Applied Pressure Difference Research Articles

Mathematical optimisation of laminar forced convection heat transfer through a vascularised solid with square channels

This paper presents a three-dimensional geometric optimisation of cooling channels in forced convection of a vascularised material with the localised self-cooling property subjected to a heat flux. A square configuration was studied with different porosities. Analytical and numerical solutions were provided. The geometrical configuration was optimised in such a way that the peak temperature was minimised at every point in the solid body. The optimisation was subject to the constraint of a fixed global volume of solid material, but the elemental volume was allowed to morph. The solid material was subject to a heat flux on one side and the cooling fluid was forced through the channels from the opposite direction with a specified pressure difference. The structure had three degrees of freedom as design variables: the elemental volume, channel hydraulic diameter and channel-to-channel spacing. A gradient-based optimisation algorithm was used to determine the optimal geometry that gave the lowest thermal resistance. This optimiser adequately handled the numerical objective function obtained from numerical simulations of the fluid flow and heat transfer. The numerical results obtained were in agreement with a theoretical formulation using scale analysis and the method of intersection of asymptotes. The results obtained show that as the pressure difference increases, the minimised thermal resistance decreases. The results also show the behaviour of the applied pressure difference on the optimised geometry. The use of the optimiser made the numerical results to be more robust with respect to the optimum internal configurations of the flow systems and the dimensionless pressure difference.

Water transport through (7,7) carbon nanotubes of different lengths using molecular dynamics

Non-equilibrium molecular dynamics simulations are used to investigate water transport through (7,7) CNTs, examining how changing the CNT length affects the internal flow dynamics. Pressure-driven water flow through CNT lengths ranging from 2.5 to 50 nm is simulated. We show that under the same applied pressure difference an increase in CNT length has a negligible effect on the resulting mass flow rate and fluid flow velocity. Flow enhancements over hydrodynamic expectations are directly proportional to the CNT length. Axial profiles of fluid properties demonstrate that entrance and exit effects are significant in the transport of water along CNTs. Large viscous losses in these entrance/exit regions lead into central “developed” regions in longer CNTs where the flow is effectively frictionless.

Vascularization for cooling and mechanical strength

In this paper we explore the use of vascular design that provides cooling and mechanical strength at the same time. We illustrate the concept with a circular plate vascularized with embedded channels. The cooling fluid enters to the plate from the center or from the rim, and leaves after it cools the plate down to an allowable temperature level. The vascular cooling channels also affect the mechanical strength of the plate. We simulated numerically the thermofluid and mechanical behavior for three different structures; radial, dendrites with one pairing level and dendrites with two pairing levels. We found that for a given set of conditions (applied pressure difference, coolant inlet position, and number of the cooling channels) there is one configuration that is best; however, there is no single configuration that is best for all conditions.

Analysis of Filtration Characteristics for Compressible Polycrystalline Particles by Partial Least Squares Regression

Crystal size and morphology have been varied by changing the initial supersaturation ratio and the temperature in reactive crystallization experiments. The influence of the chord length distribution, average cake porosity, and filtration pressure difference on the average cake resistance of polycrystalline particles of an industrially produced aromatic amine has been investigated by means of partial least squares (PLS) regression and sensitivity analysis. Analysis of the results has disclosed that wider chord length distributions as well as lower values of the measured average porosity lead to higher values for the average cake resistance. However, PLS regression and sensitivity analysis have identified the applied pressure difference itself as the most significant parameter influencing the magnitude of the cake resistance. This unexpected behavior is accounted for by compression of the filter cake occurring predominantly in small layers above the filter cloth characteristic for highly compressible cakes.

