Former Democratic Alderman Edward R. Vrdolyak was expected to join the 1989 special mayoral election in Chicago by announcing his candidacy today for the Republican nomination. Another late-filing candidate, Alderman Juan Soliz, became the first Latino to enter the racially polarized race. Vrdolyak would be making his second attempt to win Chicago’s top political plum, and political observers see his candidacy as a threat to Democratic front-runner Richard M. Daley, who is also seeking the job for the second time. Both Daley, son of legendary Mayor Richard J. Daley, who ruled the city for 21 years, and Vrdolyak were defeated in their previous runs by the late Harold Washington, the city’s first black mayor. The winner of the April 4 general election will serve out the remaining term of Washington, who died Nov. 25, 1987.