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Characterization of Flow, Particles and Interfaces by Jinghai Li

By Jinghai Li

Multi-scale research and simulation of chemical processing and reactions have obtained unheard of recognition in recent times; although, size expertise concerned about multi-scale constructions, quite on meso-scale phenomena, has now not been sufficiently addressed.  This quantity of Advances in Chemical Engineering makes a speciality of the "Characterization of circulation, debris and Interfaces" to alert the chemical engineering group to this difficult factor featuring six meso-scale dimension applied sciences.

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However, these small forces mean that it is not appropriate for investigating the response of samples to large deformations, especially if the sample has a cell wall. 1 Experimental setup In this technique, an individual particle is compressed between two flat parallel surfaces, usually until it ruptures. By measuring the force being applied to the particle and the displacement of the surfaces, forcedeformation data can be found. Figure 5 shows an illustration of a particle during compression where a force (F) is deforming it between two surfaces separated by a known distance (2¯Z).

Liquid velocity distribution subtracted from mean liquid velocity of each velocity profile (m/s) average liquid velocity (m/s) gas phase superficial velocity (m/s) liquid phase superficial velocity (m/s) liquid velocity values, cylindrical coordinates (m/s) liquid velocity values, Cartesian coordinates (m/s) channel width (m) Weber number vertical distance from the tip of the transducer to the gas– liquid interface (mm) GREEK SYMBOLS a de j l mde n y r s sde sj,k sj sk gas phase void fraction difference between the actual liquid flow rate Qa and the estimated liquid flow rate Qe thickness of the standing wave (mm) ultrasound wavelength (m) average of de values kinematic viscosity of the liquid angle of the ultrasonic transducer with respect to the flow (degrees) liquid-phase density (kg/m3) surface tension of the liquid (N/m) standard deviation of de values covariance of the gas–liquid interface height for series j and k standard deviation of the gas–liquid interface height for series j (transducer 2); series j consists of N–i elements, where j ¼ 2 standard deviation of the gas–liquid interface height for series k (transducers 1 and 3); series k consists of N–i elements, where k ¼ 1, 3 ACKNOWLEDGMENTS The authors wish to thank the New Energy Development Organization of Japan for their support of this study, project number 05A45002d.

2006) as n X Fi eÀt=ti (10) FðtÞ ¼ F1 þ i¼1 where F(t) is the time-dependent force, FN the force when the relaxation reaches equilibrium and Fi are proportionality constants. Mattice et al. , 2006). , 2006) via F1 K0 ¼ À pffiffiffiffi Á 3=2 hp max 8 R=3 43 (13) and Ki ¼ Fi ðRCFi Þ hp max 3=2 À pffiffiffiffi Á ði ¼ 1; 2; 3; . . ; nÞ 8 R=3 where RCFi is called the ‘‘ramp correction factor’’ given by à ti  tR=t e i À 1 ði ¼ 1; 2; 3; . . ; nÞ RCFi ¼ tR (14) (15) where tR is the time taken to compress the material.

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