Simplified models of the symmetric single-pass parallel-plate counterflow heat exchanger: a tutorial.

The heat exchanger is important in practical thermal processes, especially those of (i) the molten-salt storage schemes, (ii) compressed air energy storage schemes and (iii) other load-shifting thermal storage presumed to undergird a Smart Grid. Such devices, although central to the utilization of energy from sustainable (but intermittent) renewable sources, will be unfamiliar to many scientists, who nevertheless need a working knowledge of them. This tutorial paper provides a largely self-contained conceptual introduction for such persons. It begins by modelling a novel quantized exchanger, impractical as a device, but useful for comprehending the underlying thermophysics. It then reviews the one-dimensional steady-state idealization which demonstrates that effectiveness of heat transfer increases monotonically with (device length)/(device throughput). Next, it presents a two-dimensional steady-state idealization for plug flow and from it derives a novel formula for effectiveness of transfer; this formula is then shown to agree well with a finite-difference time-domain solution of the two-dimensional idealization under Hagen-Poiseuille flow. These results are consistent with a conclusion that effectiveness of heat exchange can approach unity, but may involve unwelcome trade-offs among device cost, size and throughput.

SEORious business: structural proteins in sieve tubes and their involvement in sieve element occlusion.

The phloem provides a network of sieve tubes for long-distance translocation of photosynthates. For over a century, structural proteins in sieve tubes have presented a conundrum since they presumably increase the hydraulic resistance of the tubes while no potential function other than sieve tube or wound sealing in the case of injury has been suggested. Here we summarize and critically evaluate current speculations regarding the roles of these proteins. Our understanding suffers from the suggestive power of images; what looks like a sieve tube plug on micrographs may not actually impede translocation very much. Recent reports of an involvement of SEOR (sieve element occlusion-related) proteins, a class of P-proteins, in the sealing of injured sieve tubes are inconclusive; various lines of evidence suggest that, in neither intact nor injured plants, are SEORs determinative of translocation stoppage. Similarly, the popular notion that P-proteins serve in the defence against phloem sap-feeding insects is unsupported by empirical facts; it is conceivable that in functional sieve tubes, aphids actually could benefit from inducing a plug. The idea that rising cytosolic Ca(2+) generally triggers sieve tube blockage by P-proteins appears widely accepted, despite lacking experimental support. Even in forisomes, P-protein assemblages restricted to one single plant family and the only Ca(2+)-responsive P-proteins known, the available evidence does not unequivocally suggest that plug formation is the cause rather than a consequence of translocation stoppage. We conclude that the physiological roles of structural P-proteins remain elusive, and that in vivo studies of their dynamics in continuous sieve tube networks combined with flow velocity measurements will be required to (hopefully) resolve this scientific roadblock.

Münch without tears: a steady-state Münch-like model of phloem so simplified that it requires only algebra to predict the speed of translocation.

The pressure-driven mass-flow hypothesis of phloem translocation associated with Ernst Münch has become hegemonic and has been mathematically modelled in many, many different fashions - but not, apparently, in one chosen so that it gives simple algebraic predictions of (i) the speed of translocation; (ii) the saccharide concentration at the source; and (iii) the pressure offset due to translocation. To overcome this deficit, the problem was drastically simplified by assuming that: (i) radial variations could be neglected; (ii) osmotic water uptake was restricted to sink and source regions of negligible thickness; (iii) there was a constant rate of saccharide loading at the source; and (iv) the sink strength was sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it becomes unimportant. The resulting system of quadratic algebraic equations was then solved for the translocation speed, which was shown to vary as the square-root of the loading rate. Also found were the offset of the intra-tube hydrostatic pressure and the sap saccharide concentration at the source, which, likewise, vary as the square-root of the loading rate.

Electromagnetic and thermal evaluation of an applicator specialized to permit high-resolution non-perturbing optical evaluation of cells being irradiated in the W-band.

To permit epi-illuminated, high-resolution optical microscopy of cells in monolayer culture during unperturbed W-band (75-110 GHz) irradiation, a new class of applicator has been developed based upon WR10 rectangular waveguide components: the cells are normally plated onto the underside of a coverslip which is then placed against the under side of a waveguide flange and receives a roughly circular exposure pattern, with the +/-1 dB central spot roughly 1 mm in diameter. Constructed and tested with 94 GHz millimeter waves, water-immersion optics, and free-convection cooling, the applicator works robustly and permits SARs at the cell layer as high as 4500 W/kg before the steady-state temperature rise at the cell layer exceeds 0.5 K.

