T. Mullin

Negative Poisson's Ratio Behavior Induced by an Elastic Instability

Negative Poissons ratio behavior has been uncovered in cellular solids that comprise a solid matrix with a square array of circular voids. The simplicity of the fabrication implies robust behavior, which is relevant over a range of scales. The behavior results from an elastic instability, which induces a pattern transformation and excellent quantitative agreement is found between calculation and experiment.

Transition to turbulence in constant-mass-flux pipe flow

We report the results of an experimental study of the transition to turbulence in a pipe under the condition of constant mass flux. The transition behaviour and structures observed in this experiment were qualitatively the same as those described in previous reported studies performed in pressure-driven systems. A variety of jet and suction devices were used to create repeatable disturbances which were then used to test the stability of developed Poiseuille flow. The Reynolds number ( Re ) and the parameters governing the disturbances were varied and the outcome, whether or not transition occurred some distance downstream of the injection point, was recorded. It was found that a critical amplitude of disturbance was required to cause transition at a given Re and that this amplitude varied in a systematic way with Re . This finite, critical level was found to be a robust feature, and was relatively insensitive to the form of disturbance. We interpret this as evidence for disconnected solutions which may provide a pointer for making progress in this fundamental, and as yet unresolved, problem in fluid mechanics.

Scaling of the Turbulence Transition Threshold in a Pipe

We report the results of an experimental investigation of the transition to turbulence in a pipe over approximately an order of magnitude range in the Reynolds number Re. A novel scaling law is uncovered using a systematic experimental procedure which permits contact to be made with modern theoretical thinking. The principal result we uncover is a scaling law which indicates that the amplitude of perturbation required to cause transition scales as O(Re-1).

Mutations of steady cellular flows in the Taylor experiment

Aspects of the various steady states of Taylor-vortex flow between concentric cylinders have been investigated by means of flow visualization. The experiments have focused principally on the evolution of the primary flow , that is, on the continuum of steady states parametrized by the Reynolds number R , beginning at small R where the primary flow is the only one possible. For any particular aspect ratio Γ, the primary flow develops a well-defined pattern of cells at higher R , but then other steady cellular flows (secondary modes) are also possible. The observations presented demonstrate mutations of the primary flow as Γ is varied through critical values: its R -dependent evolution is thereby switched from one to another array of cells realized at higher R . In each of four cases (4–6, 6–8, 8–10 and 10–12 cells), the mutation is shown to involve hysteresis of the primary-flow locus and complicated interactions with secondary modes. Following a description of the apparatus in §2, a discussion of the experimental method used to observe the often delicate hysteresis effects is given in §3. The experimental results in §4 are in broad agreement with abstract mathematical ideas that have been previously shown to bear on the Taylor experiments, but several new and surprising features, such as the coupling between pairs of cells, have been uncovered.

Bifurcation phenomena in Taylor-Couette flow in a very short annulus

We present the results of an experimental and numerical investigation into Taylor-Couette flow with gap-length to width ratios (Γ = l / d ) ranging from 0.3 to 1.4. Laser-Doppler-velocimetry is used to obtain quantitative information on the bifurcation set experimentally, and novel flow phenomena are uncovered. These results are compared with those obtained using numerical bifurcation techniques applied to a finite-element discretization of the Navier-Stokes equations. In general, the agreement is good and most of the observations are satisfactorily explained.

Finite-amplitude thresholds for transition in pipe flow

We report the results of an experimental study of the finite-amplitude thresholds for transition to turbulence in a constant mass flux pipe flow. The flow was perturbed using small impulsive jets and push-pull disturbances from holes in the pipe wall. The flux of the disturbance is used to define an amplitude for the perturbation and the critical value required to cause transition scales in proportion to Re -1 for jets. In this case, the transition is catastrophic and the scaling suggests a simple balance between inertia and viscosity. On the other hand, the threshold scales as Re- 1.3 or Re- 1.5 for push-pull disturbances with the precise value depending on the orientation of the perturbation. Further, the amplitudes required to cause transition are typically an order of magnitude smaller than for jets. When the push-pull perturbation was applied in the oblique direction, streaks and hairpin vortices appeared during the growth phase of the disturbance. The scaling of the threshold and the growth of structures are both consistent with ideas associated with temporary algebraic growth.

Magnetohydrodynamic convection in molten gallium

We present the results of an experimental and numerical study of the effects of a steady magnetic field on sidewall convection in molten gallium. The magnetic field is applied in a direction which is orthogonal to the main flow which reduces the convection and good agreement is found for the scaling of this effect with the relevant parameters. Moreover, qualitatively similar changes in the structure of the bulk of the flow are observed in the experiment and the numerical simulations. In particular, the flow is restricted to two dimensions by the magnetic field, but it remains different to that found in two-dimensional free convection calculations. We also show that oscillations found at even greater temperature gradients can be suppressed by the magnetic field.

Three-dimensional free convection in molten gallium

Convective flow of molten gallium is studied in a small-aspect-ratio rectangular, dierentially heated enclosure. The three-dimensional nature of the steady flow is clearly demonstrated by quantitative comparison between experimental temperature measurements, which give an indication of the strength of the convective flow, and the results of numerical simulations. The three-dimensional flow structure is characterized by cross-flows which are an order of magnitude smaller than the main circulation, and spread from the endwall regions to the entire enclosure when the Grashof number is increased beyond Gr =1 0 4 . The mergence of these eects in the centre of the enclosure leads to a complex central divergent flow structure which underpins the observed transition to oscillatory convection.

Free convection in liquid gallium

Free convection in liquid metals is of significant practical interest to the crystal-growing community since the adverse effects of convective instabilities in the melt phase can be frozen into the solid product. Here, we present the results of a combined numerical and experimental study of steady convective flows in a sample of liquid gallium which is heated at one end and cooled at the other. Experimental measurements of temperature distributions in the flow are compared with the standard Hadley-cell solution and with the numerical results obtained from a two-dimensional model. Excellent quantitative agreement is found between all three for low Grashof numbers but a systematic divergence between the results is seen as this parameter is increased.

Granular segregation as a critical phenomenon

We present the results of an experimental study of patterned segregation in a horizontally shaken shallow layer of a binary mixture of dry particles. An order parameter for the segregated domains is defined and the effect of the variation of the combined filling fraction, C, of the mixture on the observed pattern formation is systematically studied. We find that there is a critical event associated with the onset of segregation, at C(c)=0.647+/-0.049, which has the characteristics of a continuous phase transition, including critical slowing down.