Micro turbulence

Chassaing, C., Stafford, H., Luckwell, J., Wright, A., and Edgington, A. (2005). A parallel micro turbulent flow chromatography-tandem mass spectrometry method for the analysis of a pharmaceutical compound in plasma. Chromatographia 62 17-24. 

On the other hand, micro-turbulence is particularly crucial in processes, which proceed in multiple phase systems (Dispersion in /L systems, shear stressing of solid agglomerates, etc.). In such cases the eddy must be of the same order of magnitude as the dispersed phase. 

The fluctuating motion of micro-turbulence results in two points separated by Ar exhibiting different velocities. However, it is also possible to define an average value for a turbulent process, which in the case of locally isotropic turbulence is independent of the spacial orientation of the distance Ar ... 

Schimpf U, Haussecker H, Jahne B (1999) Studies of air-sea gas transfer and micro-turbulence at the ocean surface using passive thermography. In The Wind-Driven Air-Sea Interface, ed ML Banner, University of New South Wales, pp 345-352... 

Typical mass balance methods to measure the air-sea gas transfer have one major drawback the response time is of the order of hours to days, making a parameterisation with parameters such as wind forcing, wave field, or surface chemical enrichments nearly impossible. The controlled flux technique uses heat as a proxy tracer for gases to measure the air-sea gas transfer rate locally and with a temporal resolution of less than a minute. This method offers an entirely new approach to measure the air-sea gas fluxes in conjunction with investigation of the wave field, surface chemical enrichments and the surface micro turbulence at the water surface. The principle of this technique is very simple a heat flux is forced onto the water surface and the skin-bulk temperature difference across the thermal sublayer is measured. 

Turnpenny P, Fraier D, Chassaing C, Duckworth J. Development of a micro-turbulent flow chromatography focus mode method for drug quantitation in discovery bioanalysis. J Chromatogr B Anal Technol Biomed Life Sci 2007 856 131-140. 

Schmitt, G., Biicken, W., and Fanebust, R., Modelling Micro-turbulences at Surface Imperfections as Related to Flow Induced Localized Corrosion and its Prevention, CORRO-SI0N/9I, NACE Annual Conference 1991, Paper No. 465. 

The short-wave turbulence (micro-turbulence), generated in the suspension in the headbox to maintain fiber deflocculation, dissipates rapidly. For this reason, good formation requires either the fiber web to be fixed very quickly or additional turbulence to be generated in the suspension to be dewatered. This can be achieved by means of pressure and vacuum impulses from table roUs, foils and blades. However, impulses that are too strong are harmful, for example by table rolls at machine speeds above approx. 500 m min or by foils with too high a foil angle at elevated machine speeds. In special cases, on fourdrinier wires, formation is improved by agitating the wire. A shaker vibrates the breast roll and thus the fourdrinier wire horizontally in the cross machine direction with a frequency of up to 10 Hz and an ampHtude of up to 25 mm. It is used at low machine speeds and... 

Since chemical reactions are on a scale much below 1 Im, and it appears that the Komolgoroff scale of isotropic turbulence turns out to be somewhere between 10 and 30 Im, other mechanisms must play a role in getting materials in and out of reaction zones and reactants in and out of those zones. One cannot really assign a shear rate magnitude to the area around a micro-scale zone, ana it is primarily an environment that particles and reactants witness in this area. 

In the viscous regime, chemical reactants become associated with each other through viscous shear stresses. These shear stresses exist at all scales (macro to micro) and until the power is dissipated continuously through the entire spectrum. This gives a different relationship for power dissipation than in the case of turbulent flow. 

In Chap. 3 the problems of single-phase flow are considered. Detailed data on flows of incompressible fluid and gas in smooth and rough micro-channels are presented. The chapter focuses on the transition from laminar to turbulent flow, and the thermal effects that cause oscillatory regimes. 

The heat transfer correlations are considered separately in the laminar and turbulent regimes in Figs. 2.21 and 2.22, respectively. The dependence of the Nusselt number on the Reynolds number is stronger in all the micro-channel predictions compared to conventional results, as indicated by the steeper slopes of the former Choi et al. (1991) predict the strongest variation of Nusselt number with Re. The predictions for all cases by Peng et al. (1996) also fall below those for a conventional channel. 

Acikalin T, Wait S, Garimella S, Raman A (2004) Experimental investigation of the thermal performance of piezoelectric fans. Heat Transfer Eng 25 4-14 Adams TM, Abdel-Khalik SI, Jeter SM, Qureshi ZH (1998) An experimental investigation of single-phase forced convection in micro-channels. Int J Heat Mass Transfer 41 851-857 Adams TM, Dowling ME, Abdel-Khalik SI, Jeter SM (1999) Applicability of traditional turbulent single phase forced convection correlations to non-circular micro-channels. Int J Heat Mass Transfer 42 4411 415... 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

In Spite of the existence of numerous experimental and theoretical investigations, a number of principal problems related to micro-fluid hydrodynamics are not well-studied. There are contradictory data on the drag in micro-channels, transition from laminar to turbulent flow, etc. That leads to difficulties in understanding the essence of this phenomenon and is a basis for questionable discoveries of special microeffects (Duncan and Peterson 1994 Ho and Tai 1998 Plam 2000 Herwig 2000 Herwig and Hausner 2003 Gad-el-Hak 2003). The latter were revealed by comparison of experimental data with predictions of a conventional theory based on the Navier-Stokes equations. The discrepancy between these data was interpreted as a display of new effects of flow in micro-channels. It should be noted that actual conditions of several experiments were often not identical to conditions that were used in the theoretical models. For this reason, the analysis of sources of disparity between the theory and experiment is of significance. 