A simplest steady-state Munch-like model of phloem translocation, with source and pathway and sink.

In the 80 years since its introduction by Münch, the pressure-driven mass-flow model of phloem translocation has become hegemonic, and has been mathematically modelled in many different fashions but not, to our knowledge, by one that incorporated the equations of hydrodynamics with those of osmosis and slice-source and slice-sink boundary conditions to yield a system that admits of an analytical steady-state solution for the sap velocity in a single sieve tube. To overcome this situation, we drastically simplified the problem by: (i) justifying a low Peclet number idealisation in which transverse variations could be neglected; (ii) justifying a low viscosity idealisation in which axial pressure drops could be neglected; and (iii) assuming a sink of strength sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it became unimportant. The resulting ordinary nonlinear second-order differential equation in sap velocity and axial position was of a generalised Liénard form with a single forcing parameter; and this is reason enough for the lack of a known analytic solution. However, since the forcing parameter was very large, it was possible to deduce approximate second-order solutions for behavior in the source, sink and transport regions: the sap velocity is zero at the slice-source, climbs with exponential rapidity to a plateau, maintains this plateau over most of the sieve tube, and then drops with exponential rapidity to zero at the slice-sink.

Modelling the swelling assay for aquaporin expression.

The standard method of assaying the water transporting capability of a putative aquaporin-like entity is to express that entity in a cell of normally low water permeability and to measure the enhancement of swelling when the cell is subjected to hypo-osmotic shock. Because of the heterogeneous nature of cytoplasm, the interplay of advection and diffusion, and the coupling of internal and external media via a semipermeable elastic membrane, even simplified mathematical models can be difficult to resolve. This class of diffusion problem seems to have been but little studied. In this paper, the cell and its surround are at first modelled as perfectly-mixed phases separated by an ideal semipermeable membrane with vanishingly small elastic modulus; and the time course of swelling is evaluated analytically. This time course was found to be non-exponential, but such unexpected behavior should not seriously affect the traditional interpretation of experimental results because its short time limit is linear as in the traditional model; and normally only short time data are available. Next, the simplifications of diffusive equilibrium and of vanishing elastic modulus are examined. It is shown that diffusive equilibrium will be true only when diffusive movement of osmolyte is rather faster than the swelling and that this will probably not be the case for many assays. On the other hand, it should often be possible to neglect the elastic modulus. Finally, a more comprehensive model is formulated for a spherical cell in a hypotonic medium and the swelling behavior described in terms as a moving boundary problem (This type of moving boundary problem is often called a Stefan problem [ http://en.wikipedia.org/wiki/Stefan_problem ]) in which two phases containing diffusive osmolyte are separated by a weakly-elastic ideally-semipermeable membrane, the water flux across which is linear in the osmolality difference across it. This type of behavior was evaluated numerically by finite-difference time-domain techniques and found to be qualitatively similar to that of the perfect-mixing simplification.

Anisotropic contraction in forisomes: simple models won't fit.

Forisomes are ATP-independent, Ca(2+)-driven contractile protein bodies acting as reversible valves in the phloem of plants of the legume family. Forisome contraction is anisotropic, as shrinkage in length is associated with radial expansion and vice versa. To test the hypothesis that changes in length and width are causally related, we monitored Ca(2+)- and pH-dependent deformations in the exceptionally large forisomes of Canavalia gladiata by high-speed photography, and computed time-courses of derived geometric parameters (including volume and surface area). Soybean forisomes, which in the resting state resemble those of Canavalia geometrically but have less than 2% of the volume, were also studied to identify size effects. Calcium induced sixfold volume increases in forisomes of both species; in soybean, responses were completed in 0.15 s, compared to about 0.5 s required for a rapid response in Canavalia followed by slow swelling for several minutes. This size-dependent behavior supports the idea that forisome contractility might rest on similar mechanisms as those of polyelectrolyte gels, a class of artificial "smart" materials. In both species, time-courses of forisome length and diameter were variable and lacked correlation, arguing against a simple causal relationship between changes in length and width. Moreover, changes in the geometry of soybean forisomes differed qualitatively between Ca(2+)- and pH-responses, suggesting that divalent cations and protons target different sites on the forisome proteins.

