Boundary layers laminar sublayer

However, the molecules percolating up into the boundary layer from beneath the soil surface tend to become trapped in the stagnant laminar sublayer of the boundary layer. This sublayer is usually much thinner than the overall turbulent boundary layer, since it is dominated by viscous and surface tension forces, rather than by velocity. Phelan and Webb call this the chemical boundary layer and state categorically that there will generally be no chemical signature above this chemical boundary layer [1, p. 52],... 

When the flow in the boundary layer is turbulent, streamline flow persists in a thin region close to the surface called the laminar sub-layer. This region is of particular importance because, in heat or mass transfer, it is where the greater part of the resistance to transfer lies. High heat and mass transfer rates therefore depend on the laminar sublayer being thin. Separating the laminar sub-layer from the turbulent part of the boundary... 

In the Taylor-Prandtl modification of the theory of heat transfer to a turbulent fluid, it was assumed that the heat passed directly from the turbulent fluid to the laminar sublayer and the existence of the buffer layer was neglected. It was therefore possible to apply the simple theory for the boundary layer in order to calculate the heat transfer. In most cases, the results so obtained are sufficiently accurate, but errors become significant when the relations are used to calculate heat transfer to liquids of high viscosities. A more accurate expression can be obtained if the temperature difference across the buffer layer is taken into account. The exact conditions in the buffer layer are difficult to define and any mathematical treatment of the problem involves a number of assumptions. However, the conditions close to the surface over which fluid is flowing can be calculated approximately using the universal velocity profile,(10)... 

Equation (6-31) applies to the laminar sublayer region in a Newtonian fluid, which has been found to correspond to 0 < y+ < 5. The intermediate region, or buffer zone, between the laminar sublayer and the turbulent boundary layer can be represented by the empirical equation... 

Any consideration of mass transfer to or from drops must eventually refer to conditions in the layers (usually thin) of each phase adjacent to the interface. These boundary layers are envisioned as extending away from the interface to a location such that the velocity gradient normal to the general flow direction is substantially zero. In the model shown in Fig. 8, the continuous-phase equatorial boundary layer extends to infinity, but the drop-phase layer stops at the stagnation ring. At drop velocities well above the creeping flow region there is a thin laminar sublayer adjacent to the interface and a thicker turbulent boundary layer between this and the main body of the continuous phase. 

The gas film coefficient is dependent on turbulence in the boundary layer over the water body. Table 4.1 provides Schmidt and Prandtl numbers for air and water. In water, Schmidt and Prandtl numbers on the order of 1,000 and 10, respectively, results in the entire concentration boundary layer being inside of the laminar sublayer of the momentum boundary layer. In air, both the Schmidt and Prandtl numbers are on the order of 1. This means that the analogy between momentum, heat, and mass transport is more precise for air than for water, and the techniques apphed to determine momentum transport away from an interface may be more applicable to heat and mass transport in air than they are to the liquid side of the interface. 

Now return to a view of the nature of flow in the boundary layer. It has been called laminar, and so it is for values of the Reynolds number below a critical value. But for years, beginning about the time of Osborne Reynolds experiments and revelations in the field of fluid flow, it has been known that the laminar property disappears, and the flow suddenly becomes turbulent, when the critical VUv is reached. Usually flow starts over a surface as laminar but after passing over a suitable length the boundary layer becomes turbulent, with a thin laminar sublayer thought to exist because of damping of normal turbulent components at the surface. See Fig. 6. 

The precise transition from laminar to turbulent flow occurs at different values of Re depending on geometry. Even in turbulent flow there exists a thin laminar hydrodynamic sublayer of thickness 8h near the metal surface. If mass transport is also occurring at the surface, there will be a diffusional boundary layer of thickness 8d. 8h is a function of v while 8d is a function of D. The Schmidt number quantifies a relationship between these two parameters ... 

A number of experimental investigations have shown that the velocity profile in a turbulent boundary layer, outside the laminar sublayer, can be described by a one-seventh-power relation... 

The zones where these gradients occur are often called boundary layers. For example, the aerodynamic boundary layer is the region near a surface where viscous forces predominate. Boundary layers exist with both laminar and turbulent flow and may be either solely laminar or turbulent with a laminar sublayer themselves (Landau and Lifshitz, 1959). 

A turbulent boundary layer is actually made up of three zones, a viscous or laminar sublayer immediately adjoining the wall, a buffer zone, and finally a turbulent zone making up the main boundary layer (Schlicting, 1968). Generally speaking, turbulent boundary layers are thicker than laminar boundary layers. 

A boundary layer is a region of a fluid next to a solid that is dominated by the shearing stresses originating at the surface of the solid such layers arise for any solid in a fluid, such as a leaf in air. Adjacent to the leaf is a laminar sublayer of air (Fig. 7-6), where air movement is predominantly parallel to the leaf surface. Air movement is arrested at the leaf surface and has increasing speed at increasing distances from the surface. Diffusion... 