Three-dimensional multi-scale plate assembly for maximum heat transfer rate density

This paper extends the design concept for generating multi-scale structures in forced convection for a finite-size flow system to a three-dimensional heat-generating plate with the objectives of maximising heat transfer rate density, or the heat transfer rate per unit volume. The heat-generating plates, arranged in a stack form channels in which the fluids are forced through by an applied pressure difference. The first stage of this work consists of numerical simulation of the flow and heat transfer in a large number of flow configurations, to determine the optimum plate spacing, and the maximum heat transfer rate density. In the subsequent stages, shorter plates are inserted in the centers at adjacent (longer) plates in the entranced region were the boundary layer are thin and there is a core of unused fluid. The heat transfer density is further increased by progressively inserting another set of even shorter plates between the plates and then optimizing the whole structure. The resulting structure is an optimized multi-scale and multi channel structure with horizontal equidistant heated plates of decreasing lengths scales. Further more the effects of plate thickness and dimensionless pressure drop number on the multi-scale structure was investigated. The numerical results are found to be in good agreement with predicted analytical results.

Pressure-Driven Ionic Transport through Nanochannels with Inhomogenous Charge Distributions

The effect of spatially inhomogeneous fixed charge distributions on the pressure-driven transport of ions through cylindrical nanopores have been investigated theoretically by means of an approximate version of the Poisson-Nernst-Planck model that can be used with confidence for moderately charged nanopores with radius smaller than the Debye screening length of the system. Salt rejection rate has been computed as a function of the applied pressure difference for various one-dimensional (1D) unipolar charge distributions and has been compared with that obtained for a homogeneously charged nanochannel with an identical average volume charge density. The ion rejection capabilities of charged nanopores can be optimized by an appropriate distribution of the fixed charge concentration. When ions are forced to enter the nanopores by the end with the lowest fixed charged concentration, the salt rejection rate exhibits a nonmonotonous variation with the applied pressure. This phenomenon has been attributed to the influence of the inhomogeneous charge distribution on the electric field that arises spontaneously so as to maintain the electroneutrality within the nanopore.

Combustion of bulk density powder mixtures in a coflow of inert gas: 6*(Fe2O3 + 2Al) + 30% Al2O3 mixtures

Investigated was the combustion of bulk density (Fe2O3 + 2Al) + 30% Al2O3 mixtures in a coflow of inert gas (Ar) in the presence/absence of blowing agents (borax, baking soda) and applied pressure difference δP. The results have been rationalized in terms of the conduction-convection theory for combustion in heterogeneous systems.

Spontaneous and Forced Imbibition of Aqueous Wettability Altering Surfactant Solution into an Initially Oil-Wet Capillary

Unforced invasion of wettability-altering aqueous surfactant solutions into an initially oil-filled oil-wet capillary tube has been observed to take place very slowly, and because this system is an analogue for certain methods of improved oil recovery from naturally fractured oil-wet reservoirs, it is important to identify the rate-controlling processes. We used a model for the process published by Tiberg et al. ( Tiberg , F. , Zhmud , B. , Hallstensson , K. and Von Bahr , M. Phys. Chem. Chem. Phys. 2000 , 2 , 5189 - 5196 ) and modified it for forced imbibitions. We show that when applied pressure differences are not too large invasion rates are controlled at large times by the value of the bulk diffusion coefficient for surfactant in the aqueous phase and at early times by the resistance to transfer of surfactant from the oil-water meniscus onto the walls of the capillary. For realistic values of the bulk diffusion coefficient, invasion rates are indeed slow, as observed. The model also predicts that the oil-water-solid contact angle during unforced displacement is close to pi/2, and so, the displacement occurs in a state of near-neutral wettability with the rate of invasion controlled by the rate of surfactant diffusion rather than a balance between capillary forces and viscous resistance. Under forced conditions, the meniscus moves faster, but the same kinds of dynamical balances between the various processes as were found in the spontaneous case operate. Once the capillary threshold pressure for entry into the initial oil-wet tube is exceeded, the effect of pressure on velocity becomes more significant, there is not sufficient time for the surfactant molecules to transfer in great quantity from the meniscus to the solid surface, and wettability alteration is then no longer important.