Laticifers and secretory ducts: two other tube systems in plants.

The plant kingdom has elaborated several conducting systems. Three are primarily for mass transport: the aerenchyma (for gas exchange in submerged parts), the phloem (for exchange of nutrients within the plant), and the xylem (largely for transport of water from soil to transpiring leaves). Two others are believed to be primarily defensive and to store under pressure aversive contents which they exude when punctured: the laticifer and the secretory duct. This review provides for the latter two systems the highlights of what is known about their general physiology and ecophysiology but not their metabolism and their molecular biology. It is argued that, given the importance of laticifers and secretory ducts to plant defense against insect herbivory, these structures are under-investigated and deserve more intensive study.

Elastic properties of the forisome.

Forisomes are elongate Ca2+-responsive contractile protein bodies and act as flow blocking gates within the phloem of legumes. Because an understanding of their mechanical properties in vitro underpins understanding of their physiology in vivo, we undertook, using a microcantilever method, microscopic tensile tests (incremental stress-relaxation measurements) on forisomes from Canavalia gladiata (Jacq.) DC Akanata Mame and Vicia faba L. Witkiem Major. Viscoelastic properties of forisomes in their longitudinal direction were investigated before and after Ca2+-induced contraction, but in the radial direction only before contraction. Forisomes showed mechanical properties typical of a biological material with a unidirectional fibrous structure, i.e. the modulus of elasticity in the direction of their fibers is much greater than in the radial direction. Creep data were collected in all tensile tests and fit with a three parameter viscoelastic model. The pre-contraction longitudinal elastic moduli of the forisomes were not differentiable between the two species (V. faba, 660 ± 360 kPa; C. gladiata, 600 ± 360 kPa). Both species showed a direction-dependent mechanical response: the elastic modulus was dramatically smaller in the radial direction than in the longitudinal direction, suggesting a weak protein cross-linking amongst longitudinal protein fibers. Activation of forisomes decreased forisome stiffness longitudinally, as evidenced by the loss of toe-region in the stress strain curve, suggesting that the forisome may have dispersed or disordered its protein structure in a controlled fashion. Contractile forces generated by single forisomes undergoing activation were also measured for V. faba (510 ± 390 nN) and C. gladiata (570 ± 310 nN).

Corrigendum to: Elastic properties of the forisome.

Forisomes are elongate Ca2+-responsive contractile protein bodies and act as flow blocking gates within the phloem of legumes. Because an understanding of their mechanical properties in vitro underpins understanding of their physiology in vivo, we undertook, using a microcantilever method, microscopic tensile tests (incremental stress-relaxation measurements) on forisomes from Canavalia gladiata (Jacq.) DC Akanata Mame and Vicia faba L. Witkiem Major. Viscoelastic properties of forisomes in their longitudinal direction were investigated before and after Ca2+-induced contraction, but in the radial direction only before contraction. Forisomes showed mechanical properties typical of a biological material with a unidirectional fibrous structure, i.e. the modulus of elasticity in the direction of their fibers is much greater than in the radial direction. Creep data were collected in all tensile tests and fit with a three parameter viscoelastic model. The pre-contraction longitudinal elastic moduli of the forisomes were not differentiable between the two species (V. faba, 660±360kPa; C. gladiata, 600±360kPa). Both species showed a direction-dependent mechanical response: the elastic modulus was dramatically smaller in the radial direction than in the longitudinal direction, suggesting a weak protein cross-linking amongst longitudinal protein fibers. Activation of forisomes decreased forisome stiffness longitudinally, as evidenced by the loss of toe-region in the stress strain curve, suggesting that the forisome may have dispersed or disordered its protein structure in a controlled fashion. Contractile forces generated by single forisomes undergoing activation were also measured for V. faba (510±390nN) and C. gladiata (570±310nN).

Electromagnetic and thermal characterization of an UHF-applicator for concurrent irradiation and high resolution non-perturbing optical microscopy of cells.

To permit trans-illuminated, high-resolution optical microscopy during unperturbed ultrahigh frequency (UHF) irradiation, a novel new class of applicator has been designed based upon a shielded-pair transmission line. As constructed and tested with water-immersion optics and air cooling, the applicator works most robustly over 700-1100 MHz and permits SARs at the cell layer as high as 50 W/kg before the steady state temperature rise at the cell-layer exceeds 0.5 K.

Absorption by a moving spherical organelle in a heterogeneous cytoplasm: implications for the role of trafficking in a symplast.

