In the mantle section of many ophiolite sequences, dunite dikes are present. Around dunite dikes at the Josephine and Trinity ophiolite, a sequence of lithologies consisting of plagioclase lherzolite, lherzolite, and harzburgite is present. This sequence of rocks has been interpreted to be the result of reactive porous flow. From trace element data, the mafic melt has been interpreted to flow both into and out of the dunite dikes. Whether the melt emanates from the dunite bodies or is collected by them has implications for the mechanisms of melt extraction beneath ridge systems. The determination of the flow direction based on tracer distributions is difficult and therefore additional constraints are important. Reactive transport theory predicts that lithological zonations around dunite bodies can indicate the direction of flow. To date no reactive transport model has been developed to test these hypotheses, and therefore I have built a reactive transport model using COMSOL v. 4.1. I developed a model for an orthopyroxene dissolution front based on the model of Chadam et al. (1986, Reactive infiltration instabilities, IMA Journal of Applied Mathematics, v. 36, p.207-221). This model includes the strong nonlinearity feedback that has been invoked to lead to the channelization of melt flow. The instability leads to the formation of elongated regions where orthopyroxene is depleted. This model predicts that the melt is focused into the dunite bodies, most flow is parallel to the dunite boundaries, and exits the fingers at the tip of the column. / text