Transient cooling response of smart vascular materials for self-cooling

Here we report the transient cooling performance of a body vascularized with tree-shaped channels supplied with coolant, which flows from one side of the body to the other. The vasculature consists of trees that alternate with upside down trees. Heat is generated volumetrically through the body at t=0. A time delay td separates the start of the flow of coolant from the start of heating. Three-dimensional simulations of conduction and convection in the solid-fluid composite show the formation and evolution of hot spots in the material. If the delay is not short enough, the maximum temperature of the body overshoots the maximum allowable level. The paper shows how to design the cooling delay time such that the hot-spot temperature does not exceed the safe level represented by the maximum temperature in the limit of steady state operation. The critical delay time is determined as a function of the applied pressure difference and the complexity of the dendritic flow architecture.

Combustion of bulk density powder mixtures in a coflow of inert gas: 4. Ti-Si and Zi-Al systems

Combustion of bulk density Ti-Si and Zi-Al mixtures an a coflow of argon was studied in the presence/absence of (1) applied pressure difference δP along the direction of wave propagation, (2) thermal treatment of green samples in vacuum, and (3) blowing agent (borax). The data on variation of the burning velocity U c were rationalized in terms of the convection-conduction combustion theory for heterogeneous condensed systems.

Synthesis of sodalite octahydrate zeolite-clay composite membrane and its use in separation of SDS

A simple two-step process for synthesis of sodalite octahydrate zeolite-clay composite, charged ultrafiltration membrane is described wherein the active layer is obtained by partial plugging of the pore-mouth of macroporous clay support with in situ grown zeolite particles. Dip-coating of zeolite synthesis solution at pH 12 is found to give higher deposition of zeolite on the clay support. Increase in amount of zeolite in the active layer obtained by repeated deposition of zeolite particles on clay-support is quantified using membrane potential measurements and it is found that four cycles of zeolite deposition gives optimum results. The membrane is characterized using SEM for surface morphology, XRD for zeolite characterization, water flux and separation of surfactant (SDS) above cmc concentration. SDS separation results show observed-rejection in the range of 10–45%. The observed-rejection is found to decrease with increase in the applied pressure difference and increase with increase in the surfactant concentration. The permeate flux is found to reduce significantly to about 0.2–0.46 times the pure water flux. The trend is similar to that reported in literature for separation of surfactant micelle by ultrafiltration membrane of pore size much larger than the size of surfactant micelle.

Aerodynamically assisted bio-jets: the development of a novel and direct non-electric field-driven methodology for engineering living organisms

We recently demonstrated the ability to use electrified jets under stable conditions for the generation of cell-bearing droplets to the formation of composite threads which are biologically active. Our studies established that processed cells were viable over several generations post-jetting and -threading. These harmless and successful techniques for jet-based cell handling to deployment for precision deposition have great potential and widespread applications in bioengineering and biotechnology. Nonetheless, our investigations into ‘bio-electrosprays’ and ‘cell electrospinning’ have elucidated these jets having direct applicability in regenerative and therapeutic medicine to studies in developmental biology. For these very reasons, jet methodologies having the capability to safely handle living organisms for drop and placing are increasingly gaining the interests of life scientists. We now demonstrate yet another technique (a non-electric field-driven approach, previously never explored with jetting living cells), possessing the ability to directly handle the processing of primary living organisms by means of the flow of a cell suspension within a needle placed in a pressure chamber in the presence of an applied pressure difference. The technique we introduce here is referred to as ‘aerodynamically assisted bio-jets/-jetting’ which is driven completely by aerodynamic forces applied over an exit orifice by way of a differential pressure. Our investigations present an operational window in which stable jetting conditions are achieved for the formation of a near-monodispersed distribution of cell-bearing droplets and droplet residues. Finally, the aerodynamically bio-jetted living primary organisms are assessed (over both short and long time points) for cellular viability by means of FACScan, a flow cytometry technology which quantifies the percentage of living and dead cells. These advanced biophysical and bioengineering studies elucidate the emergence of a non-electric field-driven bio-jetting technology which now joins the cell jetting race.

