Figure 1. Limiting system properties for the maximal space–time yield in reactors with immobilized biocatalysts as a function of the biocatalyst content (as % of reactor volume) and particle radius R.

Figure 2. Oxygen concentration gradient outside a spherical particle (radius R » 300 µm) with immobilized glucose oxidase that catalyzes the oxidation of glucose with oxygen: (a) without stirring (Sh = 2); (b) with stirring (Sh » 10). The oxygen concentration was measured using oxygen microelectrodes with a tip diameter of several micrometers. Note that the thickness of the diffusion layer given by the intersection of the gradient (tangent) at the particle surface and the bulk oxygen content approximately equals the particle radius in the unstirred system. This is in agreement with the theoretical analysis (Kasche and Kuhlmann, 1980).

Figure 3. Determination of the stationary effectiveness factor η.

Figure 4. Determination of the operational effectiveness factor η _o = t ₁₂/ from progress curves.

Figure 5. as a function of particle radius calculated from Eq. ( 10) for the initial bulk substrate concentrations of 1 M (solid line) and 0.1 M (dashed line).

Figure 6. The substrate concentration (c _S) inside and outside a particle (radius R) with immobilized biocatalyst (enzyme, cell) at steady state.

Figure 7. The stationary effectiveness factor η for simple Michaelis–Menten kinetics (one substrate, no inhibition) as a function of the square of the Thiele modulus, different Sherwood numbers (Sh), and for different substrate concentrations, given in units of (Kasche, 1983).

Figure 8. The operational effectiveness factor η _o for simple Michaelis–Menten kinetics (one substrate, no inhibition) as a function of the square of the Thiele modulus, different Sherwood numbers (Sh), and for different initial substrate concentrations, given as γ/K _m, for spherical particles and 90% substrate conversion. Calculated (curves) and experimental (circles) data for such processes are compared (Kasche, 1983).

Figure 9. Continuous stirred tank reactor; operational details.

Figure 10. Packed bed reactor; operational details.

Figure 11. The electrical double layer formed by stationary charges on the surface of pores in particles with immobilized enzymes. In the double layer, the pH and ionic strength differ from the corresponding values in the bulk phase. This can change the intrinsic properties of the enzyme that is located in the double layer (Hunter, 1993; González-Caballero and Shilov, 2002).

Figure 12. Effects of pH gradients in stirred batch reactors for enzyme processes where H ⁺ is produced. Influence of buffer capacity and particle radius on the determination of and for α-chymotrypsin immobilized in Sepharose 4B particles (n _E = 90 µM), from rate measurements using Eq. (13). (a) R = 60 µm; (b) R = 3 µm (homogenized particles from (a)) at 25 °C and pH 10.0. Total ionic strength 0.25 M of which for buffer 0.05 M (open circles) or 0.001 M (closed circles). Substrate: N-acetyl-(S)-tyrosine ethyl ester (Kasche and Bergwall, 1973).

Figure 13. Turnover number for the hydrolysis of penicillin G and 6-nitro-3-(phenylacetamido)benzoic acid (NIPAB) by penicillin amidase from E. coli immobilized in different supports, determined in stirred batch reactors. The ionic strength is only due to the phosphate buffer used (B. Galunsky and V. Kasche, unpublished data).

Figure 14. Effects of pH gradients in immobilized enzyme particles in packed bed reactors for an enzyme process where H ⁺ is produced. Influence of buffer capacity and linear flow rate on average pH in particles with immobilized biocatalysts. Filled symbols: with buffer; open symbols: without buffer. The average pH in the particles was determined from the fluorescence intensity of coimmobilized fluorescein, the fluorescence intensity of which is pH dependent below pH 9. A small packed bed reactor (length 3–5 mm) was used, where the pH decrease over the reactor was less than one pH unit. The stationary effectiveness factor at the initial substrate content was »1; that is, the systems used were not mass transfer controlled. (a) Hydrolysis of 300 mM penicillin by penicillin amidase from E. coli immobilized in Eupergit C (n _E = 20 µM; average particle radius 100 µm) with and without phosphate buffer (I = 0.05) at 310 °C. The pH of the substrate solution at the reactor inlet was 7.9. (b) Hydrolysis of 40 mM (circles) glutaryl-7-aminocephalosporanic acid (Glu-7-ACA) with and without phosphate buffer (I = 0.2 M), and 135 mM Glu-7-ACA (squares) with buffering components ammonia, carbonate, and acetate (I » 0.6 M) at 25 °C, with glutaryl amidase immobilized in particles similar to Eupergit C produced by former Hoechst AG (n _E = 100 µM; average particle radius 100 µm). The pH of the substrate solution at the reactor inlet was 10.0 (Spieß et al., 1999).

