Abstract: The present invention is directed to novel methods and apparatus for conducting chemical and biological reactions. A reactor is provided that includes a reaction matrix member formed from microporous ceramic. A chemical or biological material is fixed within the pores of the porous matrix, and reaction solution is passed through the porous matrix member at a controlled rate. Preferably, the matrix member is tubular in shape and comprises a plurality of concentric layers of ceramic material, each layer having a substantially uniform pore size, but the plurality of layers having a progressively decreasing pore size with respect to the preceding layer. Each layer may also have a different thickness than other layers. Reaction solution is introduced into an axial bore through the ceramic matrix member, and the product solution is collected from the outside of the ceramic matrix member. Optionally, lumens within one or more adjacent ceramic layers, and/or spaces between layers can be provided.