Reynolds Number kinematic viscosity

In order to estimate an upper bound for attainable TZ s, consider a LG with lattice spacing Iq, speed-of-sound Cg, kinematic viscosity v. Reynold s number is then given by... 

The property of the fluid which appears in the Reynolds number is the kinematic viscosity pfp. The kinematic viscosity of water at 294 K and atmospheric pressure is 10 6 m2/s compared with 15.5 x 10 6 nr/s for air. Thus, gases typically have higher kinematic viscosities than liquids at atmospheric pressure. 

For developed laminar flow in smooth channels of t/h > 1 mm, the product ARe = const. Its value depends on the geometry of the channel. For a circular pipe ARe = 64, where Re = Gdh/v is the Reynolds number, and v is the kinematic viscosity. 

Flow of the liquid past the electrode is found in electrochemical cells where a liquid electrolyte is agitated with a stirrer or by pumping. The character of liquid flow near a solid wall depends on the flow velocity v, on the characteristic length L of the solid, and on the kinematic viscosity (which is the ratio of the usual rheological viscosity q and the liquid s density p). A convenient criterion is the dimensionless parameter Re = vLN, called the Reynolds number. The flow is laminar when this number is smaller than some critical value (which is about 10 for rough surfaces and about 10 for smooth surfaces) in this case the liquid moves in the form of layers parallel to the surface. At high Reynolds numbers (high flow velocities) the motion becomes turbulent and eddies develop at random in the flow. We shall only be concerned with laminar flow of the liquid. 

For axial capillary flow in the z direction the Reynolds number, Re = vzmaxI/v = inertial force/viscous force , characterizes the flow in terms of the kinematic viscosity v the average axial velocity, vzmax, and capillary cross sectional length scale l by indicating the magnitude of the inertial terms on the left-hand side of Eq. (5.1.5). In capillary systems for Re < 2000, flow is laminar, only the axial component of the velocity vector is present and the velocity is rectilinear, i.e., depends only on the cross sectional coordinates not the axial position, v= [0,0, vz(x,y). In turbulent flow with Re > 2000 or flows which exhibit hydrodynamic instabilities, the non-linear inertial term generates complexity in the flow such that in a steady state v= [vx(x,y,z), vy(x,y,z), vz(x,y,z). ... 

The Peclet number Pe = v /Dc, where Dc is the diffusion coefficient of a solute particle in the fluid, measures the ratio of convective transport to diffusive transport. The diffusion time Tp = 2/D< is the time it takes a particle with characteristic length to diffuse a distance comparable to its size. We may then write the Peclet number as Pe = xD/xs, where xv is again the Stokes time. For Pe > 1 the particle will move convectively over distances greater than its size. The Peclet number can also be written Pe = Re(v/Dc), so in MPC simulations the extent to which this number can be tuned depends on the Reynolds number and the ratio of the kinematic viscosity and the particle diffusion coefficient. 

The side-by-side diffusion cell has also been calibrated for drug delivery mass transport studies using polymeric membranes [12], The mass transport coefficient, D/h, was evaluated with diffusion data for benzoic acid in aqueous solutions of polyethylene glycol 400 at 37°C. By varying the polyethylene glycol 400 content incrementally from 0 to 40%, the kinematic viscosity of the diffusion medium, saturation solubility for benzoic acid, and diffusivity of benzoic acid could be varied. The resulting mass transport coefficients, D/h, were correlated with the Sherwood number (Sh), Reynolds number (Re), and Schmidt number (Sc) according to the relationships... 

Re Reynolds number Q)/2/V co = radial velocity v = kinematic viscosity l = characteristic length... 

The modified Reynolds number therefore is based on the velocity in the void fraction v/s, the kinematic viscosity v, and an equivalent diameter s/a, where s is total area per unit volume and a is the dimensional coefficient derived from a correlation of pressure drop data ... 