Figure 15. The influence of the support charge on (a) the stereoselectivity E _kin (Eq. (16)) and (b) selectivity in kinetically controlled synthesis (Eq. (1)) for reactions with charged substrates catalyzed by free and immobilized penicillin amidase (PA). The DSM support is based on gelatin (Spieß and Kasche, 2001) and the magnetic support on polyvinyl alcohol (Bozhinova et al., 2004). (a) stereoselectivity in the kinetically controlled synthesis of (R)-phenylglycyl-(R,S)-Phe from 20 mM (R)-phenylglycine amide and 100 mM-(R,S)-Phe at pH 9.0 and 25 °C, catalyzed by PA from different sources (open bars: from E. coli; gray bars: from A. faecalis; black bars: from B. megaterium). E-values above 1000 cannot be accurately determined; the experimental error in the values below 1000 is ±10%. (b) Selectivity in the kinetically controlled synthesis of cephalexin from 200 mM (R)-phenylglycine amide and 50 mM 7-aminodesacetoxycephalosporanic acid in phosphate buffer (I = 0.05) at pH 7.5 and 5 °C, catalyzed by free and immobilized PA from E. coli. The measurements were performed without (open bars) and with (black bars) addition of 1 M NaCl. For the Eupergit support measurements were also carried without NaCl in homogenized supports (gray bars). After homogenization, the average particle size was 2.3 and 1.1 µm for Eupergit 250L and Eupergit C, respectively.

Figure 16. Hydrolysis of 300 mM penicillin G at 310 °C and pH 7.10 (phosphate buffer I = 0.05 M) with free (open circles, 9000 U l ^–1 reactor) and immobilized (closed circles, 13 000 U l ^–1 reactor) penicillin amidase (PA) from E. coli in a stirred batch reactor. The pH in the reaction solution was kept constant by titration with 3 M NH ₃. The PA was adsorbed to the bifunctional support (see Table 4) phenylbutylamine-Eupergit (PBA-Eupergit, average particle radius 100 µm) and cross-linked with glutaraldehyde. The concentration of active immobilized enzyme, determined by active-site determination, was 3.4 mg ml ^–1 wet support (or 130 000 U l ^–1 wet support). The penicillin G concentration was determined by HPLC.

Figure 17. Kinetically controlled synthesis of N-acetyl-Tyr-Arg-NH ₂ (circles) in aqueous suspensions with precipitated substrate N-acetyl-Tyr-ethyl ester (ATEE), with free (open symbols) and immobilized (closed symbols) α-chymotrypsin at 25 °C. Starting conditions: pH 9.0 (carbonate buffer, I = 0.2 M), 750 mM ATEE and 1000 mM Arg-NH ₂; free enzyme 20 µg ml ^–1; immobilized enzyme 200 µl ml ^–1 immobilized in Sepharose (20 µM in the support). The product N-acetyl-Tyr (squares) did not precipitate during the reaction. The pH was kept constant at pH 9.0 during the reaction. The free ATEE concentration was £20 mM (Kasche and Galunsky, 1995).

Figure 18. Influence of product precipitation on the initial rate as a percentage of rate for the first use for the hydrolysis of 400 mM (R)-phenylglycine amide at pH 7.5 and 25 °C catalyzed by penicillin amidase from E. coli immobilized in supports with different radii. The support pore radius and the immobilized enzyme concentration are given in the parentheses after the support (Kasche and Galunsky, 1995).

Figure 19. The fraction of a particle–particle contact area with a distance <1 µm (between the horizontal lines) of the total particle surface increases, when the particle diameter decreases. This affects the effective particle surface for convective mass transfer when the particle radius becomes less than 50 µm (Renken, 1993).