David G. Thomas

Transport characteristics of suspension: VIII. A note on the viscosity of Newtonian suspensions of uniform spherical particles

Abstract A critical analysis was made of the extensive experimental data on the relative viscosity of suspensions of uniform spherical particles. By appropriate extrapolation techniques, non-Newtonian, inertial, and nonhomogeneous suspension effects were minimized. As a result, the scatter of the data was reduced from ±75% to ±13% at a volume fraction solids of 0.50. The coefficients of different power series relating relative viscosity and volume fraction solids were determined using a nonlinear least squares procedure. It was shown that a new expression containing three terms of a power series with coefficients determined from previous theoretical analyses and an exponential term with two adjustable constants fit the data as well as a power series with six terms, either three or four of which were adjustable constants with the remaining coefficients being theoretical values.

Interaction of Vortex Streets

Vortex street eddies shed from multiple cylinders located one behind the other in the plane of flow were observed to interact in a very complex fashion. Contraction, expansion, cancellation, and coalescence of vortices occurred for different values of cylinder separation and Reynolds number. The results appear to have important implications both for turbulence promotion during heat or mass transfer and for theoretical interpretation of vortex street phenomena.

The role of turbulence promoters in hyperfiltration plant optimization

Abstract Numerical calculations were performed to obtain process parameters for hyperfiltration with membranes having characteristics similar to cellulose acetate. The concentration polarization and friction loss equations used in the calculation were modified to include provision for a wide range of turbulence promoter characteristics. The characteristics of the turbulence promoters were based on potential performance curves derived from an extensive literature survey. The presence of turbulence promoters causes marked reduction of optimum entrance velocity and tube length. As a result, the channel pressure drop for tubes with turbulence promoters is always less under optimum conditions than the value for tubes with no promoters provided the friction factor with promoters is less than 100 times the value with no promoters. While none of these affect costs greatly, there is direct cost advantage for turbulence promoters which minimize fouling, thereby giving higher average fluxes for longer periods of time. Only where the membrane is strained to produce water of required quality is there a direct effect of turbulence promoters on product water cost because of this beneficial effect on concentration polarization.

Effect of high axial velocity on performance of cellulose acetate hyperfiltration membranes

Abstract The effect of axial velocity on performance characteristics of a commercial cellulose acetate membrane was determined in a parallel plate test channel over a 270-fold velocity range, from 0.09 to 24 ft/sec and an applied pressure range of 200 to 1200 psig. Feed was demineralized water or untreated river water spiked with MgCl 2 to give solution concentrations of 0.04 to 0.08 M . At 800 psig system pressure and 24 ft/sec circulation velocity, intrinsic rejection was ∼ 97% and permeability was 0.6 gal/day · ft 2 · atm with demineralized water feed spiked with MgCl 2 . Substantially no flux decline was observed with demineralized water feed in a 93-hour run at 24 ft/sec. Even with untreated river water feed containing 10–100 ppm suspended solids, flux decline was relatively modest (a slope of -0.03 on a plot of log flux vs . log time) at a circulation velocity of 24 ft/sec. Reduction of circulation velocity to 1.64 ft/sec resulted in a marked decline in flux with time.

Membrane Fouling Part IV. Parallel operation of four tubular hyperfiltration modules at different velocities with feeds of high fouling potential

Abstract When tubular hyperfiltration modules were operated with the same river water feed, but with different feed velocities, the rate of flux decline varied with feed velocity as, (Δ log flux/Δ log time) ∝ u 1 2 , provided u was less than some threshold velocity. Operation at feed velocities in excess of the threshold velocity prevented accumulation of particulates on the membrane and the rate of flux decline was significantly less than predicted by extrapolation based on the half-power relationship.

Engineering development of hyperfiltration with dynamic membranes Part I. Process and module development

Abstract Techniques were developed for precoating ceramic tubes with a 0.006-in. layer of fine particle size ZrO 2 powder; dynamic membranes formed on the precoated porous surfaces possessed fluxes of 95 to 100 gal/ft 2 ·day and rejections of 85 to 90% for 0.05 M NaCl compared with values of 20 gal/ft 2 ·day and 40 to 60% obtained with nonprecoated tubes. These ceramic tubes were then incorporated in a seven-tube bundle with a total area of 6 ft 2 . A module consisted of two of these bundles fitted into a pressure housing fabricated from standard 2-in. pipe; this module then possessed a flux density of 4453 gal/day per cubic ft. compared with values of 1350 and 3000 gal/day per cubic ft for hollow fine fiber and spiral wrap modules, respectively (1) . Since 1971 the flux density for hollow fine fibers has been 13,000–18,000. Similarly, the flux of membranes utilized in spiral wound or tubular systems has also increased very significantly, but not by an order of magnitude. The procedure developed for forming dynamic membranes on the ceramic tube modules consists of the following steps: 1. Adjust the pH of the 0.05 M NaCl feed solution to pH = 4 and add sufficient hydrous zirconium oxide to give a concentration of 50 mg/liter. 2. Within one-half to one hour after introduction of the feed to the system at a pressure of 1000 psig and a velocity of 30 ft/sec, either the flux will be of the order of 1000 gal/ft 2 ·day or the rejection will be 35 %; whichever value occurs first is not critical. At that time adjust the pH of the flowing stream to 2 and add sufficient PAA to give a concentration of 50 mg/liter. 3. Approximately one hour after addition of the PAA begin neutralization of the flowing stream with NaOH solution. The pH should be increased in steps over an interval of one to two hours until the circulating stream is near neutral. At this time the dynamic membrane should have a rejection of 85 to 90% and a flux of 95 to 100 gal/ft 2 ·day when the feed is 0.05 M NaCl. The velocity can then be reduced to 15 ft/sec with little loss in flux or rejection.