Streaming Electric Potential in Pressure-Driven Flows Through Reservoir-Connected Microchannels

Electrical power generation employing pressure-driven flows is a fundamental problem in microfluidics. In the present work, analytical and numerical analyses are performed to study the interplaying effects of electrolyte motion with the associated electrical current in a flat microchannel with and without fluid reservoirs. The modified Navier–Stokes equations as well as a Poisson equation for the distribution of electric potential and the Nernst–Planck equations for the distribution of charge densities are solved for the steady flow of a Newtonian liquid. The results show that for a pressure-driven flow, an electric potential is induced due to the motion of charged particles, which increases linearly along the microchannel. This streaming potential generates an opposing conduction current in the core region of the channel as well as in the immediate vicinity of the walls, where the streaming current is negligible. The streaming potential varies in a nonlinear manner with the zeta potential at the walls such that a maximum potential exists at a certain zeta potential. The maximum potential is also observed to increase with both the applied pressure difference and the electric double layer thickness in the range studied. The presence of reservoirs adds significant complexity to this electrokinetic flow.

Interfacial aspects of water drop formation at micro-engineered orifices

The formation of emulsions with micro-engineered silicon based arrays of micro-orifices is a relatively new technique. Until now, only the preparation of oil-in-water emulsions was studied due to the hydrophilic nature of silicon. This work evaluates the emulsification of water into n-hexadecane with hydrophobized arrays of micro-orifices. We have studied the drop formation rate, the number of active pores and the drop size. In contrast to conventional macroporous membranes used for membrane emulsification, we observed high dispersed phase fluxes up to 4600 L h −1 m −2 bar −1 while all pores being active at applied pressures below 2 times the critical pressure. The drop diameter was independent from the applied pressure difference. We observed a pressure dependent lag time between drop formations at low emulsification pressures. The lag time is related to the rate of surfactant diffusion to the water–oil interface causing a reduction of the interfacial tension. A significant influence of the used hydrophobization agents, perfluorinated octyltrichlorosilane (FOTS) and octyltrichlorosilane (OTS), was found for the resulting drop sizes and the number of active pores.

Pore-network study of methane hydrate dissociation

A two-dimensional pore-network model based on invasion percolation is used to study the patterns obtained from the release of methane during the dissociation of methane hydrates (without including dissociation kinetics) caused by a sudden pressure reduction in the system below the hydrate equilibrium pressure. The concept of the critical gas saturation S(gc) (volume fraction of the gas phase at the onset of bulk gas flow) is introduced to analyze gas hydrate dissociation. The effects of throat-size distribution (corresponding to off-shore oceanic sediments or on-shore sediments under permafrost), applied pressure difference across the network, and initial hydrate saturation on the resulting gas patterns and on the critical gas saturation are examined to determine the possibility of producing methane. As expected, large throat sizes or wide throat distributions, large pressure drops, and higher initial hydrate saturation act as promoters for the production of the released gas. For typical deep ocean sediments with small pore sizes and low hydrate saturation, it may be difficult to produce methane resulting from hydrate dissociation.

Axial annular flow of plastic fluids: dead zones and plug-free flow

In axial annular flow, the shear stress decreases from its value τ(κR) at the inner cylinder to 0 at r = λR and increases from then on to τ(R) at the outer cylinder. For plastic fluids with a yield stress τ c, λ will be such that flow commences when τ(κR) = τ(R) = τ c. For fluids with position-dependent yield stresses (electro- and magnetorheological fluids are examples), the situation is more complex. While it is possible that yielding and flow occur everywhere, it is also possible that flow occurs only in parts of the fluid-filled space, and a dead zone (region in which the fluid is at rest) close to one of the walls exists. In that case, the fluid will flow no matter how small the applied pressure difference \( P = \Delta p \mathord{\left/ {\vphantom {p L}} \right. \kern-\nulldelimiterspace} L \) is. If P is large enough, the dead zone ceases to exist and flow without any plug is possible. The fluid flows as if no yield stress exists.

