An apparatus includes a substrate and a matrix having multiple cells embedded within the substrate. The matrix is configured to generate electrostatic fields to define at least one flow path for liquid metal. The apparatus also includes a pump configured to create movement of the liquid metal through the at least one flow path defined by the matrix. The matrix is configured to transport the liquid metal through the at least one flow path in order to remove thermal energy from one or more areas of the substrate. The matrix could include a matrix of capacitors, and polarities of charges stored on the capacitors could define which cells allow passage of the liquid metal and which cells block or restrict passage of the liquid metal. The cells that block or restrict passage of the liquid metal could be configured to increase a viscosity of the liquid metal.