Engineering development of hyperfiltration with dynamic membranes Part III. The pilot plant and its performance with brackish water feed

Abstract A dynamic membrane pilot plant was constructed that consisted of a 200-gal feed tank, a 100-gal/min 1000 psig triplex piston pump, a heat exchanger (required only for the recirculating mode of operation), a pH control system, and a rack of eight interconnected (in series) modules fabricated from 2-in. pipe. Each pipe section contains two seven-rod clusters of ceramic tubes giving a total area of 40 ft 2 for membrane formation. Valves are provided to permit any of the eight sections to be valved out of the flow stream without shutting down the plant. After initial formation of a dynamic Zr(IV)-PAA membrane on a full load of bundles in the pilot plant, feed was switched to pretreated simulated Roswell water (∼2000 ppm TDS). At an axial inlet velocity of 30 ft/sec, pressure through the plant decreased from 1000 psig at the inlet to 400 psig at the outlet. Initially, rejection of sulfate decreased from 99% at the pilot plant inlet to 92% at the outlet with an average of 96.5% while rejection of chloride decreased from 93% at the inlet to 83% at the outlet with an average of 89.5%. Flux was 105 gal/ft 2 ·day. After one month of operation, the membrane was removed in situ by acid (pH = 2) and base (pH = 12) washing. A new membrane was then formed at an axial velocity of 15 ft/sec; with an inlet pressure of 1000 psig, the outlet pressure was 825 psig. After switching to pretreated simulated Roswell feed, sulfate rejection was ∼99% and chloride rejection was 91 % at a flux of 93 gal/ft 2 ·day; there was little variation of flux or rejection from one end of the plant to the other.

Prospects for further improvement in enhanced heat transfer surfaces

Abstract The current state-of-the-art of commercial enhanced surfaces for thin film evaporation and condensation on vertical tubes is exemplified by fluted tubes having overall heat-transfer coefficients of 1300 to 2000 Btu/hr ft2 °F at atmospheric pressure. Experimental surfaces have been tested which gave overall coefficients up to 5000 Btu/hr ft2 °F. Oxidative fouling factors as small as 10-4 (Btu/hr ft2 °F)-1 have been reported for fluted enhanced surfaces. It is hypothesized that such small fouling factors occur because high shear forces developed in the thin-film region prevent formation of all except very thin oxide films. Limited data also suggest that the fouling resistance may decrease with increasing heat-transfer coefficient (i.e., with increased shear rate); if true this would provide an important incentive for development of improved enhanced heat transfer surfaces. Although the mechanism responsible for high performance on the condensing side of fluted or finned tubes seems relatively well understood and upper limits can be estimated, the mechanism on the evaporating side seems to be much more complicated. Consequently an upper limit for heat transfer rates on the evaporative side was estimated assuming that the upper limit occurred when the water film thickness was just sufficient to prevent dry spot formation. Assuming a metal wall resistance of 0.00004 and upper limits of 18,000 and 14,200 Btu/hr ft2 °F on the condensing and evaporative sides, respectively, gives an estimated upper limit on performance of enhanced surfaces of ∼6000 Btu/hr ft2 °F.

Periodic Phenomena Observed with Spherical Particles in Horizontal Pipes

A thin layer of spherical particles resting on the bottom of a round pipe was observed to form into essentially equally spaced clumps or islands at fluid velocities only slightly greater than those required to initiate particle movement. This phenomenon appeared to be similar to dune formation in open channels since the ratio of the square of the stream velocity, U, and the product of the gravitational constant, gL, and the island wavelength, λ, was correlated by the same function of island height and velocity, particle diameter, and fluid depth regardless of whether the flow was through a closed conduit or an open channel.

Engineering development of hyperfiltration with dynamic membranes Part II. Brackish water pretreatment pilot plant

Abstract Exploratory studies showed that feed hardness less than 10 ppm as CaCO 3 was required to maintain high fluxes (∼100 gal/ft 2 ·day) from a dynamically formed Zr(IV)-PAA membrane. Consequently, a softening pilot plant was developed based on conventional lime-soda softening chemistry: however, because of the small scale, NaOH was substituted for lime and CO 2 was substituted for soda. The pilot plant consisted of a stirred reaction tank, a mixer-settler, and a separate filtration system containing a holdup tank, a recirculating pump, and a cross-flow filter (16 ft of fire hose jacket with a total filtration area of 4.5 ft 2 ). Concentrated solids (18% by wt) were discharged from the mixer-settler. It was discovered that by precoating the cross-flow filter with precipitated CaCO 3 , the adverse effects of Mg(OH) 2 on the rate of filtration could be ameliorated. In one test of ∼300 hr duration the product from the cross-flow filter had a hardness of less than 10 ppm as CaCO 3 with an average flux of ∼500 gal/ft 2 · day when the axial velocity was 16 ft/sec and the average pressure was 32 psig.