All of the linear dimensions of the model are scaled to the corresponding dimensions of the commercial bed by the ratio of the kinematic viscosities of the gas raised to the two-thirds power. By taking the ratio of Reynolds number based on the particle diameter to Reynolds number based on the bed diameter... 

The viscosity (dynamic, 17, or kinematic, v) and density, p (Eq. 47), influence the dissolution rate if the dissolution is transport-controlled, but not if the dissolution is reaction-controlled. In transport-controlled dissolution, increasing 17 or v will decrease D (Eq. 53), will increase h (Eqs. 46 and 49) and will reduce J (Eqs. 51 and 52). These effects are complex. For example, if an additional solute (such as a macromolecule) is added to the dissolution medium to increase 17, it may also change p and D. The ratio of 17/p = v (Eq. 47) and D directly influence h and J in the rotating disc technique, while v directly influences the Reynolds number (and hence J) for transport-controlled dissolution in general [104]. 

As mentioned before in Eq. (3), the most common source of SGS phenomena is turbulence due to the Reynolds number of the flow. It is thus important to understand what the principal length and time scales in turbulent flow are, and how they depend on Reynolds number. In a CFD code, a turbulence model will provide the local values of the turbulent kinetic energy k and the turbulent dissipation rate s. These quantities, combined with the kinematic viscosity of the fluid v, define the length and time scales given in Table I. Moreover, they define the local turbulent Reynolds number ReL also given in the table. 

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

The relationship between the various length scales can be best understood by looking at their dependence on the turbulence Reynolds number defined in terms of the turbulent kinetic energy k, the turbulent dissipation rate e, and the kinematic viscosity v by... 

As mentioned earlier, Reynolds numbers determined for the bulk flow have to be discerned from Reynolds numbers characterizing a particle-liquid dissolution system. The latter were calculated for drug particles of different sizes using the Reynolds term according to the combination model. The kinematic viscosity of the dissolution medium at 37°C is about 7 x 10-03 cm2/sec. The fluid velocities (Ua) employing the paddle method at stirring rates of 50-150 rpm can be taken from the literature and may arbitrarily be used as the slip velocities at the particle surfaces. 

Relaxing the restriction of low Reynolds number, Rimmer (1968,1969) used a matched asymptotic expansion technique to develop a solution in terms of Pe and the Schmidt number Sc (or Prandtl number Pr for heat transfer), where Sc = v/D.j and Pr = v/a in which v is the kinematic viscosity of the flowing fluid. His solution, valid for Pe < 1 and Sc = 0(1), is... 

An experimentally based rule-of-thumb is that laminar flow often occurs when the pipe Reynolds number, Vdjv, is less than 2,000, or when an open channel Reynolds number, Vhjv, is less than 500, where V is the cross-sectional mean velocity, d is the pipe diameter, v is the kinematic viscosity of the fluid, and h is the channel depth. The diameter or depth that would not be exceeded to have laminar flow by these experimental criteria is given in Table 5.1. 

L T ), and v is the kinematic viscosity ofthe hquid (L" T ). Ihe dimensionless groups include N/v) = Reynolds number (Re) d N /g) = Froude number (Fr) and (Q/N d = aeration number (Na), which is proportional to the ratio of the superficial gas velocity with respect to the tank cross section to the impeller tip speed. 

Flexibility in the choice of parameters and their reliable extrapolation within the range covered by the dimensionless numbers. These advantages become clear if one considers the well-known Reynolds number. Re = vL/v, which can be varied by altering the characteristic velocity V or a characteristic length L or the kinematic viscosity v. By choosing... 

Brauer (B14), 1956 Extensive experimental study of film flow outside tube 4.3X130 cm. films of water, water + surfactant, aqueous diethylene glycol solutions, kinematic viscosity 0.9-12.7 cs. Nr = 20-1800. Data on film thicknesses, waves, maximum and minimum thicknesses, characteristic Reynolds numbers of flow, onset of rippling and turbulence, wall shear stress, etc. 

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