We consider the problem of liquid and gas flow in micro-channels under the conditions of small Knudsen and Mach numbers that correspond to the continuum model. Data from the literature on pressure drop in micro-channels of circular, rectangular, triangular and trapezoidal cross-sections are analyzed, whereas the hydraulic diameter ranges from 1.01 to 4,010 pm. The Reynolds number at the transition from laminar to turbulent flow is considered. Attention is paid to a comparison between predictions of the conventional theory and experimental data, obtained during the last decade, as well as to a discussion of possible sources of unexpected effects which were revealed by a number of previous investigations. 

This chapter has the following structure in Sect. 3.2 the common characteristics of experiments are discussed. Conditions that are needed for proper comparison of experimental and theoretical results are formulated in Sect. 3.3. In Sect. 3.4 the data of flow of incompressible fluids in smooth and rough micro-channels are discussed. Section 3.5 deals with gas flows. The data on transition from laminar to turbulent flow are presented in Sect. 3.6. Effect of measurement accuracy is estimated in Sect. 3.7. A discussion on the flow in capillary tubes is given in Sect. 3.8. 

Glass and silicon tubes with diameters of 79.9-166.3 iim, and 100.25-205.3 am, respectively, were employed by Li et al. (2003) to study the characteristics of friction factors for de-ionized water flow in micro-tubes in the Re range of 350 to 2,300. Figure 3.1 shows that for fully developed water flow in smooth glass and silicon micro-tubes, the Poiseuille number remained approximately 64, which is consistent with the results in macro-tubes. The Reynolds number corresponding to the transition from laminar to turbulent flow was Re = 1,700—2,000. 

The transition to turbulent flow occurred at Re of about 1,500. The authors noted that for smaller micro-channels, the flow transition would occur at lower Re. The early transition phenomenon might be affected by surface roughness and other factors. 

Wu and Cheng (2003) measured the friction factor of laminar flow of de-ionized water in smooth silicon micro-channels of trapezoidal cross-section with hydraulic diameters in the range of 25.9 to 291.0 pm. The experimental data were found to be in agreement within 11% with an existing theoretical solution for an incompressible, fully developed, laminar flow in trapezoidal channels under the no-slip boundary condition. It is confirmed that Navier-Stokes equations are still valid for the laminar flow of de-ionized water in smooth micro-channels having hydraulic diameter as small as 25.9 pm. For smooth channels with larger hydraulic diameters of 103.4-103.4-291.0pm, transition from laminar to turbulent flow occurred at Re = 1,500-2,000. 

The existence of roughness leads also to decreasing the value of the critical Reynolds number, at which transition from laminar to turbulent flow occurs. The character of the dependence of the friction factor on the Reynolds number in laminar flow remains the same for both smooth and rough micro-channels, i.e., X = const/Re. 

The hypothesis on the earlier transition from laminar to turbulent flow in micro-tubes is based on analysis of the dependence of pressure gradient on Reynolds number. As shown by the experimental data by Mala and Li (1999), this dependence may be approximated by three power functions AP Re (Re < 600),... 

For the most part of the experiments one can conclude that transition from laminar to turbulent flow in smooth and rough circular micro-tubes occurs at Reynolds numbers about RCcr = 2,000, corresponding to those in macro-channels. Note that other results were also reported. According to Yang et al. (2003) RCcr derived from the dependence of pressure drop on Reynolds number varied from RCcr = 1,200 to RCcr = 3,800. The lower value was obtained for the flow in a tube 4.01 mm in diameter, whereas the higher one was obtained for flow in a tube of 0.502mm diameter. These results look highly questionable since they contradict the data related to the flow in tubes of diameter d> mm. Actually, the 4.01 mm tube may be considered... 

The transition from laminar to turbulent flow in micro-channels with diameters ranging from 50 to 247 pm was studied by Sharp and Adrian (2004). The transition to turbulent flow was studied for liquids of different polarities in glass micro-tubes having diameters between 50 and 247 pm. The onset of transition occurred at the Reynolds number of about 1,800-2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. 

Hwang and Kim (2006) investigated the pressure drop in circular stainless steel smooth micro-tubes ks/d <0.1%) with inner diameters of 244 pm, 430 pm and 792 pm. The measurements showed that the onset of flow transition from laminar to turbulent motion occurs at the Reynolds number of slightly less than 2,000. It... 

Hao et al. (2007) investigated the water flow in a glass tube with diameter of 230 Lim using micro particle velocimetry. The streamwise and mean velocity profile and turbulence intensities were measured at Reynolds number ranging from 1,540 to 2,960. Experimental results indicate that the transition from laminar to turbulent flow occurs at Re = 1,700—1,900 and the turbulence becomes fully developed at Re > 2,500. 

An experimental study of the laminar-turbulent transition in water flow in long circular micro-tubes, with diameter and length in the range of 16.6-32.2 pm and 1-30 mm, respectively, was carried out by Rands et al. (2006). The measurements allowed to estimate the effect of heat released by energy dissipation on fluid viscosity under conditions of laminar and turbulent flow in long micro-tubes. 

The dependence of the measured rise in fluid mixed-cup temperature on Reynolds number is illustrated in Fig. 3.12. The difference between outlet and inlet temperatures increases monotonically with increasing Re at laminar and turbulent flows. Under conditions of the given experiments, the temperature rise due to energy dissipation is very significant AT = 15—35 K at L/ i = 900—1,470 and Re = 2,500. The data on rising temperature in long micro-tubes can be presented in the form of the dependence of dimensionless viscous heating parameter Re/[Ec(L/(i)] on Reynolds number (Fig. 3.13). 

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