Biomedical subjects

Stephen W Morris

Publications and source records attributed to Stephen W Morris.

7 recordsLinked to original sources

PubMed2006

Experimental investigation of the scaling of columnar joints.

Columnar jointing is a fracture pattern common in igneous rocks in which cracks self-organize into a roughly hexagonal arrangement, leaving behind an ordered colonnade. We report observations of columnar jointing in a laboratory analog system, desiccated corn starch slurries. Using measurements of moisture density, evaporation rates, and fracture advance rates as evidence, we suggest that an advective-diffusive system is responsible for the rough scaling behavior of columnar joints. This theory explains the order of magnitude difference in scales between jointing in lavas and in starches. We investigated the scaling of average columnar cross-sectional areas due to the evaporation rate, the analog of the cooling rate of igneous columnar joints. We measured column areas in experiments where the evaporation rate depended on lamp height and time, in experiments where the evaporation rate was fixed using feedback methods, and in experiments where gelatin was added to vary the rheology of the starch. Our results suggest that the column area at a particular depth is related to both the current conditions, and hysteretically to the geometry of the pattern at previous depths. We argue that there exists a range of stable column scales allowed for any particular evaporation rate.

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PubMed2005

Charge transport scaling in turbulent electroconvection.

We describe a local-power-law scaling theory for the mean dimensionless electric current Nu in turbulent electroconvection. The experimental system consists of a weakly conducting, submicron-thick liquid-crystal film supported in the annulus between concentric circular electrodes. It is driven into electroconvection by an applied voltage between its inner and outer edges. At sufficiently large voltage differences, the flow is unsteady and electric charge is turbulently transported between the electrodes. Our theoretical development, which closely parallels the Grossmann-Lohse model for turbulent thermal convection, predicts the local-power law Nu approximately F(gamma)R(gamma)P(delta). R and P are dimensionless numbers that are similar to the Rayleigh and Prandtl numbers of thermal convection, respectively. The dimensionless function F(gamma), which is specified by the model, describes the dependence of Nu on the aspect ratio gamma. We find that measurements of Nu are consistent with the theoretical model.

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PubMed2005

Codimension-two points in annular electroconvection as a function of aspect ratio.

We rigorously derive from first principles the generic Landau amplitude equation that describes the primary bifurcation in electrically driven convection. Our model accurately represents the experimental system: a weakly conducting, submicron thick liquid crystal film suspended between concentric circular electrodes and driven by an applied voltage between its inner and outer edges. We explicitly calculate the coefficient g of the leading cubic nonlinearity and systematically study its dependence on the system's geometrical and material parameters. The radius ratio alpha quantifies the film's geometry while a dimensionless number P , similar to the Prandtl number, fixes the ratio of the fluid's electrical and viscous relaxation times. Our calculations show that for fixed alpha, g is a decreasing function of P , as P becomes smaller, and is nearly constant for P> or =1 . As P-->0, g-->infinity. We find that g is a nontrivial and discontinuous function of alpha. We show that the discontinuities occur at codimension-two points that are accessed by varying alpha.

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PubMed2005

Buoyant plumes and vortex rings in an autocatalytic chemical reaction.

Buoyant plumes, evolving free of boundary constraints, may develop well-defined mushroom-shaped heads. In conventional plumes, overturning flow in the head entrains less buoyant fluid from the surroundings as the head rises, robbing the plume of its driving force. We consider here a new type of plume in which the source of buoyancy is an autocatalytic chemical reaction. The reaction occurs at a sharp front which separates reactants from less dense products. In this type of autocatalytic plume, entrainment assists the reaction, producing new buoyancy which fuels an accelerating plume head. When the head has grown to a critical size, it detaches from the upwelling conduit, forming an accelerating, buoyant vortex ring. A second-generation head then develops at the point of detachment. Multiple generations of autocatalytic vortex rings can detach from a single triggering event.

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PubMed2005

Subdiffusive axial transport of granular materials in a long drum mixer.

Granular mixtures segregate radially by size when tumbled in a partially filled horizontal drum. The smaller component moves toward the axis of rotation and forms a buried core, which then splits into axial bands. Models have generally assumed that the axial segregation is opposed by diffusion. Using narrow pulses of the smaller component as initial conditions, we have characterized axial transport in the core. We find that the axial advance of the segregated core is well described by a self-similar concentration profile whose width scales as talpha, with alpha approximately 0.3<1/2. Thus, the process is subdiffusive rather than diffusive as previously assumed. We compare our results to two one-dimensional model equations which contain self-similarity and subdiffusion: a linear fractional diffusion model and the nonlinear porous medium equation.

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PubMed2004

Aspect-ratio dependence of charge transport in turbulent electroconvection.

We present measurements of the normalized charge transport or Nusselt number Nu as a function of the aspect ratio Gamma for turbulent convection in an electrically driven film. In analogy with turbulent Rayleigh-Bénard convection, we develop the relevant theoretical framework in which we discuss the local power-law scaling of Nu with a dimensionless electrical forcing parameter R. For these experiments where 10(4) less, similar R less, similar 2 x 10(5) we find that Nu approximately F(Gamma)Rgamma with either gamma=0.26 (+/-0.02) or gamma=0.20 (+/-0.03), in excellent agreement with the theoretical predictions of gamma=1/4 and 1/5. Our measurements of the aspect-ratio dependence of Nu for 0.3</=Gamma</=17 compares favorably with the function F(Gamma) from the scaling theory.

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PubMed2002

Sequential bifurcations in sheared annular electroconvection.

A sequence of bifurcations is studied in a one-dimensional pattern forming system subject to the variation of two experimental control parameters: a dimensionless electrical forcing number R and a shear Reynolds number Re. The pattern is an azimuthally periodic array of traveling vortices with integer mode number m. Varying R and Re permits the passage through several codimension-two (CoD2) points. We find that the coefficients of the nonlinear terms in a generic Landau equation for the primary bifurcation are discontinuous at the CoD2 points. Further, we map the stability boundaries in the space of the two parameters by studying the subcritical secondary bifurcations in which m-->m+1 when R is increased at constant Re.

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