Laminar flow conditions

M ass Transfer. Exhaust gas catalytic treatment depends on the efficient contact of the exhaust gas and the catalyst. During the initial seconds after start of the engine, hot gases from the exhaust valve of the engine pass through the exhaust manifold and encounter the catalytic converter. Turbulent flow conditions (Reynolds numbers above 2000) exist in response to the exhaust stroke of each cylinder (about 6 to 25 times per second) times the number of cylinders. However, laminar flow conditions are reached a short (- 0.6 cm) distance after entering the cell passages of the honeycomb (5,49—52). 

Laminar Flow For films falling down vertical flat surfaces, as shown in Fig. 6-52, or vertical tubes with small film thickness compared to tube radius, laminar flow conditions prevail for Reynolds numbers less than about 2,000, where the Reynolds number is given by... 

The rate of mass transfer in the liquid phase in wetted-waU columns is highly dependent on surface conditions. When laminar-flow conditions prevail without the presence of wave formation, the laminar-penetration theory prevails. When, however, ripples form at the surface, and they may occur at a Reynolds number exceeding 4, a significant rate of surface regeneration develops, resulting in an increase in mass-transfer rate. 

Shear stresses are developed in a fluid when a layer of fluid moves faster or slower than a nearby layer of fluid or a solid surface. In laminar flow, the shear stress is equal to the product of fluid viscosity and velocity gradient or rate of shear. Under laminar-flow conditions, shear forces are larger than inertial forces in the fluid. 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

A deflagration can best be described as a combustion mode in which the propagation rate is dominated by both molecular and turbulent transport processes. In the absence of turbulence (i.e., under laminar or near-laminar conditions), flame speeds for normal hydrocarbons are in the order of 5 to 30 meters per second. Such speeds are too low to produce any significant blast overpressure. Thus, under near-laminar-flow conditions, the vapor cloud will merely bum, and the event would simply be described as a large fiash fire. Therefore, turbulence is always present in vapor cloud explosions. Research tests have shown that turbulence will significantly enhance the combustion rate in defiagrations. 

Mori, S., M. Kataya, and A. Tanimoto, Performance of Counter-flows, Parallel Plate Heat Exchangers Under Laminar Flow Conditions, Heat Trans. Eng, V. 2, July-Sept. (1980) p. 29. 

Using the mathematical technique of dimensionless group analysis, the rate of mass transport (/ m) in terms of moles per unit area per unit time can be shown to be a function of these variables, which when grouped together can be related to the rate by a power term. For many systems under laminar flow conditions it has been shown that the following relationship holds ... 

The calculation of heat transfer film coefficients in an air-lift bioreactor is more complex, as small reactors may operate under laminar flow conditions whereas large-scale vessels operate under turbulent flow conditions. It has been found that under laminar flow conditions, the fermentation broths show non-Newtonian behaviour, so the heat transfer coefficient can be evaluated with a modified form of the equation known as the Graetz-Leveque equation 9... 

Because concentrated flocculated suspensions generally have high apparent viscosities at the shear rates existing in pipelines, they are frequently transported under laminar flow conditions. Pressure drops are then readily calculated from their rheology, as described in Chapter 3. When the flow is turbulent, the pressure drop is difficult to predict accurately and will generally be somewhat less than that calculated assuming Newtonian behaviour. As the Reynolds number becomes greater, the effects of non-Newtonian behaviour become... 

Show that the volumetric flowrate of this fluid in a horizontal pipe of radius a under isothermal laminar flow conditions with a pressure gradient —AP/l per unit length is ... 

In contrast to bioreactors, viscosimeters at laminar flow conditions have the advantage of relatively uniform and defined flow conditions, which permits the calculation of a certain shear stress. This is not the case for the other model reactors. 