Aerodynamically assisted jetting: a pressure driven approach for processing nanomaterials

An investigation into aerodynamically assisted jetting (AAJ), an emerging pressure-driven process fabrication approach, for handling concentrated nano-suspensions is reported. A wide range of nano-scaled materials (≪50 nm) were suspended in a polymer grade ethylene glycol and jetted. The jetting process was optimised for identifying a parametric space for a given flowrate to applied pressure difference, where the finest possible near mono-dispersed droplets containing nanomaterials were generated. The droplet size distributions generated were measured using a Sympatec laser spectrometer. These droplets were collected on holey carbon grids where transmission electron microscopy was carried out. The results in this investigation elucidate AAJ as a novel nanofabrication approach.

Subdynamic asymptotic behavior of microfluidic valves

Decreasing the Reynolds number of microfluidic no-moving-part flow control valves considerably below the usual operating range leads to a distinct "subdynamic" regime of viscosity-dominated flow, usually entered through a clearly defined transition. In this regime, the dynamic effects on which the operation of large-scale no-moving-part fluidic valves is based, cease to be useful, but fluid may be driven through the valve (and any connected load) by an applied pressure difference, maintained by an external pressure regulator. Reynolds number ceases to characterize the valve operation, but the driving pressure effect is usefully characterized by a newly introduced dimensionless number and it is this parameter which determines the valve behavior. This summary paper presents information about the subdynamic regime using data (otherwise difficult to access) obtained for several recently developed flow control valves. The purely subdynamic regime is an extreme. Most present-day microfluidic valves are operated at higher Re, but the paper shows that the laws governing subdynamic flows provide relations useful as an asymptotic reference.

Effects of surface heterogeneity on flow circulation in electroosmotic flow in microchannels

The characteristics of electroosmotic flow in a cylindrical microchannel with non-uniform zeta potential distribution are investigated in this paper. Two-dimensional full Navier–Stokes equation is used to model the flow field and the pressure field. The numerical results show the distorted electroosmotic velocity profiles and various kinds of flow circulation resulting from the axial variation of the zeta potential. The influences of heterogeneous patterns of zeta potential on the velocity profile, the induced pressure distribution and the volumetric flow rate are discussed in this paper. This work shows that using either heterogeneous patterns of zeta potential or a combination of a heterogeneous zeta potential distribution and an applied pressure difference over the channel can generate local flow circulations and hence provide effective means to improve the mixing between different solutions in microchannels.

Rate-Based Design of Non-Fouled Cross-Flow Hollow-Fibre Membrane Modules for Hyperfiltration

Although hyperfiltration has replaced many liquid phase separation equipment, it is still considered as a ‘non-unit operation’ process because the sizing of hyperfiltration equipment could not be calculated using either the equilibrium stage or the ratebased methods. Previous design methods using the dead-end and the complete-mixing models are unsatisfactory because the dead-end model tends to underestimate the membrane area due to the use of the feed concentration in the driving force while the complete-mixing model tends to overestimate the membrane area due to the use of the more concentrated rejection concentration in the driving force. In this paper, a cross-flow model for hyperfiltration is developed by considering mass balance at a differential element of the cross-flow module and then integrating the expression over the whole module to get the module length. Since the modelling is rate-based, the length of the module could be expressed as the product of theheight of a transfer unit (HTU) and the number of transfer units (NTU). The solution of the integral representing the NTU of hyperfiltration is found to be the difference between two hypergeometric functions. The poles of the solution represent the flux extinction curves of hyperfiltration. The NTU for hyperfiltration is found to depend on four parameters: the rejection, R , the recovery, S , the polarization, β , and the dimensionless applied pressure difference, ψ. For any given ψ and R , the recovery, S , is limited by the corresponding flux extinction curve. The NTU for hyperfiltration is found to be generally small and less than unity, but increases rapidly to infinity near the poles due to flux extinction. Polarization is found to increase the NTU and hence the length and membrane area of the hollow fibre module for hyperfiltration.