non-phagocytic leukocytosis is probably due more to stimulation of blood-making organs than to chemotaxis.
phagocyte phag·o·cyte (fāg'ə-sīt')
A cell, such as a white blood cell, that engulfs and absorbs waste material, harmful microorganisms, or other foreign bodies in the bloodstream and tissues.
Any of various organisms or specialized cells that engulf and ingest other cells or particles. In vertebrate animals, phagocytes are white blood cells that break down bacteria and other microorganisms, foreign particles, and cellular debris. These include monocytes, macrophages, and most granulocytes. ◇ The process by which phagocytes engulf and break down bacteria or particles is called phagocytosis (fāg'ə-sī-tō'sĭs). During phagocytosis the cell encloses foreign material and the extracellular fluid surrounding it by an infolding of a part of the cell membrane, which then pinches off to form a vesicle, called a phagosome. The phagosomes fuse with lysosomes, resulting in digestion of the ingested matter. Unicellular protists such as amoebas ingest food by the process of phagocytosis.