Figure 7-6. Schematic illustration of originally nonturbulent air (straight anrows in upwind side on left) flowing over the top of a flat leaf, indicating the laminar sublayer (shorter straight anrows), the turbulent region (curved arrows), and the effective boundary layer thickness, 5bl. The length of an arrow indicates the relative speed, and the curvature indicates the local direction of air movement. A similar airflow pattern occurs on the lower leaf surface.

A laminar boundary layer develops on the upwind side of a cylinder (Fig. 7-8). This layer is analogous to the laminar sublayer for flat plates (Fig. 7-6), and air movements in it can be described analytically. On the downwind side of the cylinder, the airflow becomes turbulent, can be opposite in direction to the wind, and in general is quite difficult to analyze. Nevertheless, an effective boundary layer thickness can be estimated for the whole cylinder (to avoid end effects, the cylinder is assumed to be infinitely long). For turbulence intensities appropriate to field conditions, in mm can be represented as follows for a cylinder ... 

Turbulent flow over a flat plate is characterized by three re-gions f l (a) a viscous sublayer often called the laminar sublayer, which exists right next to the plate, (b) an adjacent turbulent boundary layer, and (c) the turbulent core. Viscous forces dominate inertial forces in the viscous sublayer, which is relatively quiescent compared to the other regions and is therefore also called the laminar sublayer. This is a bit of a misnomer, since it is not really laminar. It is in this viscous sublayer that the velocity changes are the greatest, so that the shear is largest. Viscous forces become less dominant in the turbulent boundary layer. These forces are not controlling factors in the turbulent core. 

In Fig. 6, we show the thickness of the boundary layer as a function of the stream velocity of supercritical CO2 for temperatures of 325 K (solid line) and 375 K (dashed line) at a fixed pressure of 300 bars. In this regime, the density of CO2 is 0.94 g/cc and its viscosity is 7.4 x lO" g/cm-s. The thickness of the laminar sublayer is seen to depend inversely on the stream velocity. This figure indicates that for a stream velocity of 200 cm/s, the boundary layer thickness is about 2 microns. 

The major resistance to the flow of heat resides in the laminar sublayer. Its thickness, therefore, is of critical importance in determining the rate of heat transfer from the fluid to the boundary. It depends on the physical properties of the fluid, the flow conditions, and the nature of the surface. Increase in flow velocity, for example, decreases the thickness of the layer and, therefore, its resistance to heat flow. 

The thin fluid layer in the immediate neighborhood of the solid surface is called the fluid film [32]. In this connection, there are instances where the fluid film is referred to as the laminar film, the boundary layer or the viscous sublayer. 

In reality the laminar sublayer is continuously transformed into the fully turbulent region. A transition region exists between the two, known as the buffer layer, so that the wall law of velocity can be split into three areas, whose boundaries are set by experimentation. The laminar sublayer extends over the region... 

Farther away from the surface the fluid velocities, though less than the velocity of the undisturbed fluid, may be fairly large, and flow in this part of the boundary layer may become turbulent. Between the zone of fully developed turbulence and the region of laminar flow is a transition, or buffer, layer of intermediate character. Thus a turbulent boundary layer is considered to consist of three zones the viscous sublayer, the buffer layer, and the turbulent zone. The existence of a completely viscous sublayer is questioned by some, since mass transfer studies suggest that some eddies penetrate all the way through the boundary layer and reach the wall. 

The behavior of the alternate forms of eM/v in the near-wall region of a turbulent boundary layer is shown in Fig. 6.35. The classical Prandtl-Taylor model assumes a sudden change from laminar flow (eM/v = 0) to fully turbulent flow (Eq. 6.173) at y = 10.8. The von Kftrman model [88] allows for the buffer region and interposes Eq. 6.174 between these two regions. The continuous models depart from the fully laminar conditions of the sublayer around y+ = 5 and asymptotically approach limiting values represented by Eq. 6.173. In finite difference calculations, eM/v is allowed to increase until it reaches the value given by Eq. 6.158 and then is either kept constant at this value or diminished by an intermittency factor found experimentally by Klebanoff [92]. 

Early theories for transpiration of air into air [114, 115] were based on the Couette flow approximation. Reference 114 extended the Reynolds analogy to include mass transfer by defining a two-part boundary layer consisting of a laminar sublayer and a fully turbulent core. Here, t = 0 in the sublayer (y < y ), and t = OAy and (i = 0 in the fully turbulent region. The density was permitted to vary with temperature. The effect of foreign gas injection in a low-speed boundary layer was studied in Ref. 116, and all these theories were improved upon in Ref. 117. 

A viscous boundary layer adjacent to the surface of some obstacle on which deposition is occurring is an impediment to all depositing species, regardless of the orientation of the target surface. Molecular (and Brownian) diffusion occurs independently of direction molecular diffusion can occur to the underside of a leaf just as easily as it can to the top surface. The flux across the quasi-laminar sublayer adjacent to the surface is expressed in terms of a dimensionless transfer coefficient, B, multiplying the concentration difference across the layer, C2 — Cj. Since, under steady-state conditions, this flux is equal to that across each layer, we write... 

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