with recent theoretical predictions. The presence of such fluctuations could possibly impact the growth of materials in microgravity.

Pattern formation and wave-number selection by Rayleigh-Bénard convection in a cylindrical container

We describe an apparatus and procedures for simultaneous heat transport measurements and computer enhanced shadowgraph flow-pattern imaging in a shallow horizontal layer of fluid heated from below. The heat transport measurements have a resolution of better than 0.1%, and the shadowgraph technique can detect the flow field for ≡ (R – Rc)/Rc as small as 10-2 (Rc is the critical value of the Rayleigh number R for onset of convection). The apparatus and procedures were used to study pattern and wave-number evolution in a cylindrical layer of water with radius-to-height ratio L = 7.5 and Prandtl number σ = 6.1. We found that dynamic sidewall forcing during the early thermal transients after a change in the heat current from a subcritical to a supercritical value establishes a cylindrical flow pattern. Once created, this pattern is stable in our apparatus over the wide range 0.16 8 even after the transients have decayed. With changing , adjustment in the wave number k takes place discontinuously by hysteretic changes at the cell center in the number of convection roll pairs. When is increased, the discontinuous changes at the cell center are towards smaller k and are preceded by a continuous loss of cylindrical symmetry (the middle roll pair moves off center). The selected wave numbers coincide neither with the zig-zag instability of the infinite system, as once suggested, nor with a linear extrapolation to = 0(1) of the recent prediction to lowest order in of Manneville and Piquemal and of Cross. Comparison of the selected k with measurements by others reveals no dependence upon L and σ. For < 0.16, the cylindrical pattern is unstable and decays on a time scale much longer than a horizontal diffusion time to patterns of rolls which tend to be perpendicular to the sidewalls and which contain defects. Once formed, these latter patterns will persist at large values of . These patterns also undergo a wave-number adjustment process with hysteretic changes mediated mostly by focus singularities near the walls. In these cases, larger values of also tend to produce smaller values of k.

Use of dynamic schlieren interferometry to study fluctuations during free diffusion

We used a form of schlieren interferometry to measure the mean-squared amplitude and temporal autocorrelation function of concentration fluctuations driven by the presence of a gradient during the free diffusion of a urea solution into water. By taking and processing sequences of images separated in time by less than the shortest correlation time of interest, we were able to simultaneously measure dynamics at a number of different wave vectors. The technique is conceptually similar to the shadowgraph method, which has been used to make similar measurements, but the schlieren method has the advantage that the transfer function is wave-vector independent rather than oscillatory.

A ±15 microdegree temperature controller

We have constructed a temperature controller utilizing a thermistor in a high impedance ac Wheatstone bridge. It maintains the temperature of a 1.3 liter volume constant to within ±15 μ°C, over a 40 h period. The controller employs a ratio transformer, a simple homemade preamplifier, a commercial lock‐in amplifier, a small bipolar power amplifier, and a thermoelectric device. Access to the controlled region can be obtained in a few seconds.

Wavenumber selection and Eckhaus instability in Couette-Taylor flow

Abstract We review a number of experimental results which pertain to pattern selection in Couette-Taylor flow. They include measurements of the harmonic contents of Taylor vortices, of the location of the Eckhaus boundary, of wavenumber selection by a spatial ramp of the Reynolds number, and of the axial variation of the wavenumber in the finite system. We show that many of the results can be understood quantitatively in terms of the Ginzburg-Landau amplitude equation.