The experimental results for hybridoma and protozoa cells given as examples in Fig. 25 indicate that much higher stress (4 to 30 times) is required under laminar flow conditions of viscosimeters than in stirred vessels to achieve the same death rate k. Here the death rate k is defined as first order deactivation constant k = 1/t In (Nq/N), where N, is the initial and N the time-dependent number of living cells in special deactivation experiments under otherwise optimal living conditions. The stress in Fig. 25 was calculated with Eq. (28) for stirred vessels and with Eq. (1) for the viscosimeter. Our own results for hybri-... 

Models based on Eqs. (47)-(50) have been used in the past to describe the disruption of unicellular micro-organisms and mammalian (hybridoma) cells [62]. The extent of cell disruption was measured in terms of loss of cell viability and was found to be dependent on both the level of stress (deformation) and the time of exposure (Fig. 25). All of the experiments were carried out in a cone and plate viscometer under laminar flow conditions by adding dextran to the solution. A critical condition for the rupture of the walls was defined in terms of shear deformation given by Eq. (44). Using micromanipulation techniques data were provided for the critical forces necessary to burst the cells (see Fig. 4)... 

Similar kinetics have been observed for some [91] but not all [116] animal/insect lines. Trials conducted over a range of average shear stresses (Fig. 2) clearly indicate a higher degree of suspension sensitivity to turbulent, rather than laminar, flow conditions. Similar effects have been reported by other workers for plant [57] and mammalian [86,114,122] systems. From these... 

Soule et al. [141] constructed a sparged, concentric cylinder bioreactor for the cultivation of suspensions of Pirus malus. Growth was reduced under all rotational conditions. Sun and Linden [106] employed a rotating wall vessel (Rotary Cell Culture System, Synthecon, Houston, TX, USA) to cultivate suspensions of Taxus cuspidata under laminar flow conditions. Shear rates were... 

Fig. 8. Sustained damage in Daucus carota suspensions, as a function of total energy expended, under laminar flow conditions in a Couette viscometer. Redrawn from Dunlop et al. (1994) Effect of fluid shear forces on plant cell suspensions. Chem Eng Sci 49 2263 - 2276, with permission of Elsevier Science...

GP 10] [R 18]The best HCN yield of 31% at a p-gauze platinum catalyst (70 ml h methane 70 ml h ammonia 500 ml h air 1 bar 963 °C) is much better than the performance of monoliths (Figure 3.49) having similar laminar flow conditions [2]. A coiled strip and a straight-channel monolith have yields of 4 and 16%, respectively. The micro-reactor performance is not much below the best yield gained in a monolith operated under turbulent-flow conditions (38%). 

Deviation from laminar shear flow [88,89],by calculating the material functions r =f( y),x12=f( Y),x11-x22=f( y),is assumed to be of a laminar type and this assumption is applied to Newtonian as well as viscoelastic fluids. Deviations from laminar flow conditions are often described as turbulent, as flow irregularities or flow instabilities. However, deviation from laminar flow conditions in cone-and-plate geometries have been observed and analysed for Newtonian and viscoelastic liquids in numerous investigations [90-95]. Theories have been derived for predicting the onset of the deviation of laminar flow between a cone and plate for Newtonian liquids [91-93] and in experiments reasonable agreements were found [95]. 

The complete expression for the effective diffusion, under laminar flow conditions, has been derived by Van den Broeck [24] for both short (t < a2/ D) time scales... 

Under all but laminar flow conditions, the steady-state pipeline network problems are described by mixed sets of linear and nonlinear equations regardless of the choice of formulations. Since these equations cannot be solved directly, an iterative procedure is usually employed. For ease of reference let us represent the steady-state equations as... 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

Under laminar flow conditions, the mass transfer will be dominated by diffusion. Based on Fick s law (Fick 1855), the relationship between... 

Under the diffusive laminar flow conditions, the ability to add reagents at specific locations or times leads to the unique ability to control and monitor the spatial and temporal domain of dynamic chemical processes. This attribute has some analogies with the control exerted on biochemical reactions by the micron-scale structures of living cells. Ex-... 

Fabbri, G. Heat Transfer Optimization in Internally Finned Tubes Under Laminar Flow Conditions. Int J Heat Mass Transfer 41 (10) 1243-1253 (1998). 

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