An organelle which absorbs (or secretes) a particular factor will find its mass transfer rate diffusion-limited if it is stationary with respect to its ambient cytoplasm; but organellar motion will raise that limit as a non-decreasing function of the Peclet number P. It is shown analytically that (i) no Whitehead paradox need be encountered in the creeping flow regime and (ii) the flux of the factor will be an even function of the Peclet number, P. By a novel analytic solution method, the flux is shown numerically to increase as P2 for P < or = 1. For P > or = 10, a quasi-planar approximating geometry yields analytically a flux which increases as P1/3. These two solutions overlap smoothly in the range 1 < or = P > or = 10. For P approximately 1, convection should increase the mass flux by roughly 100%.

Measurement of DNA damage and apoptosis in Molt-4 cells after in vitro exposure to radiofrequency radiation.

To determine whether exposure to radiofrequency (RF) radiation can induce DNA damage or apoptosis, Molt-4 T lymphoblastoid cells were exposed with RF fields at frequencies and modulations of the type used by wireless communication devices. Four types of frequency/modulation forms were studied: 847.74 MHz code-division multiple-access (CDMA), 835.62 MHz frequency-division multiple-access (FDMA), 813.56 MHz iDEN(R) (iDEN), and 836.55 MHz time-division multiple-access (TDMA). Exponentially growing cells were exposed to RF radiation for periods up to 24 h using a radial transmission line (RTL) exposure system. The specific absorption rates used were 3.2 W/kg for CDMA and FDMA, 2.4 or 24 mW/kg for iDEN, and 2.6 or 26 mW/kg for TDMA. The temperature in the RTLs was maintained at 37 degrees C +/- 0.3 degrees C. DNA damage was measured using the single-cell gel electrophoresis assay. The annexin V affinity assay was used to detect apoptosis. No statistically significant difference in the level of DNA damage or apoptosis was observed between sham-treated cells and cells exposed to RF radiation for any frequency, modulation or exposure time. Our results show that exposure of Molt-4 cells to CDMA, FDMA, iDEN or TDMA modulated RF radiation does not induce alterations in level of DNA damage or induce apoptosis.

The effect of chronic exposure to 835.62 MHz FDMA or 847.74 MHz CDMA radiofrequency radiation on the incidence of spontaneous tumors in rats.

This study was designed to determine whether chronic exposure to radiofrequency (RF) radiation from cellular phones increased the incidence of spontaneous tumors in F344 rats. Eighty male and 80 female rats were randomly placed in each of three irradiation groups. The sham group received no irradiation; the Frequency Division Multiple Access (FDMA) group was exposed to 835.62 MHz FDMA RF radiation; and the Code Division Multiple Access (CDMA) group was exposed to 847.74 MHz CDMA RF radiation. Rats were irradiated 4 h per day, 5 days per week over 2 years. The nominal time-averaged specific absorption rate (SAR) in the brain for the irradiated animals was 0.85 +/- 0.34 W/kg (mean +/- SD) per time-averaged watt of antenna power. Antennas were driven with a time-averaged power of 1.50 +/- 0.25 W (range). That is, the nominal time-averaged brain SAR was 1.3 +/- 0.5 W/kg (mean +/- SD). This number was an average from several measurement locations inside the brain, and it takes into account changes in animal weight and head position during irradiation. All major organs were evaluated grossly and histologically. The number of tumors, tumor types and incidence of hyperplasia for each organ were recorded. There were no significant differences among final body weights or survival days for either males or females in any group. No significant differences were found between treated and sham-exposed animals for any tumor in any organ. We conclude that chronic exposure to 835.62 MHz FDMA or 847.74 MHz CDMA RF radiation had no significant effect on the incidence of spontaneous tumors in F344 rats.

The riddle of root pressure. II. Root exudation at extreme osmolalities.

To test the predictions of a recent theory of root pressure and exudation, exudation from detopped tomato seedlings was studied. Experimental findings were generally in qualitative accord with the theory. Two confirmed predictions are of particular interest. First, when a normally exuding stump was challenged by having its roots exposed to concentrated osmolyte, the exudation rate dropped quickly to zero but later often recovered to a higher level. Second, when exudation from a plant challenged by concentrated osmolyte did not recover, flushing the soil solution away with tap water usually resulted in a sudden resumption of exudation followed by a rapid falloff.